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50 Important Learning Concepts (Explained with Examples)

Learning concepts examples and definition, explained below

A learning concept is an overarching idea or principle that explains how learners acquire knowledge or skills.

It serves as a foundation for educators and learners to understand, design, and engage in educational experiences more effectively.

Historically, learning concepts were focused on rote learning, memorization, and repetition. But since the rise of cognitive psychology and social learning theories, things have changed.

Educators are increasingly using learning concepts that embrace trial-and-error, talking things through, and experimentation.

Some examples are provided below.

Learning Concepts

1. Active Learning Active Learning is an instruction method in which students engage with the material directly, whether through problem-solving, discussion, review, or case studies. It eclipses passive learning strategies by directly involving the student in their educational process.

2. Blended Learning Blended Learning leverages both traditional face-to-face classroom methods and digital mediums to provide a comprehensive learning experience. This approach allows the integration of online resources and enhanced flexibility for learners, while maintaining the personal touch of physical classroom interaction.

3. Constructivism Constructivism is a theory that asserts learners constuct knowledge on their own, building upon existing understandings to gain new knowledge. It emphasizes the active role of the learner in shaping their understanding rather than passively receiving information.

4. Cooperative Learning Cooperative Learning is a technique where students work together in small groups on a common task. The group activities are designed so that students rely on each other to achieve the goal, fostering teamwork, leadership, and interpersonal skills alongside academic knowledge.

5. Critical Thinking Critical Thinking refers to the learner’s ability to analyze, interpret, and evaluate information to make well-founded judgments and decisions. Involving careful reasoning and logic, it requires learners to go beyond mere acquisition of facts and embrace deeper, more thoughtful analysis.

6. Deep Learning Deep Learning, in an educational context (not to be confused with the AI computing concept), refers to a student’s ability to understand a subject matter at a profound level that allows for complex application of concepts. It goes beyond rote memorization of facts, encouraging comprehension, application, and synthesis of new knowledge.

7. Discovery Learning Discovery Learning involves students learning through exploration and problem-solving, leading to a deeper understanding of the subject matter. This technique stimulates curiosity, encourages intellectual investment, and hinges on self-motivated exploration of topics.

8. Distributed Practice Distributed Practice is a learning strategy where studying is spread out over time, rather than being concentrated in long, intensive sessions. This spacing effect tends to produce better long-term retention of material, making it an effective method for lasting learning.

9. Experiential Learning Experiential Learning is a method where learners gain knowledge and skills through direct experience, usually outside of the traditional academic setting. This could involve internships, study abroad programs, or field work, providing learners with practical, real-world engagement with the subject matter.

10. Flipped Classroom The Flipped Classroom strategy entails providing learners with instructional content– typically digital materials or online videos– to study outside of class, while class time is devoted to discussion, exercises, and projects that enhance understanding. This format allows for a more personalized learning experience, catering to a student’s unique pace and needs.

11. Formative Assessment Formative Assessment is an instructional tool used for continuous feedback and guidance during the learning process. Unlike summative assessments which evaluate learning at its conclusion, formative assessments monitor student learning, identifying areas of weakness and strength to guide ongoing instruction.

12. Gamification Gamification is the incorporation of game-like elements into non-game contexts, like learning, to increase engagement and motivation. This approach can make learning experiences more enjoyable and interactive, increasing learners’ willingness to participate and their retention of information.

13. Andragogy Andragogy refers to the methods and principles used in adult education, recognizing adults’ independent self-concept, life experiences, readiness to learn, practicality, internal motivation, and problem-solving orientation. It emphasizes the value of the learner’s experience, and encourages learners to become active participants in their education.

14. Heutagogy Heutagogy, or self-determined learning, involves learners deciding what and how to learn, extending beyond problem-solving to include capacity building for learners. It prioritizes autonomy and capability development, encouraging learners to determine not only the learning path but also the learning methods and resources.

15. Inquiry-based Learning Inquiry-based Learning promotes curiosity by allowing learners to explore and investigate questions, problems or scenarios themselves. It fosters critical thinking and encourages learners to become actively involved in the learning process, rather than remaining passive recipients of information.

16. Just-in-time Learning Just-in-time Learning is an approach that provides specific information exactly when a learner needs it. Focused primarily on applicability and timeliness, it enables learners to immediately apply the knowledge they gain, enhancing the learning effect.

17. Kinesthetic Learning Kinesthetic Learning is a learning style that requires physical activities to understand new information. By participating in hands-on experiences, learners can better remember and understand the concepts they’re being taught.

18. Lifelong Learning Lifelong Learning refers to the continuous, self-motivated pursuit of knowledge for either personal or professional reasons. It extends beyond traditional schooling to encompass learning opportunities in various forms and at multiple stages of life.

19. Mastery Learning Mastery Learning is a strategy wherein students must achieve a level of mastery in prerequisite knowledge before moving forward to learn subsequent information. The approach focuses on the premise that students will acquire a deeper understanding of the subject matter through a structured system that measures and achieves learning outcomes.

20. Metacognition Metacognition involves awareness and understanding of one’s cognitive processes. The concept focuses on “thinking about thinking”, helping learners to actively control the learning process and improve comprehension and problem-solving abilities.

21. Microlearning Microlearning involves learning through bite-sized lessons, typically ranging from a few seconds to 15 minutes. The intention is to minimize cognitive overload and integrate the learning process seamlessly into the learner’s daily workflow, thus enhancing retention and understanding.

22. Mind Mapping Mind Mapping is a learning tool that allows learners to visually organize information, typically around a central concept. By illustrating and linking key concepts, mind mapping can facilitate better understanding and recall of complex ideas.

23. Mobile Learning Mobile Learning leverages portable technology to facilitate learning anytime and anywhere. Using devices such as smartphones or tablets, students can access learning resources, participate in interactive assignments, or collaborate with peers remotely.

24. Memorization Memorization is a learning technique that involves repeating information until it is committed to memory. While often viewed as less effective than understanding concepts, it remains an essential part of learning, especially for the acquisition of factual content or mastering foundational skills.

25. Multimodal Learning Multimodal Learning incorporates various methods of learning, such as visual aids, auditory stimuli, and hands-on experiences, to reinforce the same information. It engages different senses and learning styles, catering to diverse learners and enhancing overall comprehension.

26. Peer Teaching Peer Teaching involves one student teaching or tutoring another, often involving cooperation or team work. This approach not only reinforces the knowledge of the teaching peer, but can also make learning more relatable and digestible for the learning student.

See Also: Peer Learning

27. Problem-based Learning Problem-based Learning is a student-centered pedagogy in which learners work to solve complex and authentic problems. It encourages deep understanding of the subject matter, develops higher-order thinking skills, and promotes self-directed learning.

28. Project-based Learning Project-based Learning uses real-world scenarios, challenges, or problems as the basis for a curriculum. Students engage deeply with content by applying it in a practical way, fostering both knowledge retention and the development of useful skills such as critical thinking, communication, and collaboration.

29. Reflective Practice Reflective Practice is a process of examining one’s own learning or work performance to discover how to improve. This involves thinking about and critically analyzing one’s actions with the goal of improving one’s professional and personal practices.

See Also: Reflective Teaching

30. Rote Learning Rote Learning involves memorizing information based on repetition. Although sometimes criticized for lack of depth, it can be effective for foundational learning needs, such as multiplication tables or spelling.

31. Scaffolding Scaffolding is an instructional method that provides step-by-step guidance to students as they tackle new concepts. As learners’ knowledge and skills increase, the scaffolding is gradually removed, fostering independence and mastery over the task or concept.

32. Self-directed Learning Self-directed Learning encourages learners to take charge of their own education, determining what they learn, how they learn, and when they learn. This method supports individual learning styles, fosters independence, and cultivates lifelong learning skills.

33. Service Learning Service Learning integrates meaningful community service with instruction and reflection, enriching learning experiences and strengthening communities. It emphasizes both serving the community and learning from the service experience.

34. Situated Learning Situated Learning is based on the principle that learning effectively takes place in the context in which it is applied. It suggests that knowledge is deeply embedded in the specific context and situation in which it is learned and used.

35. Social Learning Social Learning suggests that we learn from observing others, absorbing information and behaviors through social interaction. This theory posits that learning is a cognitive process that takes place in the social context and can occur purely through observation or direct instruction.

36. Spiral Curriculum Spiral Curriculum is an educational approach by Jerome Bruner in which students revisit the same topics, themes or skills throughout their school years. Each encounter is intended to be more complex than the previous, promoting deeper understanding and mastery over time.

37. Student-centered Learning Student-centered Learning places students at the center of the learning process, encouraging active participation and giving them control over the pace, style, and direction of learning. This personalized method promotes self-motivation, engagement, and autonomy in learners.

38. Summative Assessment Summative Assessment is used to evaluate what a student has learned at the culmination of a specific instructional period. Akin to a final review or a post-test, these assessments provide an overall view of student understanding and information retention.

39. Synaptic Learning Synaptic Learning is an approach based on the brain’s natural learning processes, particularly the strengthening of synaptic connections responsible for memory and learning. The aim is to maximize the mind’s ability to learn, recall, and apply information.

40. Tactile Learning Tactile Learning, also known as tactile-kinesthetic learning, involves physical action to learn new information, often through touch and movement. This mode is beneficial for learners who perform better when they can manipulate or do something physically to internalize a concept.

41. Team-based Learning Team-based Learning is a strategy that employs multiple small teams in a single classroom, initially working independently, then collaborating on complex tasks. This method promotes the development of higher-level cognitive skills and teamwork capabilities.

42. Thematic Learning Thematic Learning revolves around selecting a particular theme and teaching a variety of skills and subjects all centered around that theme. By integrating multiple disciplines, it provides a more wholistic educational experience and enables understanding of the interconnectedness of subjects.

43. Transfer of Learning Transfer of Learning references the application of skills, knowledge, or attitudes learned in one context to another context. It is crucial in understanding the interplay between subjects and the practical application of theoretical knowledge.

44. Universal Design for Learning Universal Design for Learning is a teaching framework that aims to offer flexible learning environments to accommodate different learning styles and needs. By presenting information in a variety of ways, it facilitates varied means of action, expression, and engagement, ensuring effective learning for all individuals.

45. Visual Learning Visual Learning, as the name suggests, depends on the use of visual aids such as charts, maps, and diagrams to grasp and retain new information. It caters to learners who absorb and recall information best when they have visual stimuli to associate with the information.

46. Learning Styles Learning Styles theory posits that people have unique ways of accumulating and processing information, and suggests that teaching should be tailored to cater to the specific learning style of each student. These styles may be auditory (listening), visual (seeing), or kinesthetic (touching or doing), among others.

47. Zone of Proximal Development The Zone of Proximal Development, a term coined by psychologist Lev Vygotsky, refers to the difference between what a learner can do without help and what they can achieve with guidance. It serves as a means to identify the potential abilities and the future development of the learner.

48. Authentic Learning Authentic Learning involves real-world tasks and projects that enable learners to connect school experiences to the work world and community. It uplifts the relevancy of the curriculum to learners’ lives, promoting engagement and building practical skills alongside theoretical knowledge.

49. Chunking Chunking is a technique used to make complex information more understandable and manageable, by breaking it down into smaller bits or “chunks.” This method makes learning more efficient by reducing cognitive load, allowing better absorption and retention of information.

50. Differentiated Instruction Differentiated Instruction is a teaching strategy that adjusts the content, process, and product of learning according to a student’s individual needs. By acknowledging that students learn in various ways, this method ensures that learning is effective for students of different abilities, interests, and learning preferences.

Knowledge about a diverse range of learning concepts helps you to be able to tailor your teaching to the learners in front of you, optimizing the learning scenario. If you find that one strategy isn’t working, pivot to a new learning concept that might help you overcome your plateau and improve your teaching and learning.

Most of these learning concept examples have learning theories underpinning them . I recommend using the search bar on this website to search for each concept (or use the hyperlinks I’ve provided in this article) to delve deeper into each concept and its theoretical connections.

Chris

Chris Drew (PhD)

Dr. Chris Drew is the founder of the Helpful Professor. He holds a PhD in education and has published over 20 articles in scholarly journals. He is the former editor of the Journal of Learning Development in Higher Education. [Image Descriptor: Photo of Chris]

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Center for Teaching Innovation

Resource library.

  • Getting Started with Establishing Ground Rules
  • Sample group work rubric
  • Problem-Based Learning Clearinghouse of Activities, University of Delaware

Problem-Based Learning

Problem-based learning  (PBL) is a student-centered approach in which students learn about a subject by working in groups to solve an open-ended problem. This problem is what drives the motivation and the learning. 

Why Use Problem-Based Learning?

Nilson (2010) lists the following learning outcomes that are associated with PBL. A well-designed PBL project provides students with the opportunity to develop skills related to:

  • Working in teams.
  • Managing projects and holding leadership roles.
  • Oral and written communication.
  • Self-awareness and evaluation of group processes.
  • Working independently.
  • Critical thinking and analysis.
  • Explaining concepts.
  • Self-directed learning.
  • Applying course content to real-world examples.
  • Researching and information literacy.
  • Problem solving across disciplines.

Considerations for Using Problem-Based Learning

Rather than teaching relevant material and subsequently having students apply the knowledge to solve problems, the problem is presented first. PBL assignments can be short, or they can be more involved and take a whole semester. PBL is often group-oriented, so it is beneficial to set aside classroom time to prepare students to   work in groups  and to allow them to engage in their PBL project.

Students generally must:

  • Examine and define the problem.
  • Explore what they already know about underlying issues related to it.
  • Determine what they need to learn and where they can acquire the information and tools necessary to solve the problem.
  • Evaluate possible ways to solve the problem.
  • Solve the problem.
  • Report on their findings.

Getting Started with Problem-Based Learning

  • Articulate the learning outcomes of the project. What do you want students to know or be able to do as a result of participating in the assignment?
  • Create the problem. Ideally, this will be a real-world situation that resembles something students may encounter in their future careers or lives. Cases are often the basis of PBL activities. Previously developed PBL activities can be found online through the University of Delaware’s PBL Clearinghouse of Activities .
  • Establish ground rules at the beginning to prepare students to work effectively in groups.
  • Introduce students to group processes and do some warm up exercises to allow them to practice assessing both their own work and that of their peers.
  • Consider having students take on different roles or divide up the work up amongst themselves. Alternatively, the project might require students to assume various perspectives, such as those of government officials, local business owners, etc.
  • Establish how you will evaluate and assess the assignment. Consider making the self and peer assessments a part of the assignment grade.

Nilson, L. B. (2010).  Teaching at its best: A research-based resource for college instructors  (2nd ed.).  San Francisco, CA: Jossey-Bass. 

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Problem-Based Learning (PBL) is a teaching method in which complex real-world problems are used as the vehicle to promote student learning of concepts and principles as opposed to direct presentation of facts and concepts. In addition to course content, PBL can promote the development of critical thinking skills, problem-solving abilities, and communication skills. It can also provide opportunities for working in groups, finding and evaluating research materials, and life-long learning (Duch et al, 2001).

PBL can be incorporated into any learning situation. In the strictest definition of PBL, the approach is used over the entire semester as the primary method of teaching. However, broader definitions and uses range from including PBL in lab and design classes, to using it simply to start a single discussion. PBL can also be used to create assessment items. The main thread connecting these various uses is the real-world problem.

Any subject area can be adapted to PBL with a little creativity. While the core problems will vary among disciplines, there are some characteristics of good PBL problems that transcend fields (Duch, Groh, and Allen, 2001):

  • The problem must motivate students to seek out a deeper understanding of concepts.
  • The problem should require students to make reasoned decisions and to defend them.
  • The problem should incorporate the content objectives in such a way as to connect it to previous courses/knowledge.
  • If used for a group project, the problem needs a level of complexity to ensure that the students must work together to solve it.
  • If used for a multistage project, the initial steps of the problem should be open-ended and engaging to draw students into the problem.

The problems can come from a variety of sources: newspapers, magazines, journals, books, textbooks, and television/ movies. Some are in such form that they can be used with little editing; however, others need to be rewritten to be of use. The following guidelines from The Power of Problem-Based Learning (Duch et al, 2001) are written for creating PBL problems for a class centered around the method; however, the general ideas can be applied in simpler uses of PBL:

  • Choose a central idea, concept, or principle that is always taught in a given course, and then think of a typical end-of-chapter problem, assignment, or homework that is usually assigned to students to help them learn that concept. List the learning objectives that students should meet when they work through the problem.
  • Think of a real-world context for the concept under consideration. Develop a storytelling aspect to an end-of-chapter problem, or research an actual case that can be adapted, adding some motivation for students to solve the problem. More complex problems will challenge students to go beyond simple plug-and-chug to solve it. Look at magazines, newspapers, and articles for ideas on the story line. Some PBL practitioners talk to professionals in the field, searching for ideas of realistic applications of the concept being taught.
  • What will the first page (or stage) look like? What open-ended questions can be asked? What learning issues will be identified?
  • How will the problem be structured?
  • How long will the problem be? How many class periods will it take to complete?
  • Will students be given information in subsequent pages (or stages) as they work through the problem?
  • What resources will the students need?
  • What end product will the students produce at the completion of the problem?
  • Write a teacher's guide detailing the instructional plans on using the problem in the course. If the course is a medium- to large-size class, a combination of mini-lectures, whole-class discussions, and small group work with regular reporting may be necessary. The teacher's guide can indicate plans or options for cycling through the pages of the problem interspersing the various modes of learning.
  • The final step is to identify key resources for students. Students need to learn to identify and utilize learning resources on their own, but it can be helpful if the instructor indicates a few good sources to get them started. Many students will want to limit their research to the Internet, so it will be important to guide them toward the library as well.

The method for distributing a PBL problem falls under three closely related teaching techniques: case studies, role-plays, and simulations. Case studies are presented to students in written form. Role-plays have students improvise scenes based on character descriptions given. Today, simulations often involve computer-based programs. Regardless of which technique is used, the heart of the method remains the same: the real-world problem.

Where can I learn more?

  • PBL through the Institute for Transforming Undergraduate Education at the University of Delaware
  • Duch, B. J., Groh, S. E, & Allen, D. E. (Eds.). (2001). The power of problem-based learning . Sterling, VA: Stylus.
  • Grasha, A. F. (1996). Teaching with style: A practical guide to enhancing learning by understanding teaching and learning styles. Pittsburgh: Alliance Publishers.

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Teaching problem solving.

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Tips and Techniques

Expert vs. novice problem solvers, communicate.

  • Have students  identify specific problems, difficulties, or confusions . Don’t waste time working through problems that students already understand.
  • If students are unable to articulate their concerns, determine where they are having trouble by  asking them to identify the specific concepts or principles associated with the problem.
  • In a one-on-one tutoring session, ask the student to  work his/her problem out loud . This slows down the thinking process, making it more accurate and allowing you to access understanding.
  • When working with larger groups you can ask students to provide a written “two-column solution.” Have students write up their solution to a problem by putting all their calculations in one column and all of their reasoning (in complete sentences) in the other column. This helps them to think critically about their own problem solving and helps you to more easily identify where they may be having problems. Two-Column Solution (Math) Two-Column Solution (Physics)

Encourage Independence

  • Model the problem solving process rather than just giving students the answer. As you work through the problem, consider how a novice might struggle with the concepts and make your thinking clear
  • Have students work through problems on their own. Ask directing questions or give helpful suggestions, but  provide only minimal assistance and only when needed to overcome obstacles.
  • Don’t fear  group work ! Students can frequently help each other, and talking about a problem helps them think more critically about the steps needed to solve the problem. Additionally, group work helps students realize that problems often have multiple solution strategies, some that might be more effective than others

Be sensitive

  • Frequently, when working problems, students are unsure of themselves. This lack of confidence may hamper their learning. It is important to recognize this when students come to us for help, and to give each student some feeling of mastery. Do this by providing  positive reinforcement to let students know when they have mastered a new concept or skill.

Encourage Thoroughness and Patience

  • Try to communicate that  the process is more important than the answer so that the student learns that it is OK to not have an instant solution. This is learned through your acceptance of his/her pace of doing things, through your refusal to let anxiety pressure you into giving the right answer, and through your example of problem solving through a step-by step process.

Experts (teachers) in a particular field are often so fluent in solving problems from that field that they can find it difficult to articulate the problem solving principles and strategies they use to novices (students) in their field because these principles and strategies are second nature to the expert. To teach students problem solving skills,  a teacher should be aware of principles and strategies of good problem solving in his or her discipline .

The mathematician George Polya captured the problem solving principles and strategies he used in his discipline in the book  How to Solve It: A New Aspect of Mathematical Method (Princeton University Press, 1957). The book includes  a summary of Polya’s problem solving heuristic as well as advice on the teaching of problem solving.

learning concepts problem solving

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  • Published: 10 August 2016

Learning strategies: a synthesis and conceptual model

  • John A C Hattie 1 &
  • Gregory M Donoghue 1  

npj Science of Learning volume  1 , Article number:  16013 ( 2016 ) Cite this article

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  • Social sciences

The purpose of this article is to explore a model of learning that proposes that various learning strategies are powerful at certain stages in the learning cycle. The model describes three inputs and outcomes (skill, will and thrill), success criteria, three phases of learning (surface, deep and transfer) and an acquiring and consolidation phase within each of the surface and deep phases. A synthesis of 228 meta-analyses led to the identification of the most effective strategies. The results indicate that there is a subset of strategies that are effective, but this effectiveness depends on the phase of the model in which they are implemented. Further, it is best not to run separate sessions on learning strategies but to embed the various strategies within the content of the subject, to be clearer about developing both surface and deep learning, and promoting their associated optimal strategies and to teach the skills of transfer of learning. The article concludes with a discussion of questions raised by the model that need further research.

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There has been a long debate about the purpose of schooling. These debates include claims that schooling is about passing on core notions of humanity and civilisation (or at least one’s own society’s view of these matters). They include claims that schooling should prepare students to live pragmatically and immediately in their current environment, should prepare students for the work force, should equip students to live independently, to participate in the life of their community, to learn to ‘give back’, to develop personal growth. 1

In the past 30 years, however, the emphasis in many western systems of education has been more on enhancing academic achievement—in domains such as reading, mathematics, and science—as the primary purpose of schooling. 2 Such an emphasis has led to curricula being increasingly based on achievement in a few privileged domains, and ‘great’ students are deemed those who attain high levels of proficiency in these narrow domains.

This has led to many countries aiming to be in the top echelon of worldwide achievement measures in a narrow range of subjects; for example, achievement measures such as PISA (tests of 15-year olds in mathematics, reading and science, across 65 countries in 2012) or PIRLS (Year-5 tests of mathematics, reading and science, across 57 countries in 2011). Indeed, within most school systems there is a plethora of achievement tests; many countries have introduced accountability pressures based on high levels of testing of achievement; and communities typically value high achievement or levels of knowledge. 3 The mantra underpinning these claims has been cast in terms of what students know and are able to do; the curriculum is compartmentalised into various disciplines of achievement; and students, teachers, parents and policy makers talk in terms of success in these achievement domains.

Despite the recent emphasis on achievement, the day-to-day focus of schools has always been on learning—how to know, how to know more efficiently and how to know more effectively. The underlying philosophy is more about what students are now ready to learn, how their learning can be enabled, and increasing the ‘how to learn’ proficiencies of students. In this scenario, the purpose of schooling is to equip students with learning strategies, or the skills of learning how to learn. Of course, learning and achievement are not dichotomous; they are related. 4 Through growth in learning in specific domains comes achievement and from achievement there can be much learning. The question in this article relates to identifying the most effective strategies for learning.

In our search, we identified >400 learning strategies: that is, those processes which learners use to enhance their own learning. Many were relabelled versions of others, some were minor modifications of others, but there remained many contenders purported to be powerful learning strategies. Such strategies help the learner structure his or her thinking so as to plan, set goals and monitor progress, make adjustments, and evaluate the process of learning and the outcomes. These strategies can be categorised in many ways according to various taxonomies and classifications (e.g., references 5 , 6 , 7 ). Boekaerts, 8 for example, argued for three types of learning strategies: (1) cognitive strategies such as elaboration, to deepen the understanding of the domain studied; (2) metacognitive strategies such as planning, to regulate the learning process; and (3) motivational strategies such as self-efficacy, to motivate oneself to engage in learning. Given the advent of newer ways to access information (e.g., the internet) and the mountain of information now at students’ fingertips, it is appropriate that Dignath, Buettner and Langfeldt 9 added a fourth category—management strategies such as finding, navigating, and evaluating resources.

But merely investigating these 400-plus strategies as if they were independent is not defensible. Thus, we begin with the development of a model of learning to provide a basis for interpreting the evidence from our meta-synthesis. The argument is that learning strategies can most effectively enhance performance when they are matched to the requirements of tasks (cf. 10 ).

A model of learning

The model comprises the following components: three inputs and three outcomes; student knowledge of the success criteria for the task; three phases of the learning process (surface, deep and transfer), with surface and deep learning each comprising an acquisition phase and a consolidation phase; and an environment for the learning ( Figure 1 ). We are proposing that various learning strategies are differentially effective depending on the degree to which the students are aware of the criteria of success, on the phases of learning process in which the strategies are used, and on whether the student is acquiring or consolidating their understanding. The following provides an overview of the components of the model (see reference 11 for a more detailed explanation of the model).

figure 1

A model of learning.

Input and outcomes

The model starts with three major sources of inputs: the skill, the will and the thrill. The ‘skill’ is the student’s prior or subsequent achievement, the ‘will’ relates to the student’s various dispositions towards learning, and the ‘thrill’ refers to the motivations held by the student. In our model, these inputs are also the major outcomes of learning. That is, developing outcomes in achievement (skill) is as valuable as enhancing the dispositions towards learning (will) and as valuable as inviting students to reinvest more into their mastery of learning (thrill or motivations).

The first component describes the prior achievement the student brings to the task. As Ausubel 12 claimed ‘if I had to reduce all of educational psychology to just one principle, I would say this ‘The most important single factor influencing learning is what the leaner already knows. Ascertain this and teach him accordingly. Other influences related to the skills students bring to learning include their working memory, beliefs, encouragement and expectations from the student’s cultural background and home.

Dispositions are more habits of mind or tendencies to respond to situations in certain ways. Claxton 13 claimed that the mind frame of a ‘powerful learner’ is based on the four major dispositions: resilience or emotional strength, resourcefulness or cognitive capabilities, reflection or strategic awareness, and relating or social sophistication. These dispositions involve the proficiency to edit, select, adapt and respond to the environment in a recurrent, characteristic manner. 14 But dispositions alone are not enough. Perkins et al. 15 outlined a model with three psychological components which must be present in order to spark dispositional behaviour: sensitivity—the perception of the appropriateness of a particular behaviour; inclination—the felt impetus toward a behaviour; and ability—the basic capacity and confidence to follow through with the behaviour.

There can be a thrill in learning but for many students, learning in some domains can be dull, uninviting and boring. There is a huge literature on various motivational aspects of learning, and a smaller literature on how the more effective motivational aspects can be taught. A typical demarcation is between mastery and performance orientations. Mastery goals are seen as being associated with intellectual development, the acquisition of knowledge and new skills, investment of greater effort, and higher-order cognitive strategies and learning outcomes. 16 Performance goals, on the other hand, have a focus on outperforming others or completing tasks to please others. A further distinction has been made between approach and avoidance performance goals. 17 – 19 The correlations of mastery and performance goals with achievement, however, are not as high as many have claimed. A recent meta-analysis found 48 studies relating goals to achievement (based on 12,466 students), and the overall correlation was 0.12 for mastery and 0.05 for performance goals on outcomes. 20 Similarly, Hulleman et al. 21 reviewed 249 studies ( N =91,087) and found an overall correlation between mastery goal and outcomes of 0.05 and performance goals and outcomes of 0.14. These are small effects and show the relatively low importance of these motivational attributes in relation to academic achievement.

An alternative model of motivation is based on Biggs 22 learning processes model, which combines motivation (why the student wants to study the task) and their related strategies (how the student approaches the task). He outlined three common approaches to learning: deep, surface and achieving. When students are taking a deep strategy, they aim to develop understanding and make sense of what they are learning, and create meaning and make ideas their own. This means they focus on the meaning of what they are learning, aim to develop their own understanding, relate ideas together and make connections with previous experiences, ask themselves questions about what they are learning, discuss their ideas with others and compare different perspectives. When students are taking a surface strategy, they aim to reproduce information and learn the facts and ideas—with little recourse to seeing relations or connections between ideas. When students are using an achieving strategy, they use a ‘minimax’ notion—minimum amount of effort for maximum return in terms of passing tests, complying with instructions, and operating strategically to meet a desired grade. It is the achieving strategy that seems most related to school outcomes.

Success criteria

The model includes a prelearning phase relating to whether the students are aware of the criteria of success in the learning task. This phase is less about whether the student desires to attain the target of the learning (which is more about motivation), but whether he or she understands what it means to be successful at the task at hand. When a student is aware of what it means to be successful before undertaking the task, this awareness leads to more goal-directed behaviours. Students who can articulate or are taught these success criteria are more likely to be strategic in their choice of learning strategies, more likely to enjoy the thrill of success in learning, and more likely to reinvest in attaining even more success criteria.

Success criteria can be taught. 23 , 24 Teachers can help students understand the criteria used for judging the students’ work, and thus teachers need to be clear about the criteria used to determine whether the learning intentions have been successfully achieved. Too often students may know the learning intention, but do not how the teacher is going to judge their performance, or how the teacher knows when or whether students have been successful. 25 The success criteria need to be as clear and specific as possible (at surface, deep, or transfer level) as this enables the teacher (and learner) to monitor progress throughout the lesson to make sure students understand and, as far as possible, attain the intended notions of success. Learning strategies that help students get an overview of what success looks like include planning and prediction, having intentions to implement goals, setting standards for judgement success, advance organisers, high levels of commitment to achieve success, and knowing about worked examples of what success looks like. 23

Environment

Underlying all components in the model is the environment in which the student is studying. Many books and internet sites on study skills claim that it is important to attend to various features of the environment such as a quiet room, no music or television, high levels of social support, giving students control over their learning, allowing students to study at preferred times of the day and ensuring sufficient sleep and exercise.

The three phases of learning: surface, deep and transfer

The model highlights the importance of both surface and deep learning and does not privilege one over the other, but rather insists that both are critical. Although the model does seem to imply an order, it must be noted that these are fuzzy distinctions (surface and deep learning can be accomplished simultaneously), but it is useful to separate them to identify the most effective learning strategies. More often than not, a student must have sufficient surface knowledge before moving to deep learning and then to the transfer of these understandings. As Entwistle 26 noted, ‘The verb ‘to learn’ takes the accusative’; that is, it only makes sense to analyse learning in relation to the subject or content area and the particular piece of work towards which the learning is directed, and also the context within which the learning takes place. The key debate, therefore, is whether the learning is directed content that is meaningful to the student, as this will directly affect student dispositions, in particular a student’s motivation to learn and willingness to reinvest in their learning.

A most powerful model to illustrate this distinction between surface and deep is the structure of observed learning outcomes, or SOLO, 27 , 28 as discussed above. The model has four levels: unistructural, multistructural, relational and extended abstract. A unistructural intervention is based on teaching or learning one idea, such as coaching one algorithm, training in underlining, using a mnemonic or anxiety reduction. The essential feature is that this idea alone is the focus, independent of the context or its adaption to or modification by content. A multistructural intervention involves a range of independent strategies or procedures, but without integrating or orchestration as to the individual differences or demands of content or context (such as teaching time management, note taking and setting goals with no attention to any strategic or higher-order understandings of these many techniques). Relational interventions involve bringing together these various multistructural ideas, and seeing patterns; it can involve the strategies of self-monitoring and self-regulation. Extended abstract interventions aim at far transfer (transfer between contexts that, initally, appear remote to one another) such that they produce structural changes in an individual’s cognitive functioning to the point where autonomous or independent learning can occur. The first two levels (one then many ideas) refer to developing surface knowing and the latter two levels (relate and extend) refer to developing deeper knowing. The parallel in learning strategies is that surface learning refers to studying without much reflecting on either purpose or strategy, learning many ideas without necessarily relating them and memorising facts and procedures routinely. Deep learning refers to seeking meaning, relating and extending ideas, looking for patterns and underlying principles, checking evidence and relating it to conclusions, examining arguments cautiously and critically, and becoming actively interested in course content (see reference 29 ).

Our model also makes a distinction between first acquiring knowledge and then consolidating it. During the acquisition phase, information from a teacher or instructional materials is attended to by the student and this is taken into short-term memory. During the consolidation phase, a learner then needs to actively process and rehearse the material as this increases the likelihood of moving that knowledge to longer-term memory. At both phases there can be a retrieval process, which involves transferring the knowing and understanding from long-term memory back into short-term working memory. 30 , 31

Acquiring surface learning

In their meta-analysis of various interventions, Hattie et al. 32 found that many learning strategies were highly effective in enhancing reproductive performances (surface learning) for virtually all students. Surface learning includes subject matter vocabulary, the content of the lesson and knowing much more. Strategies include record keeping, summarisation, underlining and highlighting, note taking, mnemonics, outlining and transforming, organising notes, training working memory, and imagery.

Consolidating surface learning

Once a student has begun to develop surface knowing it is then important to encode it in a manner such that it can retrieved at later appropriate moments. This encoding involves two groups of learning strategies: the first develops storage strength (the degree to which a memory is durably established or ‘well learned’) and the second develops strategies that develop retrieval strength (the degree to which a memory is accessible at a given point in time). 33 ‘Encoding’ strategies are aimed to develop both, but with a particular emphasis on developing retrieval strength. 34 Both groups of strategies invoke an investment in learning, and this involves ‘the tendency to seek out, engage in, enjoy and continuously pursue opportunities for effortful cognitive activity. 35 Although some may not ‘enjoy’ this phase, it does involve a willingness to practice, to be curious and to explore again, and a willingness to tolerate ambiguity and uncertainty during this investment phase. In turn, this requires sufficient metacognition and a calibrated sense of progress towards the desired learning outcomes. Strategies include practice testing, spaced versus mass practice, teaching test taking, interleaved practice, rehearsal, maximising effort, help seeking, time on task, reviewing records, learning how to receive feedback and deliberate practice (i.e., practice with help of an expert, or receiving feedback during practice).

Acquiring deep learning

Students who have high levels of awareness, control or strategic choice of multiple strategies are often referred to as ‘self-regulated’ or having high levels of metacognition. In Visible Learning , Hattie 36 described these self-regulated students as ‘becoming like teachers’, as they had a repertoire of strategies to apply when their current strategy was not working, and they had clear conceptions of what success on the task looked like. 37 More technically, Pintrich et al. 38 described self-regulation as ‘an active, constructive process whereby learners set goals for their learning and then attempt to monitor, regulate and control their cognition, motivation and behaviour, guided and constrained by their goals and the contextual features in the environment’. These students know the what, where, who, when and why of learning, and the how, when and why to use which learning strategies. 39 They know what to do when they do not know what to do. Self-regulation strategies include elaboration and organisation, strategy monitoring, concept mapping, metacognitive strategies, self-regulation and elaborative interrogation.

Consolidating deep learning

Once a student has acquired surface and deep learning to the extent that it becomes part of their repertoire of skills and strategies, we may claim that they have ‘automatised’ such learning—and in many senses this automatisation becomes an ‘idea’, and so the cycle continues from surface idea to deeper knowing that then becomes a surface idea, and so on. 40 There is a series of learning strategies that develop the learner’s proficiency to consolidate deeper thinking and to be more strategic about learning. These include self-verbalisation, self-questioning, self-monitoring, self-explanation, self-verbalising the steps in a problem, seeking help from peers and peer tutoring, collaborative learning, evaluation and reflection, problem solving and critical thinking techniques.

There are skills involved in transferring knowledge and understanding from one situation to a new situation. Indeed, some have considered that successful transfer could be thought as synonymous with learning. 41 , 42 There are many distinctions relating to transfer: near and far transfer, 43 low and high transfer, 44 transfer to new situations and problem solving transfer, 5 and positive and negative transfer. 45 Transfer is a dynamic, not static, process that requires learners to actively choose and evaluate strategies, consider resources and surface information, and, when available, to receive or seek feedback to enhance these adaptive skills. Reciprocal teaching is one program specifically aiming to teach these skills; for example, Bereiter and Scardamalia 46 have developed programs in the teaching of transfer in writing, where students are taught to identify goals, improve and elaborate existing ideas, strive for idea cohesion, present their ideas to groups and think aloud about how they might proceed. Similarly, Schoenfeld 47 outlined a problem-solving approach to mathematics that involves the transfer of skills and knowledge from one situation to another. Marton 48 argued that transfer occurs when the learner learns strategies that apply in a certain situation such that they are enabled to do the same thing in another situation when they realise that the second situation resembles (or is perceived to resemble) the first situation. He claimed that not only sameness, similarity, or identity might connect situations to each other, but also small differences might connect them as well. Learning how to detect such differences is critical for the transfer of learning. As Heraclitus claimed, no two experiences are identical; you do not step into the same river twice.

Overall messages from the model

There are four main messages to be taken from the model. First, if the success criteria is the retention of accurate detail (surface learning) then lower-level learning strategies will be more effective than higher-level strategies. However, if the intention is to help students understand context (deeper learning) with a view to applying it in a new context (transfer), then higher level strategies are also needed. An explicit assumption is that higher level thinking requires a sufficient corpus of lower level surface knowledge to be effective—one cannot move straight to higher level thinking (e.g., problem solving and creative thought) without sufficient level of content knowledge. Second, the model proposes that when students are made aware of the nature of success for the task, they are more likely to be more involved in investing in the strategies to attain this target. Third, transfer is a major outcome of learning and is more likely to occur if students are taught how to detect similarities and differences between one situation and a new situation before they try to transfer their learning to the new situation. Hence, not one strategy may necessarily be best for all purposes. Fourth, the model also suggests that students can be advantaged when strategy training is taught with an understanding of the conditions under which the strategy best works—when and under what circumstance it is most appropriate.

The current study

The current study synthesises the many studies that have related various learning strategies to outcomes. This study only pertains to achievement outcomes (skill, on the model of learning); further work is needed to identify the strategies that optimise the dispositions (will) and the motivation (thrill) outcomes. The studies synthesised here are from four sources. First, there are the meta-analyses among the 1,200 meta-analyses in Visible Learning that relate to strategies for learning. 36 , 49 , 50 Second, there is the meta-analysis conducted by Lavery 51 on 223 effect-sizes derived from 31 studies relating to self-regulated learning interventions. The third source is two major meta-analyses by a Dutch team of various learning strategies, especially self-regulation. And the fourth is a meta-analysis conducted by Donoghue et al. 52 based on a previous analysis by Dunlosky et al. 53

The data in Visible Learning is based on 800 meta-analyses relating influences from the home, school, teacher, curriculum and teaching methods to academic achievement. Since its publication in 2009, the number of meta-analyses now exceeds 1,200, and those influences specific to learning strategies are retained in the present study. Lavery 51 identified 14 different learning strategies and the overall effect was 0.46—with greater effects for organising and transforming (i.e., deliberate rearrangement of instructional materials to improve learning, d =0.85) and self-consequences (i.e., student expectation of rewards or punishment for success or failure, d =0.70). The lowest effects were for imagery (i.e., creating or recalling vivid mental images to assist learning, d =0.44) and environmental restructuring (i.e., efforts to select or arrange the physical setting to make learning easier, d =0.22). She concluded that the higher effects involved ‘teaching techniques’ and related to more ‘deep learning strategies’, such as organising and transforming, self-consequences, self-instruction, self-evaluation, help-seeking, keeping records, rehearsing/memorising, reviewing and goal-setting. The lower ranked strategies were more ‘surface learning strategies’, such as time management and environmental restructuring.

Of the two meta-analyses conducted by the Dutch team, the first study, by Dignath et al. 9 analysed 357 effects from 74 studies ( N =8,619). They found an overall effect of 0.73 from teaching methods of self-regulation. The effects were large for achievement (elementary school, 0.68; high school, 0.71), mathematics (0.96, 1.21), reading and writing (0.44, 0.55), strategy use (0.72, 0.79) and motivation (0.75, 0.92). In the second study, Donker et al. 54 reviewed 180 effects from 58 studies relating to self-regulation training, reporting an overall effect of 0.73 in science, 0.66 in mathematics and 0.36 in reading comprehension. The most effective strategies were cognitive strategies (rehearsal 1.39, organisation 0.81 and elaboration 0.75), metacognitive strategies (planning 0.80, monitoring 0.71 and evaluation 0.75) and management strategies (effort 0.77, peer tutoring 0.83, environment 0.59 and metacognitive knowledge 0.97). Performance was almost always improved by a combination of strategies, as was metacognitive knowledge. This led to their conclusion that students should not only be taught which strategies to use and how to apply them (declarative knowledge or factual knowledge) but also when (procedural or how to use the strategies) and why to use them (conditional knowledge or knowing when to use a strategy).

Donoghue et al. 52 conducted a meta-analysis based on the articles referenced in Dunlosky et al. 53 They reviewed 10 learning strategies and a feature of their review is a careful analysis of possible moderators to the conclusions about the effectiveness of these learning strategies, such as learning conditions (e.g., study alone or in groups), student characteristics (e.g., age, ability), materials (e.g., simple concepts to problem-based analyses) and criterion tasks (different outcome measures).

In the current study, we independently assigned all strategies to the various parts of the model—this was a straightforward process, and the few minor disagreements were resolved by mutual agreement. All results are presented in Appendix 1.

Results: the meta-synthesis of learning strategies

There are 302 effects derived from the 228 meta-analyses from the above four sources that have related some form of learning strategy to an achievement outcome. Most are experimental–control studies or pre–post studies, whereas some are correlations ( N =37). There are 18,956 studies (although some may overlap across meta-analyses). Only 125 meta-analyses reported the sample size ( N =11,006,839), but if the average (excluding the outlier 7 million from one meta-analysis) is used for the missing sample sizes, the best estimate of sample size is between 13 and 20 million students.

The average effect is 0.53 but there is considerable variance ( Figure 2 ), and the overall number of meta-analyses, studies, number of people (where provided), effects and average effect-sizes for the various phases of the model are provided in Table 1 . The effects are lowest for management of the environment and ‘thrill’ (motivation), and highest for developing success criteria across the learning phases. The variance is sufficiently large, however, that it is important to look at specific strategies within each phase of the model.

figure 2

The average and the distribution of all effect sizes.

Synthesis of the input phases of the model

The inputs: skills.

There are nine meta-analyses that have investigated the relation between prior achievement and subsequent achievement, and not surprisingly these relations are high ( Table 2 ). The average effect-size is 0.77 (s.e.=0.10), which translates to a correlation of 0.36—substantial for any single variable. The effects of prior achievement are lowest in the early years, and highest from high school to university. One of the purposes of school, however, is to identify those students who are underperforming relative to their abilities and thus to not merely accept prior achievement as destiny. The other important skill is working memory—which relates to the amount of information that can be retained in short-term working memory when engaged in processing, learning, comprehension, problem solving or goal-directed thinking. 55 Working memory is strongly related to a person’s ability to reason with novel information (i.e., general fluid intelligence. 56

The inputs: will

There are 28 meta-analyses related to the dispositions of learning from 1,304 studies and the average effect-size is 0.48 (s.e.=0.09; Table 3 ). The effect of self-efficacy is highest ( d =0.90), followed by increasing the perceived value of the task ( d = 0.46), reducing anxiety ( d =0.45) and enhancing the attitude to the content ( d =0.35). Teachers could profitably increase students’ levels of confidence and efficacy to tackle difficult problems; not only does this increase the probability of subsequent learning but it can also help reduce students’ levels of anxiety. It is worth noting the major movement in the anxiety and stress literature in the 1980s moved from a preoccupation on understanding levels of stress to providing coping strategies—and these strategies were powerful mediators in whether people coped or not. 57 Similarly in learning, it is less the levels of anxiety and stress but the development of coping strategies to deal with anxiety and stress. These strategies include being taught to effectively regulate negative emotions; 58 increasing self-efficacy, which relates to developing the students conviction in their own competence to attain desired outcomes; 59 focusing on the positive skills already developed; increasing social support and help seeking; reducing self-blame; and learning to cope with error and making mistakes. 60 Increasing coping strategies to deal with anxiety and promoting confidence to tackle difficult and challenging learning tasks frees up essential cognitive resources required for the academic work.

There has been much discussion about students having growth—or incremental—mindsets (human attributes are malleable not fixed) rather than fixed mindsets (attributes are fixed and invariant). 61 However, the evidence in Table 3 ( d =0.19) shows how difficult it is to change to growth mindsets, which should not be surprising as many students work in a world of schools dominated by fixed notions—high achievement, ability groups, and peer comparison.

The inputs: thrill

The thrill relates to the motivation for learning: what is the purpose or approach to learning that the student adopts? Having a surface or performance approach motivation (learning to merely pass tests or for short-term gains) or mastery goals is not conducive to maximising learning, whereas having a deep or achieving approach or motivation is helpful ( Table 4 ). A possible reason why mastery goals are not successful is that too often the outcomes of tasks and assessments are at the surface level and having mastery goals with no strategic sense of when to maximise them can be counter-productive. 62 Having goals, per se , is worthwhile—and this relates back to the general principle of having notions of what success looks like before investing in the learning. The first step is to teach students to have goals relating to their upcoming work, preferably the appropriate mix of achieving and deep goals, ensure the goals are appropriately challenging and then encourage students to have specific intentions to achieve these goals. Teaching students that success can then be attributed to their effort and investment can help cement this power of goal setting, alongside deliberate teaching.

The environment

Despite the inordinate attention, particularly by parents, on structuring the environment as a precondition for effective study, such effects are generally relatively small ( Table 5 ). It seems to make no differences if there is background music, a sense of control over learning, the time of day to study, the degree of social support or the use of exercise. Given that most students receive sufficient sleep and exercise, it is perhaps not surprising that these are low effects; of course, extreme sleep or food deprivation may have marked effects.

Knowing the success criteria

A prediction from the model of learning is that when students learn how to gain an overall picture of what is to be learnt, have an understanding of the success criteria for the lessons to come and are somewhat clear at the outset about what it means to master the lessons, then their subsequent learning is maximised. The overall effect across the 31 meta-analyses is 0.54, with the greatest effects relating to providing students with success criteria, planning and prediction, having intentions to implement goals, setting standards for self-judgements and the difficulty of goals ( Table 6 ). All these learning strategies allow students to see the ‘whole’ or the gestalt of what is targeted to learn before starting the series of lessons. It thus provides a ‘coat hanger’ on which surface-level knowledge can be organised. When a teacher provides students with a concept map, for example, the effect on student learning is very low; but in contrast, when teachers work together with students to develop a concept map, the effect is much higher. It is the working with students to develop the main ideas, and to show the relations between these ideas to allow students to see higher-order notions, that influences learning. Thus, when students begin learning of the ideas, they can begin to know how these ideas relate to each other, how the ideas are meant to form higher order notions, and how they can begin to have some control or self-regulation on the relation between the ideas.

Synthesis of the learning phases of the model

There are many strategies, such as organising, summarising, underlining, note taking and mnemonics that can help students master the surface knowledge ( Table 7 ). These strategies can be deliberately taught, and indeed may be the only set of strategies that can be taught irrespective of the content. However, it may be that for some of these strategies, the impact is likely to be higher if they are taught within each content domain, as some of the skills (such as highlighting, note taking and summarising) may require specific ideas germane to the content being studied.

While it appears that training working memory can have reasonable effects ( d =0.53) there is less evidence that training working memory transfers into substantial gains in academic attainment. 63 There are many emerging and popular computer games that aim to increase working memory. For example, CogMed is a computer set of adaptive routines that is intended to be used 30–40 min a day for 25 days. A recent meta-analysis (by the commercial owners 64 ) found average effect-sizes (across 43 studies) exceed 0.70, but in a separate meta-analysis of 21 studies on the longer term effects of CogMed, there was zero evidence of transfer to subjects such as mathematics or reading 65 . Although there were large effects in the short term, they found that these gains were not maintained at follow up (about 9 months later) and no evidence to support the claim that working memory training produces generalised gains to the other skills that have been investigated (verbal ability, word decoding or arithmetic) even when assessment takes place immediately after training. For the most robust studies, the effect of transfer is zero. It may be better to reduce working memory demands in the classroom. 66

The investment of effort and deliberate practice is critical at this consolidation phase, as are the abilities to listen, seek and interpret the feedback that is provided ( Table 8 ). At this consolidation phase, the task is to review and practice (or overlearn) the material. Such investment is more valuable if it is spaced over time rather than massed. Rehearsal and memorisation is valuable—but note that memorisation is not so worthwhile at the acquisition phase. The difficult task is to make this investment in learning worthwhile, to make adjustments to the rehearsal as it progresses in light of high levels of feedback, and not engage in drill and practice. These strategies relating to consolidating learning are heavily dependent on the student’s proficiency to invest time on task wisely, 67 to practice and learn from this practice and to overlearn such that the learning is more readily available in working memory for the deeper understanding.

Acquiring deeper learning

Nearly all the strategies at this phase are powerful in enhancing learning ( Table 9 ). The ability to elaborate and organise, monitor the uses of the learning strategies, and have a variety of metacognitive strategies are the critical determinants of success at this phase of learning. A major purpose is for the student to deliberately activate prior knowledge and then make relations and extensions beyond what they have learned at the surface phase.

At this phase, the power of working with others is most apparent ( Table 10 ). This involves skills in seeking help from others, listening to others in discussion and developing strategies to ‘speak’ the language of learning. It is through such listening and speaking about their learning that students and teachers realise what they do deeply know, what they do not know and where they are struggling to find relations and extensions. An important strategy is when students become teachers of others and learn from peers, as this involves high levels of regulation, monitoring, anticipation and listening to their impact on the learner.

There has been much research confirming that teaching help-seeking strategies is successful, but how this strategy then works in classrooms is more complex. Teachers have to welcome students seeking help, and there needs to be knowledgeable others (e.g., peers) from whom to seek the help—too often students left in unsupported environments can seek and gain incorrect help and not know the help is incorrect. 68 Ryan and Shin 69 also distinguished between adaptive help seeking (seeking help from others, such as an explanation, a hint, or an example, that would further learning and promote independent problem solving in the future) and expedient help seeking (seeking help that expedites task completion, such as help that provides the answer and is not focused on learning). They showed that adaptive help seeking from peers declines and expedient help seeking increases during early adolescence. Further, increases in expedient help seeking were associated with declines in achievement but changes in adaptive help seeking were unrelated to achievement. The key is for teachers to teach adaptive help seeking, to ensure the help is dependable and correct and to see this more of a student than a teacher skill. Help seeking needs to be welcomed before it can have an effect.

The transfer model promoted by Marton 48 seems to be supported in that a key in teaching for transfer involves understanding the patterns, similarities and differences in the transfer before applying the strategies to new task ( Table 11 ). Marton argued that transfer occurs when students learn strategies that apply in a certain situation such that they are enabled to do the same thing in another situation to the degree that they realise how the second situation does (or does not) resemble the first situation. It is learning to detect differences and similarities that is the key that leads to transfer of learning.

Discussion and Conclusions

There is much debate about the optimal strategies of learning, and indeed we identified >400 terms used to describe these strategies. Our initial aim was to rank the various strategies in terms of their effectiveness but this soon was abandoned. There was too much variability in the effectiveness of most strategies depending on when they were used during the learning process, and thus we developed the model of learning presented in this article. Like all models, it is a conjecture, it aims to say much and it is falsifiable. The efficacy of any model can be seen as an expression of its capacity to generate a scalable solution to a problem or need in ways that resolve more issues than prevailing theories or approaches. 70 The model posits that learning must be embedded in some content (something worth knowing) and thus the current claims about developing 21st century skills sui generis are most misleading. These skills often are promoted as content free and are able to be developed in separate courses (e.g., critical thinking, resilience). Our model, however, suggests that such skills are likely to be best developed relative to some content. There is no need to develop learning strategy courses, or teach the various strategies outside the context of the content. Instead, the strategies should be an integral part of the teaching and learning process, and can be taught within this process.

The model includes three major inputs and outcomes. These relate to what the students bring to the learning encounter (skill), their dispositions about learning (will) and their motivations towards the task (thrill). The first set of strategies relate to teaching students the standards for what is to be learned (the success criteria). We propose that effective learning strategies will be different depending on the phase of the learning—the strategies will be different when a student is first acquiring the matters to be learnt compared with when the student is embedding or consolidating this learning. That is, the strategies are differentially effective depending on whether the learning intention is surface learning (the content), deep learning (the relations between content) or the transfer of the skills to new situations or tasks. In many ways this demarcation is arbitrary (but not capricious) and more experimental research is needed to explore these conjectures. Further, the model is presented as linear whereas there is often much overlap in the various phases. For example, to learn subject matter (surface) deeply (i.e., to encode in memory) is helped by exploring and understanding its meaning; success criteria can have a mix of surface and deep and even demonstrate the transfer to other (real world) situations; and often deep learning necessitates returning to acquire specific surface level vocabulary and understanding. In some cases, there can be multiple overlapping processes. A reviewer provided a clear example: in learning that the internal angles of a quadrilateral add up to 360°, this might involve surface learning, which then requires rehearsal to consolidate, some self-questioning to apply, some detection of similarities to then work out what the internal angles of a hexagon might be, and spotting similarities to the triangle rule. There may be no easy way to know the right moment, or no easy demarcation of the various phases. The proposal in this paper is but a ‘model’ to help clarify the various phases of learning, and in many real world situations there can be considerable overlap.

We have derived six sets of propositions from our conceptual model of learning and the results of our meta-synthesis of research on learning strategies. The first set relates to the differential role played by what students bring to and take from the learning encounter—the inputs and outcomes. Second, there are some strategies that are more effective than others—but their relative effectiveness depends on the phase in the model of learning in which they take place. Third is the distinction between surface learning, deep learning and the transfer of learning. The fourth set relates to the skills of transfer, the fifth to how the model of learning can be used to resolve some unexpected findings about the effectiveness of some strategies, and the sixth set discusses the question ‘what is learning?’.

The intertwining role of skill, will, and thrill

Our first set of claims relates to the differential role of what students bring to and take from the learning encounter. Rather than arguing that many factors contribute to achievement (an important but sometimes the only privileged outcome of learning), we are promoting the notion that the skill, will and thrill can intertwine during learning and that these three inputs are also important outcomes of learning—the aim is to enhance the will (e.g., the willingness to reinvest in more and deeper learning), the thrill (e.g., the emotions associated with successful learning, the curiosity and the willingness to explore what one does not know) and the skills (e.g., the content and the deeper understanding). The relation between the thrill, will and skill can vary depending on the student and the requirements of the task. Certainly, negative emotions, such as those induced by fear, anxiety, and stress can directly and negatively affect learning and memory. Such negative emotions block learning: ‘If the student is faced with sources of stress in an educational context which go beyond the positive challenge threshold—for instance, aggressive teachers, bullying students or incomprehensible learning materials whether books or computers—it triggers fear and cognitive function is negatively affected. 71 Our argument is that learning can lead to enhanced skills, dispositions, motivations and excitements that can be reinvested in learning, and can lead to students setting higher standards for their success criteria. When skill, will, and thrill overlap, this should be considered a bonus; developing each is a worthwhile outcome of schooling in its own right.

It is all in the timing

Our second set of claims is that while it is possible to nominate the top 10 learning strategies the more critical conclusion is that the optimal strategies depend on where in the learning cycle the student is located. This strategic skill in using the strategies at the right moment is akin to the message in the Kenny Rogers song—you need to ‘know when to hold ‘em, know when to fold ‘em’. For example, when starting a teaching sequence, it is most important to be concerned that students have confidence they can understand the lessons, see value in the lessons and are not overly anxious about their skills to be mastered. Providing them early on with an overview of what successful learning in the lessons will look like (knowing the success criteria) will help them reduce their anxiety, increase their motivation, and build both surface and deeper understandings.

To acquire surface learning, it is worthwhile knowing how to summarise, outline and relate the learning to prior achievement; and then to consolidate this learning by engaging in deliberate practice, rehearsing over time and learning how to seek and receive feedback to modify this effort. To acquire deep understanding requires the strategies of planning and evaluation and learning to monitor the use of one’s learning strategies; and then to consolidate deep understanding calls on the strategy of self-talk, self-evaluation and self-questioning and seeking help from peers. Such consolidation requires the learner to think aloud, learn the ‘language of thinking’, 72 know how to seek help, self-question and work through the consequences of the next steps in learning. To transfer learning to new situations involves knowing how to detect similarities and differences between the old and the new problem or situations.

We recommend that these strategies are developed by embedding them into the cycle of teaching rather than by running separate sessions, such as ‘how to learn’ or study skills courses. There is a disappointing history of educational programs aimed at teaching students how to learn. 30 , 73 , 74 Wiliam 75 made this case for why teaching these learning strategies (e.g., critical thinking) out of context is unlikely to develop a generic skill applicable to many subjects. He noted that in a ‘mathematics proof, critical thinking might involve ensuring that each step follows from the previous one (e.g., by checking that there has not been a division by zero). In reading a historical account, critical thinking might involve considering the author of the account, the potential biases and limitations that the author may be bringing to the account, and what other knowledge the reader has about the events being described. The important point here is that although there is some commonality between the processes in mathematics and history, they are not the same. Developing a capacity for critical thinking in history does not make one better at critical thinking in mathematics. For all of the apparent similarities, critical thinking in history and critical thinking in mathematics are different, and they are developed in different ways’. Many others have noted that metacognition is not knowledge-free but needs to be taught in the context of the individual subject areas. 76 , 77 Perkins 78 also noted that there is a certain art to infusing the teaching of thinking into content learning. Sometimes, ‘teachers think it is enough simply to establish a generally thoughtful atmosphere in a classroom, with regular expectations for thinking critically and creatively...teaching for know-how about learning to learn is a much more time-consuming enterprise than teaching for just learning the ideas... Building active know-how requires much more attention’.

Another aspect to consider is the difference, identified in the model, between being first exposed to learning and the consolidation of this learning. This distinction is far from novel. Shuell, 79 for example, distinguished between initial, intermediate, and final phases of learning. In the initial phase, the students can encounter a ‘large array of facts and pieces of information that are more-or-less isolated conceptually... there appears to be little more than a wasteland with few landmarks to guide the traveller on his or her journey towards understanding and mastery’. Students can use existing schema to make sense of this new information, or can be guided to have more appropriate schema (and thus experience early stages of concept learning and relation between ideas) otherwise the information may remain as isolated facts, or be linked erroneously to previous understandings. At the intermediate phase, the learner begins to see similarities and relationships among these seemingly conceptually isolated pieces of information. ‘The fog continues to lift but still has not burnt off completely’. During the final phase, the knowledge structure becomes well integrated and functions more autonomously, and the emphasis is more on performance or exhibiting the outcome of learning.

Horses for courses: matching strategies with phases

The third set of claims relates to the distinction between surface, deep, and transfer of learning. Although not a hard and fast set of demarcations, surface learning refers more to the content and underlying skills; deep learning to the relationships between, and extensions of, ideas; and transfer to the proficiency to apply learning to new problems and situations. During the surface learning phase, an aim is to assist students to overlearn certain ideas and thus reduce the needs of their working memory to work with these new facts when moving into the deeper understanding phase. Note, for example, that Marton et al. 80 made an important distinction between memorising without understanding first and called this rote memorisation (which has long term effect), and memorisation when you have understood and called this meaningful memorisation (which can be powerful). The evidence in the current study supports this distinction.

It is when students have much information, or many seemingly unrelated ideas, that the learning strategies for the deep phase are optimally invoked. This is when they should be asked to integrate ideas with previous schema or modify their previous schema to integrate new ideas and ways of thinking. The key to this process is first gaining ideas—a fact often missed by those advocating deeper thinking strategies when they try to teach these skills prior to developing sufficient knowledge within the content domain. The students need to first have ideas before they can relate them. The model does not propose discarding the teaching or learning skills that have been developed to learn surface knowing, but advocates the benefits of a more appropriate balance of surface and deeper strategies and skills that then lead to transfer. The correct balance of surface to deep learning depends on the demands of the task. It is likely that more emphasis on surface strategies is probably needed as students learn new ideas, moving to an emphasis on deeper strategies as they become more proficient.

Pause and reflect: detecting similarities and differences

The fourth set of claims relate to the skills of transfer, and how important it is to teach students to pause and detect the similarities and differences between previous tasks and the new one, before attempting to answer a new problem. Such transfer can be positive, such as when a learner accurately remembers a learning outcome reached in a certain situation and appropriately applies it in a new and similar situation, or negative, such as when a learner applies a strategy used successfully in one situation in a new situation where this strategy is not appropriate. Too many (particularly struggling) students over-rehearse a few learning strategies (e.g., copying and highlighting) and apply them in situations regardless of the demands of new tasks. Certainly, the fundamental skill for positive transfer is stopping before addressing the problem and asking about the differences and similarities of the new to any older task situation. This skill can be taught.

This ability to notice similarities and differences over content is quite different for novices and experts 81 , 82 and we do not simply learn from experience but we also learn to experience. 83 Preparation for future learning involves opportunities to try our hunches in different contexts, receive feedback, engage in productive failure and learn to revise our knowing based on feedback. The aim is to solve problems more efficiently, and also to ‘let go’ of previously acquired knowledge in light of more sophisticated understandings—and this can have emotional consequences: ‘Failure to change strategies in new situations has been described as the tyranny of success’. 84 It is not always productive for students to try the same thing that worked last time. Hence there may need to be an emphasis on knowledge-building rather than knowledge-telling, 85 and systematic inquiry based on theory-building and disconfirmation rather than simply following processes for how to find some result.

Why some strategies do not work

The fifth set of claims relate to how the model can be used to resolve some of the unexpected findings about the impact of various teaching methods. In Visible Learning , 36 it was noted that many programs that seem to lead to developing deeper processing have very low effect sizes (e.g., inquiry based methods, d =0.31; problem-based learning, d =0.15). For example, there have been 11 meta-analyses relating to problem-based learning based on 509 studies, leading to an average small effect ( d =0.15). It hardly seems necessary to run another problem-based program (particularly in first-year medicine, where four of the meta-analyses were completed) to know that the effects of problem-based learning on outcomes are small. The reason for this low effect seems to be related to using problem-based methods before attaining sufficient surface knowledge. When problem-based learning is used in later medical years, the effects seem to increase. Albanese and Mitchell 86 claimed that increased years of exposure to medical education increases the effect of problem-based learning. They argued that lack of experience (and lack of essential surface knowledge) leads the student to make more errors in their knowledge base, add irrelevant material to their explanations and engage in backward reasoning (from the unknown to the givens), whereas experts engaged in forward reasoning (also see references 87 , 88 ). Walker et al. 89 also noted that novice problem-based learning students tended to engage in far more backward-driven reasoning, which results in more errors during problem solving and may persist even after the educational intervention is complete. It is likely that problem-based learning works more successfully when students engage in forward reasoning and this depends on having sufficient content knowledge to make connections.

Deep understanding in problem-based learning requires a differentiated knowledge structure, 90 and this may need to be explicitly taught—as there is no assumption that students will see similarities and differences in contexts by themselves. There is a limit to what we can reasonably expect students to discover, and it may require teaching students to make predictions based on features that were told to them and that they may not notice on their own. Deliberate teaching of these surface features can offer a higher level of explanation that would be difficult or time consuming to discover. A higher level explanation is important because it provides a generative framework that can extend one understanding beyond the specific cases that have been analysed and experienced. On the other hand, the problems need not be too overly structured, as then students do not gain experience of searching out conceptual tools or homing in on particular cases of application. 78

Another example of the different requirements of surface and deep learning is the effect of asking students to explore errors and misconceptions during their learning. Using meta-analysis, Keith and Frese 91 found that the average effect of using these strategies when the outcome was surface learning was −0.15 and when the outcome was deep learning and far transfer to new problems, it was 0.80.

So: what is learning?

The sixth set of claims relate to the notion of ‘what is learning?’. The argument in this article is that learning is the outcome of the processes of moving from surface to deep to transfer. Only then will students be able to go beyond the information given to ‘figure things out’, which is one of the few untarnishable joys of life. 92 One of the greatest triumphs of learning is what Perkins 78 calls ‘knowing one’s way around’ a particular topic or ‘playing the whole game’ of history, mathematics, science or whatever. This is a function of knowing much and then using this knowledge in the exploration of relations and to make extensions to other ideas, and being able to know what to do when one does not know what to do (the act of transfer).

Concluding comments

Like all models, the one proposed in this article invites as many conjectures and directions for further research as it provide a basis for interpreting the evidence from the meta-synthesis. It helps make sense of much of the current literature but it is speculative in that it also makes some untested predictions. There is much solace in Popper's 93 claim that ‘Bold ideas, unjustified anticipations, and speculative thought, are our only means for interpreting nature: our only organon, our only instrument, for grasping her. And we must hazard them to win our prize. Those among us who are unwilling to expose their ideas to the hazard of refutation do not take part in the scientific game.’ Further research is needed, for example, to better understand the optimal order through the various phases; there may be circumstances where it may be beneficial to learn the deeper notions before developing the surface knowledge. It is highly likely that as one develops many ideas and even relates and extends them, these become ‘ideas’ and the cycle continues. 94 We know much, but we need to know much more, and in particular we need to know how these many learning strategies might be better presented in another competing model. Such testing of a bold model and making predictions from models is, according to Popper, how science progresses.

Further research is needed that asks whether the distinction between the acquisition and the consolidation of learning is a distinctive difference, a melding from one to the other or whether both can occur simultaneously. If there is a difference, then more research on ascertaining the best time to move from acquisition to consolidation would be informative. Similarly, there is no hard rule in the model of a sequence from surface to deep to transfer. In some ways, teaching the strategies of knowing what success looks like upfront implies an exposure to both surface and deep learning. Also, the many arguments (but surprisingly there is a lack of evidence) for the popular notions of flipped classrooms could be supported with more evidence of introducing the success criteria upfront to students. A typical flipped lesson starts with students accessing online video lectures or resources prior to in-class sessions so that students are prepared to participate in more interactive and higher-order activities such as problem solving, discussions and debates. 95 The most needed research concerns transfer—the variation theory of Marton, 48 the claims by Perkins 78 and others need more focused attention and the usual (and often unsubstantiated) claims that doing x will assist learning y should come back as a focus of learning sciences.

We are proposing that it is worthwhile to develop the skill, will and thrill of learning, and that there are many powerful strategies for learning. Students can be taught these strategies (declarative knowledge), how to use them (procedural knowledge), under what conditions it may be more or less useful to apply them (conditional knowledge) and how to evaluate them. It may be necessary to teach when best to use these strategies according the nature of the outcomes (surface and deep), according to the timing of learning (first acquiring and then consolidating learning) and to teach the skill of transferring learning to new situations. We need to think in terms of ‘surface to deep’ and not one alone; we need to think in terms of developing dispositions, motivations and achievement, and not one alone. This invites considering multiple outcomes from our schools. Singapore, 96 for example, is now committed to developing an educational system which will produce young people who have the moral courage to stand up for what is right; pursue a healthy lifestyle and have an appreciation of aesthetics; are proud to be Singaporeans; are resilient in the face of difficulty, innovative and enterprising; are purposeful in the pursuit of excellence; are able to collaborate across cultures; and can think critically and communicate persuasively. Academic achievement is but one desirable learning outcomes of many.

Another important message is that developing a few learning strategies may not be optimal. The failure to change strategies in new situations has been described as the tyranny of success; 84 and the current meta-synthesis suggests that choosing different strategies as one progresses through the learning cycle (from first exposure to embedding, from surface to deep to transfer) demands cognitive flexibility. It may not be the best option for students to use the same strategies that worked last time, as when the context is changed the old strategies may no longer work.

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Acknowledgements

The Science of Learning Research Centre is a Special Research Initiative of the Australian Research Council. Project Number SR120300015. We thank the following for critiquing earlier drafts of this article: Dan Willingham, Jason Lodge, Debra Masters, Rob Hester, Jared Horvath and Luke Rowe.

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Hattie, J., Donoghue, G. Learning strategies: a synthesis and conceptual model. npj Science Learn 1 , 16013 (2016). https://doi.org/10.1038/npjscilearn.2016.13

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DOI : https://doi.org/10.1038/npjscilearn.2016.13

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Effective Learning Behavior in Problem-Based Learning: a Scoping Review

Azril shahreez abdul ghani.

1 Department of Basic Medical Sciences, Kulliyah of Medicine, Bandar Indera Mahkota Campus, International Islamic University Malaysia, Kuantan, 25200 Pahang Malaysia

2 Department of Medical Education, School of Medical Sciences, Health Campus, Universiti Sains Malaysia, Kubang Kerian, Kota Bharu, 16150 Kelantan Malaysia

Ahmad Fuad Abdul Rahim

Muhamad saiful bahri yusoff, siti nurma hanim hadie.

3 Department of Anatomy, School of Medical Sciences, Health Campus, Universiti Sains Malaysia, Kubang Kerian, 16150 Kota Bharu, Kelantan Malaysia

Problem-based learning (PBL) emphasizes learning behavior that leads to critical thinking, problem-solving, communication, and collaborative skills in preparing students for a professional medical career. However, learning behavior that develops these skills has not been systematically described. This review aimed to unearth the elements of effective learning behavior in a PBL context, using the protocol by Arksey and O’Malley. The protocol identified the research question, selected relevant studies, charted and collected data, and collated, summarized, and reported results. We discovered three categories of elements—intrinsic empowerment, entrustment, and functional skills—proven effective in the achievement of learning outcomes in PBL.

Introduction

Problem-based learning (PBL) is an educational approach that utilizes the principles of collaborative learning in small groups, first introduced by McMaster Medical University [ 1 ]. The shift of the higher education curriculum from traditional, lecture-based approaches to an integrated, student-centered approach was triggered by concern over the content-driven nature of medical knowledge with minimal clinical application [ 2 ]. The PBL pedagogy uses a systematic approach, starting with an authentic, real-life problem scenario as a context in which learning is not separated from practice as students collaborate and learn [ 3 ]. The tutor acts as a facilitator who guides the students’ learning, while students are required to solve the problems by discussing them with group members [ 4 ]. The essential aspect of the PBL process is the ability of the students to recognize their current knowledge, determine the gaps in their knowledge and experience, and acquire new knowledge to bridge the gaps [ 5 ]. PBL is a holistic approach that gives students an active role in their learning.

Since its inception, PBL has been used in many undergraduate and postgraduate degree programs, such as medicine [ 6 , 7 ], nursing [ 8 ], social work education [ 9 ], law [ 10 ], architecture [ 11 ], economics [ 12 ], business [ 13 ], science [ 14 ], and engineering [ 15 ]. It has also been applied in elementary and secondary education [ 16 – 18 ]. Despite its many applications, its implementation is based on a single universal workflow framework that contains three elements: problem as the initiator for learning, tutor as a facilitator in the group versions, and group work as a stimulus for collaborative interaction [ 19 ]. However, there are various versions of PBL workflow, such as the seven-step technique based on the Maastricht “seven jumps” process. The tutor’s role is to ensure the achievement of learning objectives and to assess students’ performance [ 20 , 21 ].

The PBL process revolves around four types of learning principles: constructive, self-directed, collaborative, and contextual [ 19 ]. Through the constructive learning process, the students are encouraged to think about what is already known and integrate their prior knowledge with their new understanding. This process helps the student understand the content, form a new opinion, and acquire new knowledge [ 22 ]. The PBL process encourages students to become self-directed learners who plan, monitor, and evaluate their own learning, enabling them to become lifelong learners [ 23 ]. The contextualized collaborative learning process also promotes interaction among students, who share similar responsibilities to achieve common goals relevant to the learning context [ 24 ]. By exchanging ideas and providing feedback during the learning session, the students can attain a greater understanding of the subject matter [ 25 ].

Dolmans et al. [ 19 ] pointed out two issues related to the implementation of PBL: dominant facilitators and dysfunctional PBL groups. These problems inhibit students’ self-directed learning and reduce their satisfaction level with the PBL session. A case study by Eryilmaz [ 26 ] that evaluated engineering students’ and tutors’ experience of PBL discovered that PBL increased the students’ self-confidence and improved essential skills such as problem-solving, communications, critical thinking, and collaboration. Although most of the participants in the study found PBL satisfactory, many complained about the tutor’s poor guidance and lack of preparation. Additionally, it was noted that 64% of the first-year students were unable to adapt to the PBL system because they had been accustomed to conventional learning settings and that 43% of students were not adequately prepared for the sessions and thus were minimally involved in the discussion.

In a case study by Cónsul-giribet [ 27 ], newly graduated nursing professionals reported a lack of perceived theoretical basic science knowledge at the end of their program, despite learning through PBL. The nurses perceived that this lack of knowledge might affect their expertise, identity, and professional image.

Likewise, a study by McKendree [ 28 ] reported the outcomes of a workshop that explored the strengths and weaknesses of PBL in an allied health sciences curriculum in the UK. The workshop found that problems related to PBL were mainly caused by students, the majority of whom came from conventional educational backgrounds either during high school or their first degree. They felt anxious when they were involved in PBL, concerned about “not knowing when to stop” in exploring the learning needs. Apart from a lack of basic science knowledge, the knowledge acquired during PBL sessions remains unorganized [ 29 ]. Hence, tutors must guide students in overcoming this situation by instilling appropriate insights and essential skills for the achievement of the learning outcomes [ 30 ]. It was also evident that the combination of intention and motivation to learn and desirable learning behavior determined the quality of learning outcomes [ 31 , 32 ]. However, effective learning behaviors that help develop these skills have not been systematically described. Thus, this scoping review aimed to unearth the elements of effective learning behavior in the PBL context.

Scoping Review Protocol

This scoping review was performed using a protocol by Arksey and O’Malley [ 33 ]. The protocol comprises five phases: (i) identification of research questions, (ii) identification of relevant articles, (iii) selection of relevant studies, (iv) data collection and charting, and (v) collating, summarizing, and reporting the results.

Identification of Research Questions

This scoping review was designed to unearth the elements of effective learning behavior that can be generated from learning through PBL instruction. The review aimed to answer one research question: “What are the effective learning behavior elements related to PBL?” For the purpose of the review, an operational definition of effective learning behavior was constructed, whereby it was defined as any learning behavior that is related to PBL instruction and has been shown to successfully attain the desired learning outcomes (i.e., cognitive, skill, or affective)—either quantitatively or qualitatively—in any intervention conducted in higher education institutions.

The positive outcome variables include student viewpoint or perception, student learning experience and performance, lecturer viewpoint and expert judgment, and other indirect variables that may be important indicators of successful PBL learning (i.e., attendance to PBL session, participation in PBL activity, number of interactions in PBL activity, and improvement in communication skills in PBL).

Identification of Relevant Articles

An extensive literature search was conducted on articles published in English between 2015 and 2019. Three databases—Google Scholar, Scopus, and PubMed—were used for the literature search. Seven search terms with the Boolean combination were used, whereby the keywords were identified from the Medical Subject Headings (MeSH) and Education Resources Information Center (ERIC) databases. The search terms were tested and refined with multiple test searches. The final search terms with the Boolean operation were as follows: “problem-based learning” AND (“learning behavior” OR “learning behaviour”) AND (student OR “medical students” OR undergraduate OR “medical education”).

Selection of Relevant Articles

The articles from the three databases were exported manually into Microsoft Excel. The duplicates were removed, and the remaining articles were reviewed based on the inclusion and exclusion criteria. These criteria were tested on titles and abstracts to ensure their robustness in capturing the articles related to learning behavior in PBL. The shortlisted articles were reviewed by two independent researchers, and a consensus was reached either to accept or reject each article based on the set criteria. When a disagreement occurred between the two reviewers, the particular article was re-evaluated independently by the third and fourth researchers (M.S.B.Y and A.F.A.R), who have vast experience in conducting qualitative research. The sets of criteria for selecting abstracts and final articles were developed. The inclusion and exclusion criteria are listed in Table ​ Table1 1 .

Inclusion and exclusion criteria

Data Charting

The selected final articles were reviewed, and several important data were extracted to provide an objective summary of the review. The extracted data were charted in a table, including the (i) title of the article, (ii) author(s), (iii) year of publication, (iv) aim or purpose of the study, (v) study design and method, (iv) intervention performed, and (v) study population and sample size.

Collating, Summarizing, and Reporting the Results

A content analysis was performed to identify the elements of effective learning behaviors in the literature by A.S.A.G and S.N.H.H, who have experience in conducting qualitative studies. The initial step of content analysis was to read the selected articles thoroughly to gain a general understanding of the articles and extract the elements of learning behavior which are available in the articles. Next, the elements of learning behavior that fulfil the inclusion criteria were extracted. The selected elements that were related to each other through their content or context were grouped into subtheme categories. Subsequently, the combinations of several subthemes expressing similar underlying meanings were grouped into themes. Each of the themes and subthemes was given a name, which was operationally defined based on the underlying elements. The selected themes and subthemes were presented to the independent researchers in the team (M.S.B.Y and A.F.A.R), and a consensus was reached either to accept or reformulate each of the themes and subthemes. The flow of the scoping review methods for this study is illustrated in Fig.  1 .

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The flow of literature search and article selection

Literature Search

Based on the keyword search, 1750 articles were obtained. Duplicate articles that were not original articles found in different databases and resources were removed. Based on the inclusion and exclusion criteria of title selection, the eligibility of 1750 abstracts was evaluated. The articles that did not fulfil the criteria were removed, leaving 328 articles for abstract screening. A total of 284 articles were screened according to the eligibility criteria for abstract selection. Based on these criteria, 284 articles were selected and screened according to the eligibility criteria for full article selection. Fourteen articles were selected for the final review. The information about these articles is summarized in Table ​ Table2 2 .

Studies characteristics

Study Characteristics

The final 14 articles were published between 2015 and 2019. The majority of the studies were conducted in Western Asian countries ( n  = 4), followed by China ( n  = 3), European countries ( n  = 2), Thailand ( n  = 2), Indonesia ( n  = 1), Singapore ( n  = 1), and South Africa ( n  = 1). Apart from traditional PBL, some studies incorporated other pedagogic modalities into their PBL sessions, such as online learning, blended learning, and gamification. The majority of the studies targeted a single-profession learner group, and one study was performed on mixed interprofessional health education learners.

Results of Thematic Analysis

The thematic analysis yielded three main themes of effective learning behavior: intrinsic empowerment, entrustment, and functional skills. Intrinsic empowerment overlies four proposed subthemes: proactivity, organization, diligence, and resourcefulness. For entrustment, there were four underlying subthemes: students as assessors, students as teachers, feedback-giving, and feedback-receiving. The functional skills theme contains four subthemes: time management, digital proficiency, data management, and collaboration.

Theme 1: Intrinsic Empowerment

Intrinsic empowerment enforces student learning behavior that can facilitate the achievement of learning outcomes. By empowering the development of these behaviors, students can become lifelong learners [ 34 ]. The first element of intrinsic empowerment is proactive behavior. In PBL, the students must be proactive in analyzing problems [ 35 , 36 ] and their learning needs [ 35 , 37 ], and this can be done by integrating prior knowledge and previous experience through a brainstorming session [ 35 , 38 ]. The students must be proactive in seeking guidance to ensure they stay focused and confident [ 39 , 40 ]. Finding ways to integrate content from different disciplines [ 35 , 41 ], formulate new explanations based on known facts [ 34 , 35 , 41 ], and incorporate hands-on activity [ 35 , 39 , 42 ] during a PBL session are also proactive behaviors.

The second element identified is “being organized” which reflects the ability of students to systematically manage their roles [ 43 ], ideas, and learning needs [ 34 ]. The students also need to understand the task for each learning role in PBL, such as chairperson or leader, scribe, recorder, and reflector. This role needs to be assigned appropriately to ensure that all members take part in the discussion [ 43 ]. Similarly, when discussing ideas or learning needs, the students need to follow the steps in the PBL process and organize and prioritize the information to ensure that the issues are discussed systematically and all aspects of the problems are covered accordingly [ 34 , 37 ]. This team organization and systematic thought process is an effective way for students to focus, plan, and finalize their learning tasks.

The third element of intrinsic empowerment is “being diligent.” Students must consistently conduct self-revision [ 40 ] and keep track of their learning plan to ensure the achievement of their learning goal [ 4 , 40 ]. The students must also be responsible for completing any given task and ensuring good understanding prior to their presentation [ 40 ]. Appropriate actions need to be undertaken to find solutions to unsolved problems [ 40 , 44 ]. This effort will help them think critically and apply their knowledge for problem-solving.

The fourth element identified is “being resourceful.” Students should be able to acquire knowledge from different resources, which include external resources (i.e., lecture notes, textbooks, journal articles, audiovisual instructions, the Internet) [ 38 , 40 , 45 ] and internal resources (i.e., students’ prior knowledge or experience) [ 35 , 39 ]. The resources must be evidence-based, and thus should be carefully selected by evaluating their cross-references and appraising them critically [ 37 ]. Students should also be able to understand and summarize the learned materials and explain them using their own words [ 4 , 34 ]. The subthemes of the intrinsic empowerment theme are summarized in Table ​ Table3 3 .

 Intrinsic empowerment subtheme with the learning behavior elements

Theme 2: Entrustment

Entrustment emphasizes the various roles of students in PBL that can promote effective learning. The first entrusted role identified is “student as an assessor.” This means that students evaluate their own performance in PBL [ 46 ]. The evaluation of their own performance must be based on the achievement of the learning outcomes and reflect actual understanding of the content as well as the ability to apply the learned information in problem-solving [ 46 ].

The second element identified in this review is “student as a teacher.” To ensure successful peer teaching in PBL, students need to comprehensively understand the content of the learning materials and summarize the content in an organized manner. The students should be able to explain the gist of the discussed information using their own words [ 4 , 34 ] and utilize teaching methods to cater to differences in learning styles (i.e., visual, auditory, and kinesthetic) [ 41 ]. These strategies help capture their group members’ attention and evoke interactive discussions among them.

The third element of entrustment is to “give feedback.” Students should try giving constructive feedback on individual and group performance in PBL. Feedback on individual performance must reflect the quality of the content and task presented in the PBL. Feedback on group performance should reflect the ways in which the group members communicate and complete the group task [ 47 ]. To ensure continuous constructive feedback, students should be able to generate feedback questions beforehand and immediately deliver them during the PBL sessions [ 44 , 47 ]. In addition, the feedback must include specific measures for improvement to help their peers to take appropriate action for the future [ 47 ].

The fourth element of entrustment is “receive feedback.” Students should listen carefully to the feedback given and ask questions to clarify the feedback [ 47 ]. They need to be attentive and learn to deal with negative feedback [ 47 ]. Also, if the student does not receive feedback, they should request it either from peers or teachers and ask specific questions, such as what aspects to improve and how to improve [ 47 ]. The data on the subthemes of the entrustment theme are summarized in Table ​ Table4 4 .

Entrustment subtheme with the learning behavior elements

Theme 3: Functional Skills

Functional skills refer to essential skills that can help students learn independently and competently. The first element identified is time management skills. In PBL, students must know how to prioritize learning tasks according to the needs and urgency of the tasks [ 40 ]. To ensure that students can self-pace their learning, a deadline should be set for each learning task within a manageable and achievable learning schedule [ 40 ].

Furthermore, students should have digital proficiency, the ability to utilize digital devices to support learning [ 38 , 40 , 44 ]. The student needs to know how to operate basic software (e.g., Words and PowerPoints) and the basic digital tools (i.e., social media, cloud storage, simulation, and online community learning platforms) to support their learning [ 39 , 40 ]. These skills are important for peer learning activities, which may require information sharing, information retrieval, online peer discussion, and online peer feedback [ 38 , 44 ].

The third functional skill identified is data management, the ability to collect key information in the PBL trigger and analyze that information to support the solution in a problem-solving activity [ 39 ]. Students need to work either individually or in a group to collect the key information from a different trigger or case format such as text lines, an interview, an investigation, or statistical results [ 39 ]. Subsequently, students also need to analyze the information and draw conclusions based on their analysis [ 39 ].

The fourth element of functional skill is collaboration. Students need to participate equally in the PBL discussion [ 41 , 46 ]. Through discussion, confusion and queries can be addressed and resolved by listening, respecting others’ viewpoints, and responding professionally [ 35 , 39 , 43 , 44 ]. In addition, the students need to learn from each other and reflect on their performance [ 48 ]. Table ​ Table5 5 summarizes the data on the subthemes of the functional skills theme.

Functional skills subtheme with the learning behavior elements

This scoping review outlines three themes of effective learning behavior elements in the PBL context: intrinsic empowerment, entrustment, and functional skills. Hence, it is evident from this review that successful PBL instruction demands students’ commitment to empower themselves with value-driven behaviors, skills, and roles.

In this review, intrinsic empowerment is viewed as enforcement of students’ internal strength in performing positive learning behaviors related to PBL. This theme requires the student to proactively engage in the learning process, organize their learning activities systematically, persevere in learning, and be intelligently resourceful. One of the elements of intrinsic empowerment is the identification and analysis of problems related to complex scenarios. This element is aligned with a study by Meyer [ 49 ], who observed students’ engagement in problem identification and clarification prior to problem-solving activities in a PBL session related to multiple engineering design. Rubenstein and colleagues [ 50 ] discovered in a semi-structured interview the importance of undergoing a problem identification process before proposing a solution during learning. It was reported that the problem identification process in PBL may enhance the attainment of learning outcomes, specifically in the domain of concept understanding [ 51 ].

The ability of the students to acquire and manage learning resources is essential for building their understanding of the learned materials and enriching discussion among team members during PBL. This is aligned with a study by Jeong and Hmelo-Silver [ 52 ], who studied the use of learning resources by students in PBL. The study concluded that in a resource-rich environment, the students need to learn how to access and understand the resources to ensure effective learning. Secondly, they need to process the content of the resources, integrate various resources, and apply them in problem-solving activities. Finally, they need to use the resources in collaborative learning activities, such as sharing and relating to peer resources.

Wong [ 53 ] documented that excellent students spent considerably more time managing academic resources than low achievers. The ability of the student to identify and utilize their internal learning resources, such as prior knowledge and experience, is also important. A study by Lee et al. [ 54 ] has shown that participants with high domain-specific prior knowledge displayed a more systematic approach and high accuracy in visual and motor reactions in solving problems compared to novice learners.

During the discussion phase in PBL, organizing ideas—e.g., arranging relevant information gathered from the learning resources into relevant categories—is essential for communicating the idea clearly [ 34 ]. This finding is in line with a typology study conducted by Larue [ 55 ] on second-year nursing students’ learning strategies during a group discussion. The study discovered that although the content presented by the student is adequate, they unable to make further progress in the group discussion until they are instructed by the tutor on how to organize the information given into a category [ 55 ].

Hence, the empowerment of student intrinsic behavior may enhance students’ learning in PBL by allowing them to make a decision in their learning objectives and instilling confidence in them to achieve goals. A study conducted by Kirk et al. [ 56 ] proved that highly empowered students obtain better grades, increase learning participation, and target higher educational aspirations.

Entrustment is the learning role given to students to be engaging and identify gaps in their learning. This theme requires the student to engage in self-assessment, prepare to teach others, give constructive feedback, and value the feedback received. One of the elements of entrustment is the ability to self-assess. In a study conducted by Mohd et al. [ 57 ] looking at the factors in PBL that can strengthen the capability of IT students, they discovered that one of the critical factors that contribute to these skills is the ability of the student to perform self-assessment in PBL. As mentioned by Daud, Kassim, and Daud [ 58 ], the self-assessment may be more reliable if the assessment is performed based on the objectives set beforehand and if the criteria of the assessment are understood by the learner. This is important to avoid the fact that the result of the self-assessment is influenced by the students’ perception of themselves rather than reflecting their true performance. However, having an assessment based on the learning objective only focuses on the immediate learning requirements in the PBL. To foster lifelong learning skills, it should also be balanced with the long-term focus of assessment, such as utilizing the assessment to foster the application of knowledge in solving real-life situations. This is aligned with the review by Boud and Falchikov [ 59 ] suggesting that students need to become assessors within the concept of participation in practice, that is, the kind that is within the context of real life and work.

The second subtheme of entrustment is “students as a teacher” in PBL. In our review, the student needs to be well prepared with the teaching materials. A cross-sectional study conducted by Charoensakulchai and colleagues discovered that student preparation is considered among the important factors in PBL success, alongside other factors such as “objective and contents,” “student assessment,” and “attitude towards group work” [ 60 ]. This is also aligned with a study conducted by Sukrajh [ 61 ] using focus group discussion on fifth-year medical students to explore their perception of preparedness before conducting peer teaching activity. In this study, the student in the focus group expressed that the preparation made them more confident in teaching others because preparing stimulated them to activate and revise prior knowledge, discover their knowledge gaps, construct new knowledge, reflect on their learning, improve their memory, inspire them to search several resources, and motivate them to learn the topics.

The next element of “student as a teacher” is using various learning styles to teach other members in the group. A study conducted by Almomani [ 62 ] showed that the most preferred learning pattern by the high school student is the visual pattern, followed by auditory pattern and then kinesthetic. However, in the university setting, Hamdani [ 63 ] discovered that students prefer a combination of the three learning styles. Anbarasi [ 64 ] also explained that incorporating teaching methods based on the student’s preferred learning style further promotes active learning among the students and significantly improved the long-term retrieval of knowledge. However, among the three learning styles group, he discovered that the kinesthetic group with the kinesthetic teaching method showed a significantly higher post-test score compared to the traditional group with the didactic teaching method, and he concluded that this is because of the involvement of more active learning activity in the kinesthetic group.

The ability of students to give constructive feedback on individual tasks is an important element in promoting student contribution in PBL because feedback from peers or teachers is needed to reassure themselves that they are on the right track in the learning process. Kamp et al. [ 65 ] performed a study on the effectiveness of midterm peer feedback on student individual cognitive, collaborative, and motivational contributions in PBL. The experimental group that received midterm peer feedback combined with goal-setting with face-to-face discussion showed an increased amount of individual contributions in PBL. Another element of effective feedback is that the feedback is given immediately after the observed behavior. Parikh and colleagues survey student feedback in PBL environments among 103 final-year medical students in five Ontario schools, including the University of Toronto, McMaster University, Queens University, the University of Ottawa, and the University of Western Ontario. They discovered that there was a dramatic difference between McMaster University and other universities in the immediacy of feedback they practiced. Seventy percent of students at McMaster reported receiving immediate feedback in PBL, compared to less than 40 percent of students from the other universities, in which most of them received feedback within one week or several weeks after the PBL had been conducted [ 66 ]. Another study, conducted among students of the International Medical University of Kuala Lumpur examining the student expectation on feedback, discovered that immediate feedback is effective if the feedback is in written form, simple but focused on the area of improvement, and delivered by a content expert. If the feedback is delivered by a content non-expert and using a model answer, it must be supplemented with teacher dialogue sessions to clarify the feedback received [ 67 ].

Requesting feedback from peers and teachers is an important element of the PBL learning environment, enabling students to discover their learning gaps and ways to fill them. This is aligned with a study conducted by de Jong and colleagues [ 68 ], who discovered that high-performing students are more motivated to seek feedback than low-performing students. The main reason for this is because high-performing students seek feedback as a tool to learn from, whereas low-performing students do so as an academic requirement. This resulted in high-performing students collecting more feedback. A study by Bose and Gijselaers [ 69 ] examined the factors that promote feedback-seeking behavior in medical residency. They discovered that feedback-seeking behavior can be promoted by providing residents with high-quality feedback to motivate them to ask for feedback for improvement.

By assigning an active role to students as teachers, assessors, and feedback providers, teachers give them the ownership and responsibility to craft their learning. The learner will then learn the skills to monitor and reflect on their learning to achieve academic success. Furthermore, an active role encourages students to be evaluative experts in their own learning, and promoting deep learning [ 70 ].

Functional skills refer to essential abilities for competently performing a task in PBL. This theme requires the student to organize and plan time for specific learning tasks, be digitally literate, use data effectively to support problem-solving, and work together efficiently to achieve agreed objectives. One of the elements in this theme is to have a schedule of learning tasks with deadlines. In a study conducted by Tadjer and colleagues [ 71 ], they discovered that setting deadlines with a restricted time period in a group activity improved students’ cognitive abilities and soft skills. Although the deadline may initially cause anxiety, coping with it encourages students to become more creative and energetic in performing various learning strategies [ 72 , 73 ]. Ballard et al. [ 74 ] reported that students tend to work harder to complete learning tasks if they face multiple deadlines.

The students also need to be digitally literate—i.e., able to demonstrate the use of technological devices and tools in PBL. Taradi et al. [ 75 ] discovered that incorporating technology in learning—blending web technology with PBL—removes time and place barriers in the creation of a collaborative environment. It was found that students who participated in web discussions achieved a significantly higher mean grade on a physiology final examination than those who used traditional methods. Also, the incorporation of an online platform in PBL can facilitate students to develop investigation and inquiry skills with high-level cognitive thought processes, which is crucial to successful problem-solving [ 76 ].

In PBL, students need to work collaboratively with their peers to solve problems. A study by Hidayati et al. [ 77 ] demonstrated that effective collaborative skills improve cognitive learning outcomes and problem-solving ability among students who undergo PBL integrated with digital mind maps. To ensure successful collaborative learning in PBL, professional communication among students is pertinent. Research by Zheng and Huang [ 78 ] has proven that co-regulation (i.e., warm and responsive communication that provides support to peers) improved collaborative effort and group performance among undergraduate and master’s students majoring in education and psychology. This is also in line with a study by Maraj and colleagues [ 79 ], which showed the strong team interaction within the PBL group leads to a high level of team efficacy and academic self-efficacy. Moreover, strengthening communication competence, such as by developing negotiation skills among partners during discussion sessions, improves student scores [ 80 ].

PBL also includes opportunities for students to learn from each other (i.e., peer learning). A study by Maraj et al. [ 79 ] discovered that the majority of the students in their study perceived improvement in their understanding of the learned subject when they learned from each other. Another study by Lyonga [ 81 ] documented the successful formation of cohesive group learning, where students could express and share their ideas with their friends and help each other. It was suggested that each student should be paired with a more knowledgeable student who has mastered certain learning components to promote purposeful structured learning within the group.

From this scoping review, it is clear that functional skills equip the students with abilities and knowledge needed for successful PBL. Studies have shown that strong time management skills, digital literacy, data management, and collaborative skills lead to positive academic achievement [ 77 , 82 , 83 ].

Limitation of the Study

This scoping review is aimed to capture the recent effective learning behavior in problem-based learning; therefore, the literature before 2015 was not included. Without denying the importance of publication before 2015, we are relying on Okoli and Schabram [ 84 ] who highlighted the impossibility of retrieving all the published articles when conducting a literature search. Based on this ground, we decided to focus on the time frame between 2015 and 2019, which is aligned with the concepts of study maturity (i.e., the more mature the field, the higher the published articles and therefore more topics were investigated) by Kraus et al. [ 85 ]. In fact, it was noted that within this time frame, a significant number of articles have been found as relevant to PBL with the recent discovery of effective learning behavior. Nevertheless, our time frame did not include the timing of the coronavirus disease 19 (COVID-19) pandemic outbreak, which began at the end of 2019. Hence, we might miss some important elements of learning behavior that are required for the successful implementation of PBL during the COVID-19 pandemic.

Surprisingly, the results obtained from this study are also applicable for the PBL sessions administration during the COVID-19 pandemic situation as one of the functional skills identified is digital proficiency. This skill is indeed important for the successful implementation of online PBL session.

This review identified the essential learning behaviors required for effective PBL in higher education and clustered them into three main themes: (i) intrinsic empowerment, (ii) entrustment, and (iii) functional skills. These learning behaviors must coexist to ensure the achievement of desired learning outcomes. In fact, the findings of this study indicated two important implications for future practice. Firstly, the identified learning behaviors can be incorporated as functional elements in the PBL framework and implementation. Secondly, the learning behaviors change and adaption can be considered to be a new domain of formative assessment related to PBL. It is noteworthy to highlight that these learning behaviors could help in fostering the development of lifelong skills for future workplace challenges. Nevertheless, considerably more work should be carried out to design a solid guideline on how to systematically adopt the learning behaviors in PBL sessions, especially during this COVID-19 pandemic situation.

This study was supported by Postgraduate Incentive Grant-PhD (GIPS-PhD, grant number: 311/PPSP/4404803).

Declarations

The study has received an ethical approval from the Human Research Ethics Committee of Universiti Sains Malaysia.

No informed consent required for the scoping review.

The authors declare no competing interests.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Module 13: Complementary Cognitive Processes – Learning Concepts

Module Overview

In our final module in the book, we will tackle what seems like a simple topic but is quite complex. Though the module is entitled Learning Concepts, we will discuss several cognitive processes related to the learning of concepts (and other elements of cognitions) and what we do with them to include problem-solving and reasoning and end with a discussion of intelligence. Consider that intelligence reflects what we have learned, whether book knowledge, how to build a kitchen table, a dance routine, language (discussed in Module 12), how to be a better spouse, how to play the guitar, or how we learn best (self-awareness). To get us going though, we will focus on one theory of how cognition develops throughout the life span. We will end with the topic of impediments to learning in the form of intellectual and learning disabilities.

Module Outline

13.1. Piaget’s Theory of Cognitive Development

13.2. the elements of cognition, 13.3. problem-solving: when we seek solutions, 13.4. reasoning: making good decisions, and learning from them.

  • 13.5. Intelligence — Putting Our Learning to Good Use

13.6. Learning Disabilities

Module Learning Outcomes

  • Describe the contributions of Jean Piaget to our understanding of cognitive development across the life span.
  • List and describe the elements of cognition and clarify their relationship to learning.
  • Describe how the complimentary cognitive process of problem-solving relates to learning.
  • Describe how the complimentary cognitive process of reasoning relates to learning.
  • Describe how intelligence relates to learning.
  • Outline intellectual and learning disabilities that serve as an impediment to learning.

Section Learning Objectives

  • Define schemas.
  • Describe how our schemas change due to direct experience with the environment.
  • Describe Piaget’s four stages of cognitive development.

13.1.1. General Concepts

Swiss psychologist, Jean Piaget (1896-1980), proposed a stage theory of how cognitive development proceeds. Before we get into it, it is important to explain a few key concepts he proposed. First, schemas are organized ways of making sense of experience. We have a schema for ‘dog’ which includes the ideas of four legs, a tail, and being furry. Piaget said that these schemas change due to direct experience with our environment; a process he called adaptation. This change occurs in one of two ways. First, assimilation is when new information is made to fit into existing schemas. Notice the word similar within assimilation. We interpret the world in terms of our current schemas and understand anything novel similar to this existing way of understanding experience. Second, we could use the process of accommodation . Simply, when novel information is obtained, we could update an existing schema or create a brand new one. Let’s say a child meets a cat for the first time. We would expect them to call the animal a dog. Why is that? The cat has four legs, a tail, and is furry. But cats and dogs are not the same and have one major difference — cats say ‘meow’ and dogs say ‘woof.’ So the child will update his/her schema for ‘dog’ to now include woof and creates a new schema for ‘cat’ which includes four legs, tail, furry, and meow.

Piaget’s theory consists of four main stages — sensorimotor, preoperational, concrete operations, and formal operations. We will cover each as they relate to how we learn, and update what we learn about our world.

13.1.2. Sensorimotor Stage

The sensorimotor stage is when infants focus on developing sensory abilities and learn to get around in their environment. You might say they think with their bodies and this stage lasts from birth to age 2. Have you ever noticed how young babies take genuine delight in putting everything in their mouths, but to the horror of their parents? This is evidence of the sensorimotor stage and thinking consists of coordinating sensory information with the movement of the body.

The sensorimotor stage has six substages. Occurring during the first month, the first substage focuses on schemas the infant is born with or as we called them in Module 3, reflexes . These schemas are beginning to be changed via accommodation. The second stage is called primary circular reactions by Piaget and lasts to about 4 months of age. The child practices these basic schemas constantly and even shows the first signs of coordinating schemas from different sensory systems. The third stage is called secondary circular reactions and involves trial-and-error learning and attempts to make events happening outside their body occur again. It occurs from 4-8 months.

Substage four, occurring from 8-12 months, is called coordination of secondary schemas and involves the child trying to get what they want and involves the combination of schemas to do so. This leads to tertiary circular reactions lasting from 12-18 months and is when the child begins experimenting or finding new ways of exploring their world and manipulating objects. Finally, mental representation lasts up to 24 months and involves the use of symbols to represent objects. The child may use a block to represent a cell phone and have a conversation much like their father does. This involves imitation, though the behavior does not have to occur in the presence of the model which recall is deferred imitation . The child may use the block as a cell phone in the middle of the day when the father is at work, remembering what they saw the night before.

Piaget also said that during the sensorimotor stage infants acquire object permanence or knowing that an object continues to exist even though we cannot see it. During the first few months it is basically “out of sight, out of mind” and around 2 months of age or substage 2, infants demonstrate a rudimentary understanding of an object’s permanency. The skill really shows signs of developing by 6 months of age or substage 3 and continues to grow after this, particularly up to about 12 months or substage 4.

13.1.3. Preoperational Stage

Piaget’s stage of cognitive development prevalent from about age 2-7 is called the preoperational stage and is characterized by acquisition of the symbolic function. There is less dependence on sensorimotor activity to learn about the world and mental reasoning emerges. Piaget said children at this stage show centration or the tendency to focus only on one aspect of a situation at the exclusion of others. Related to this, Piaget believed that children could not take another person’s point of view because they see the world only from their frame of reference, which he called egocentrism (Piaget, 1954). Children also show animistic thinking or assigning lifelike qualities to inanimate objects and have trouble with reversibility or reversing the order of operations such as they understand that 3 times 5 equals 15 but do not realize that 15 divided by 5 equals 3.

Preoperational children have also not developed conservation or understanding that an object is fundamentally the same despite changing its properties. For instance, if two glasses are filled with the same amount of liquid and children confirm they are the same, and we take one glass and pour it into a flat container which stands much lower than the glass, children will choose the glass if asked which one they want. When asked why they say that the glass has more liquid than the container.

13.1.4. Concrete Operations Stage

Piaget’s third stage of cognitive development is concrete operations. Children now understand conservation, reversibility, and cause and effect but their thinking is still grounded in concrete experiences and concepts. They can now decenter or take multiple aspects of a situation into account due to them being less egocentric.

13.1.5. Formal Operations Stage

Piaget’s fourth and final stage of cognitive development is formal operations which begins in adolescence and lasts into adulthood. Teens become capable of abstract thinking and understand that ideas can be compared and classified, just as objects can. They search systematically for answers to questions/problems that they experience. Piaget said there are two major developments at this time. First, propositional thought is when teens gain the ability to examine the logic of verbal statements without referring to real-world situations. This leads to many debates with their parents over the morality of rules and curfews. Second, hypothetico-deductive reasoning is the use of the scientific method to test theories with hypotheses. It begins with a general theory of all possible factors that could affect the outcome and from them, deduces specific hypotheses about what may happen. These hypotheses are then tested in an orderly fashion to see which ones hold up in the real world.

  • Define cognition.
  • Describe the four main elements of cognition.

13.2.1. What is Cognition?

Cognition concerns thinking and includes such processes as attention, learning, memory, language, reasoning, decision making, problem-solving, and learning. It consists of four main elements — concepts, schemas, propositions, and images.

13.2.2. Concepts

Concepts are mental categories of objects, ideas, abstractions, events, relations, or activities that have common properties and are shared by all members of the category.

The concept of “textbook” includes having a table of contents, preface, chapters with summaries at the end of each, a glossary, index, and references. Concepts summarize information making it manageable and allow us to make comparisons. If we were asked which was heavier, a feather or a brick, we would be able to decide easily based on our concept of each object. Concepts can take two forms — formal and natural.

Formal concepts are more rigid and defined for us as in the case of a square. All squares have four equal sides and four right angles. Natural concepts have only a typical set of characteristics. An example is the natural concept of bird and the characteristic of being able to fly. An exception to this is the penguin which has wings but cannot fly as we typically think of flying. They instead “fly” underwater at speeds of up to 15 to 25 miles per hour but like other birds, lay eggs and raise their chicks on land.

When trying to determine if something belongs in a natural concept, we need to compare it against a member that shares most of the characteristic features. This member is called a prototype. In our example, a penguin was found to be a bird, but maybe not the best example since it does not fly in the typical sense. Instead, a prototypical bird would be a pigeon or a woodpecker and a person would not have trouble deciding quickly if it was one.

13.2.3. Propositions

Propositions are units of meaning that are composed of concepts and express a relationship between the concepts. They express a unitary or single idea and can express nearly any type of knowledge. Let’s say we consider our friend, John, to be a good friend. This would be an example of a proposition. What if he spoke some gossip about another friend and so we had to resolve the cognitive dissonance this event created in relation to our previously held belief or proposition. We want to believe it is true and Chris is a good friend, but we have evidence to the contrary which creates tension.

13.2.4. Schemas

Propositions are linked together in a network of associations, knowledge, beliefs, and expectations called schemas. A schema is an organized way of making sense of experience.

13.2.4.1. Types of schemas. We have several types of schemas that we use to assign meaning to our world. First, there are role schemas , which relate to how people carrying out certain roles or jobs are to act. For instance, what it the role schema you have for someone working in your Human Resources office at work? What about the cashier at your local grocery store?

Another schema we have is called the person schema and relates to certain types of people such as firefighters, geeks, or jocks. For each of these people, we have specific beliefs and expectations about what their personality is like and how they are to behave in various situations. What traits do you believe cheerleaders hold?

The final schema is called an event schema or script . This type of schema tells us what is to occur in certain situations such as at a party or in a chemistry lab. The parking garage I use daily requires me to swipe my card as I enter. Now the garage houses more than just those with my special permit. It is used as a public parking lot too. Recently, the gate as you exit has been broken and so left up. Usually, when I leave I would swipe my card again, thereby causing the gate to go up. What I have to do when entering and exiting the lot is usually pretty clear. Since the gate is just up now, I have been confused about what to do when I get to the pay station. I have been trying to swipe my card again but really, it is not needed. The gate is up already. I finally asked what to do and the parking attendant told me that those with parking permits can just pass through. Until this point, I was afraid to just go through, even though I have an orange permit sticker on the bottom left of my windshield. I was not sure if the university would consider my behavior to be trying to skip payment and send the police after me. The broken gate has left my event schema in turmoil. Hopefully, it is fixed soon. That is the gate, not my event schema. I guess you could say by fixing the gate they restore my event schema too.

Let’s put them all three schemas together. Imagine you are at a football game for your favorite team, whether high school, college, or professional. Who are some of the people there? Fans, coaches, players, referees, announcers, cheerleaders, and medical staff are all present. We expect the fans to be rowdy and supportive of the team by doing the wave or cheering. We expect the head coach to make good decisions and to challenge poor decisions by the referees. To that end, we expect the referees to be fair, impartial, and accurate in the judgments they make. We would not be surprised if they threw a flag or blew a whistle. Cheerleaders should be peppy, cheerful, and do all types of gymnastics on the field and wave pom poms, etc… These are the main people involved in the football game. In terms of roles, the head coach fulfills the role of leader of the team along with the Quarterback. The role of promoting team spirit and energizing the crowd goes to the cheerleaders and maybe some key players on the field. The medical staff is there to diagnose and treat injuries as they occur and so their role is to keep everyone safe. Finally, what do we do as a fan when we attend a football game? We have to enter the stadium and likely go through a search of our bags and present our ticket. We walk to our assigned seat. Though we cheer our team on, we need to be respectful of those around us such as not yelling obscenities if children are nearby. We also are expected to participate in the wave and sing the team’s fight song, etc…. This is the event schema that dictates our behavior.

13.2.4.2. Benefits of schemas. It should not be surprising to learn that schemas make cognitive processing move quicker . But they also complete incomplete pictures in terms of what we know about someone. Though we may not know Johnny personally, placing him in the schema football player helps us to fill in these blanks about what his personality is like and how he might behave. Using our schema for football player we can now predict what a future interaction with Johnny might involve. Let’s say he is assigned to be our lab partner in chemistry. We use our schema to make a quick assessment if the experience of working with him might be pleasant or unpleasant and we might be able to predict what his level of involvement in the project will be as well as the potential quality of his work.

13.2.5. Mental Images

Mental images are like pictures in the mind’s eye. If you are asked to picture an apple in your mind, can you do it? Maybe we recall previous times when we saw, touched, smelled, or tasted an apple. As we recall more and more memories, we can form a more complete mental image. Or maybe we have had limited experience with an apple, or maybe some exotic fruit, and so seek them out to gain additional sensory information? These images become more complete as we gain additional information either from existing memories or new information from our world. In the case of the latter, we learn about the object in question.

  • Define problems.
  • Describe insight learning.
  • Define and exemplify functional fixedness.

Let’s face it. Hardly anything in life runs smoothly. Even with the best-laid plan, and clearest goals we can formulate, success can be elusive. We might even be unsure how to proceed or to solve what are called problems or when we cannot achieve a goal due to an obstacle that we are unsure how to overcome.  In Section 10.4.2 we discussed Gestalt principles of perceptual organization but in this section, we focus on what they said about problem-solving. Simply, when it comes to problem-solving, the Gestalt psychologists said that we had to proceed from the whole problem down to its parts. How so? Kohler studied the problem-solving abilities of chimpanzees and used simple props such as the bars of the cages, bananas, sticks, and a box. Chimps were placed in a cage with bananas hanging overhead. They could use any prop they needed to get them, but no one prop alone would suffice. The chimps had to figure out what combination of props would aid them in getting the bananas. At first, they did not do well but then out of nowhere saw the solution to the problem. He called this insight learning or the spontaneous understanding of relationships. The chimps had to look at the whole situation and the relationships among stimuli, or to restructure their perceptual field, before the solution to the problem could be seen.

One obstacle to problem-solving is what is called functional fixedness or when we focus on a typical use or familiar function of an object. Duncker (1945) demonstrated this phenomenon using what he called the candle problem. Essentially, participants were given candles, tacks, and matches in a matchbox and were asked to mount a candle on a vertical corkboard attached to the wall such that it would not drip wax on the floor. To successfully complete the task, the participant must realize that the matchbox can be used as a support and not just a container. In his study, Duncker presented one group with small cardboard boxes containing the materials and another group with all the same materials but not in the boxes (they were sitting beside the boxes). The group for which the materials were in the boxes found the task more difficult than the group for which the materials were outside. In the case of the latter, these participants were able to see the box as not just a container, but as another tool to use to solve the problem.

As you can see from the candle problem, and other related problem-solving tasks, we sometimes have to think outside of the box or to demonstrate creativity . This is called divergent thinking or thinking that involves more than one possible solution and that is open-ended.  Part of the open-endedness is coming up with ideas on how to solve the problem, which we call brainstorming .  Really, any idea could have merit so just saying whatever comes to mind is important.  

  • Differentiate deductive from inductive reasoning.
  • Define heuristics and describe types.
  • Outline errors we make when reasoning.

13.4.1. Types of Reasoning

Though you are sitting in a college classroom now, how did you get there? Did you have to choose between two or more universities? Did you have to debate which area to major in? Did you have to decide which classes to take this semester to fit your schedule? Did you have to decide whether you were walking, riding a bike, or taking the bus to school? To answer any of these questions, you engaged in reasoning centered on making a good decision or judgment. There are two types of reasoning we will briefly discuss — formal or deductive and informal or inductive.

First, we use formal or deductive reasoning when the procedure needed to draw a conclusion is clear and only one answer is possible. This approach makes use of algorithms or a logical sequence of steps that always produces a correct solution to the problem. For instance, solve the following problem:

3x + 20 = 41

  • Step 1 — Subtract 20 from both sides resulting in: 3x = 21
  • Step 2 — Divide each side by 3 resulting in x = 7
  • Check your answer by substituting 7 for x in the original problem resulting in 21+20=41 which is correct.

Deductive reasoning also uses the syllogism which is a logical argument consisting of premises and a conclusion. For example:

  • Premise 1 — All people die eventually.
  • Premise 2 — I am a person.
  • Conclusion — Therefore, I will die eventually.

Second, informal or inductive reasoning is used when there is no single correct solution to a problem. A conclusion may or may not follow from premises or facts. Consider the following:

  • Observation — It has snowed in my town for the past five years during winter.
  • Conclusion — It will snow this winter.

Though it has snowed for the past five years it may not this year. The conclusion does not necessarily follow from the observation. What might affect the strength of an inductive argument then? First, the number of observations is important. In our example, we are basing our conclusion on just five years of data. If the first statement said that it snowed for the past 50 years during winter, then our conclusion would be much stronger. Second, we need to consider how representative our observations are. Since they are only about our town and our conclusion only concerns it, the observations are representative. Finally, we need to examine the quality of the evidence. We could include meteorological data from those five years showing exactly how much snow we obtained. If by saying it snowed, we are talking only about a trace amount each year, though technically it did snow, this is not as strong as saying we had over a foot of snow during each year of the observation period.

13.4.2. Heuristics and Cognitive Errors

We use our past experiences as a guide or shortcut to make decisions quickly. These mental shortcuts are called heuristics. Though they work well, they are not fool proof. First, the availability heuristic is used when we make estimates about how often an event occurs based on how easily we can remember examples (Tversky & Kahneman, 1974). The easier we can remember examples, the more often we think the event occurs. This sounds like a correlation between events and is. The problem is that the correlation may not actually exist, called an illusory correlation .

Another commonly used heuristic is the representative heuristic or believing something comes from a larger category based on how well it represents the properties of the category. It can lead to the base rate fallacy or when we overestimate the chances that some object or event has a rare property, or we underestimate that something has a common property.

A third heuristic is the affect heuristic or thinking with our heart and not our head. As such, we are driven by emotion and not reason. Fear appeals are an example. Being reminded that we can die from lung cancer if we smoke may fill us with dread.

In terms of errors in reasoning, we sometimes tend to look back over past events and claim that we knew it all along. This is called the hindsight bias and is exemplified by knowing that a relationship would not last after a breakup. Confirmation bias occurs when we seek information and arrive at conclusions that confirm our existing beliefs. If we are in love with someone, we will only see their good qualities but after a breakup, we only see their negative qualities. Finally, mental set is when we attempt to solve a problem using what worked well in the past. Of course, what worked well then may not now and so we could miss out on a solution to the problem.

13.5. Intelligence – Putting Our Learning to Good Use

  • Define intelligence.
  • Contrast the two main types.
  • Describe the development of intelligence tests over time.
  • Propose whether intelligence is more complex than we first thought.
  • Define emotional intelligence (EI).
  • List and discuss EI’s four core skills and two primary competencies.
  • Clarify what research says about EI and its benefit.

13.5.1. What is Intelligence?

Intelligence includes the ability to solve problems, acquire language and knowledge, think abstractly, adapt to one’s environment, and engage in the manipulation of one’s environment. It consists of two types – crystalized and fluid. Crystalized intelligence is our accumulated knowledge acquired across life. Fluid intelligence is used when we solve problems, remember information, and reason abstractly.

13.5.2. The Development of Intelligence Tests

In 1890, while at the University of Pennsylvania, James McKeen Cattell (1860-1944) coined the term mental tests or tests of motor skills and sensory functioning. They included rate of movement, just noticeable differences in judging weights, time to name colors, reaction time for sound, and dynamometer pressure. Though Cattell coined the term, Francis Galton (1822 – 1911 and mentor of Cattell) originated the idea and believed intelligence was linked to a person’s sensory capabilities such that individuals with greater intelligence would have more advanced sensory functioning. Were Galton and Cattell correct? In 1901 Cattell obtained enough data to be able to correlate test scores with academic performance. The results produced extremely low correlations leading Cattell to conclude that the tests were not adequate predictors of college performance or intellectual ability.

Unlike Galton and Cattell who focused on sensorimotor functioning, Alfred Binet (1857-1911) believed intelligence should be measured through cognitive processes such as learning, memory, attention, and comprehension. He had a chance to develop a test when the French Ministry of Education appointed Theodore Simon and himself to identify children who were having difficulties in school so that remedial work could be assigned to them. The ministry was reluctant to ask teachers to undertake the task as they feared bias would creep into the decision. A more objective approach was needed. Binet and Simon’s work yielded a test consisting of 30 problems assessing comprehension, reasoning, and judgment. It was revised three years later to include the concept of mental age or a child’s level of intellectual development compared to other children. Let’s say a six-year-old child is given the test and performances as well as seven-year-old children given the same test, then he would be assigned a mental age of seven.

After Binet’s death in 1911, the development of intelligence tests shifted to the United States. Henry Goddard translated Binet’s test and presented it to American psychologists in 1908. He called his translation the Binet-Simon Measuring Scale for Intelligence . In 1916 Lewis Terman developed the Stanford-Binet Test , named after the university he was affiliated with, and introduced the concept of intelligence quotient (IQ) , or a measure of intelligence calculated by dividing the child’s mental age by his/her chronological age and multiplying by 100. If a child’s mental age and chronological age were the same, he/she would have an IQ of 100, considered to be “average” intelligence. If a child had a mental age of 7 and a chronological age of 5, his/her IQ score would be 140 and above average. Finally, a mental age of 8 and chronological age of 10 yields an IQ of 80 or below average.

Today, the Stanford-Binet test is still used though other scales have been created too. David Wechsler designed a test only for adults, the Wechsler Adult Intelligence Scale (WAIS). Later, the Wechsler Intelligence Scale for Children (WISC) was created. The two Wechsler tests include a general IQ score as well as scores for different types of abilities to include perceptual reasoning, working memory, verbal comprehension, and processing speed.

13.5.3. Types of Intelligence

The discussion of the development of IQ tests leads us to one important question — is there more than one type of intelligence? To examine this question, the work of Robert Sternberg and Howard Gardner will be examined briefly.

13.5.3.1. Sternberg’s triarchic theory of intelligence. Sternberg proposed his triarchic theory of intelligence which says there are three different types (Sternberg, 1988). Componential (analytic) intelligence is the first. This type of intelligence is measured by traditional intelligence tests and aids you in solving problems by first identifying a problem, deciding on a strategy to solve it, learning and then executing the strategy, and finally evaluating the result of your strategy. Creative (experiential) intelligence is the type of intelligence used to compose music. People with this ability cope with new situations well and learn quickly. Practical (contextual) intelligence reflects your ability to adapt to your environment or to consider the different contexts you may find yourself in. This type of intelligence would help you figure out what to do if stranded in the forest.

13.5.3.2. Gardner’s multiple intelligences. Howard Gardner (Gardner, 1999) proposed the existence of several intelligences, each which involve a different set of skills and which can function independently of one another. They include linguistic (verbal skills), logical-mathematical (math and reasoning skills), and spatial (relationships between objects) intelligences which are the only three of the eight assessed by standard IQ tests, as well as musical (shown through skills in tempo and rhythm), body-kinesthetic (having skill in dancing and athletics), intrapersonal (self-understanding), interpersonal (how well you interact with others), and naturalistic (seeing patterns in nature).

We may also develop some of these intelligences more than others. To assess these other intelligences, Gardner suggests assessing a child’s music ability, sampling writing, and asking teachers what strengths and weaknesses students have in terms of athletic ability and social skills.

13.5.4. Emotional Intelligence

Emotional intelligence or EI is our ability to manage the emotions of others as well as ourselves and includes skills such as empathy, emotional awareness, managing emotions, and self-control. According to a 2014 Forbes article by Travis Bradberry, EI consists of four core skills falling under two primary competencies: personal and social.

First, personal competence focuses on us individually and not on our social interactions. Through personal competence, we are self-aware or can accurately perceive our emotions and remain aware of them as they occur. We also can engage in self-management or using this awareness of our emotions to stay flexible and direct our behavior to positive ends.

Second, social competence focuses on social awareness and how we manage our relationships with others. Through it, we can understand the behaviors, moods, and motives of others. This allows us to improve the quality of our relationships. In terms of social awareness , we pick up on the emotions of others to understand what is going on. Relationship management allows us to be aware of the emotions of others and ourselves so that we can manage interactions successfully.

EI is not the same as IQ or intelligence quotient as EI can be improved upon over time while IQ cannot. This is not to say that some people are not naturally more emotionally intelligent than others, but that all can develop higher levels of it with time.

How do we effectively use emotional intelligence? Mayer and Salovey (1997) offer four uses. First, flexible planning involves mood swings which cause us to break our mindset and consider other alternatives or possible outcomes. Second, EI fosters creative thinking during problem-solving tasks. Third, the authors write that “ attention is directed to new problems when powerful emotions occur.” Attending to our feelings allows us to shift from one problem to a new, more immediate one (consider that this can be adaptive too). Finally, moods can be used to motivate persistence when a task is challenging. Anxiety about an impending test may motivate better preparation or concern about passing preliminary examinations or may motivate a graduate student to pay extra careful attention to details in the research articles he/she has been assigned.

Utilizing a sample of 330 college students, Brackett, Mayer, and Warner (2004) found that women scored higher than men on EI and that lower EI in males was associated with maladjustment and negative behaviors such as illegal drug and alcohol use, poor relationships with friends, and deviant behavior. Individuals scoring higher in the ability to manage emotions were found by Lopes, Salovey, and Staus (2003) to report positive relations with others, report fewer negative interactions with their close friends, and to perceive greater levels of parental support. They also found that global satisfaction with relationships was linked to effectively managing one’s emotions, the personality trait of extraversion (positive correlation), and was negatively associated with neuroticism. In terms of the academic performance of students in British secondary education, those high in EI were less likely to have unauthorized absences or be excluded from school and demonstrated greater levels of scholastic achievement (Petrides, Frederickson, & Furham, 2004) while EI is also shown to be related positively to academic success in college (Parker, Summerfeldt, Hogan, & Majeski, 2004).

Finally, Ciarrochi, Deane, and Anderson (2002) investigated the relationship of stress with the mental health variables of depression, hopelessness, and suicidal ideation. They found that stress was related to greater reported levels of the three mental health variables for those high in emotional perception and suicidal ideation was higher in those low in managing other’s emotions.  

  • Describe the presentation and associated features of ID.
  • Describe the presentation and associated features of LDs.
  • Clarify the differences and similarities between ID and LD.
  • Describe treatment options for ID and LDs.

In the final section of Module 13, we will discuss matters related to intellectual disability and learning disorders. Be advised a more thorough description of these disorders is beyond the scope of this book, but you can read more in the Behavioral Disorders of Childhood OER by Kristy McRaney, Alexis Bridley, and Lee Daffin (2021) by visiting:

https://opentext.wsu.edu/behavioral-disorders-childhood/chapter/module-7-intellectual-disability-intellectual-developmental-disorder-ididd-learning-disorders/

13.6.1. What is Intellectual Disability?

At the core of an Intellectual Disability is a deficit in cognitive or intellectual functioning. Historically, we labeled individuals with this presentation of deficits as having Mental Retardation. Due to significant stigma and social misuse of the term, when the DSM 5 was published, the term changed from Mental Retardation to Intellectual Disability (also described as an Intellectual Developmental Disorder). While the terms Intellectual Disability and Intellectual Developmental Disorder are considered interchangeable, we will use the term Intellectual Disability (ID) for the purposes of this book. This disorder leads to two primary areas of major deficits – cognitive functioning and adaptive functioning (APA, 2013).

13.6.1.1. Cognitive functioning. Cognition or intellectual functioning refers, in a general sense, to our ability to problem solve, understand and analyze complex material, absorb information from our environment, and reason. An individual with ID has a significant deficit in this area. Cognitive functioning is most often measured using an intelligence test (more on this later in this chapter). An IQ score under 70 – 75 indicates a severe deficit in cognitive functioning, although there is some flexibility within this criterion.

13.6.1.2. Adaptive functioning. Adaptive skills are skills that help us navigate our daily lives successfully such as understanding safety signs in our environment, making appointments, interacting with others, completing hygiene routines, etc. Essentially, these are the skills that one would ultimately need to live independently. Individuals with ID typically have adaptive skills that are far below what would be expected given their chronological age. This is typically measured by a standardized scale (more on this later, as well).

When both cognitive and adaptive functioning is delayed, the likelihood of ID is high. ID is also categorized into different severities based on the level of delays related to adaptive functioning. The more support someone needs, the more severe the ID diagnosis. Severity ranges from mild (least severe), moderate, severe, and profound (most severe; APA, 2013).

ID is present in the early neurodevelopmental period. As such, it is most frequently diagnosed in children. ID is not something one would “acquire” in adulthood. If an individual experiences cognitive and adaptive function decline in later years, this is not considered ID (which is a neurodevelopmental disorder) but is more likely a neurocognitive disorder that may be due to several things (e.g., traumatic brain injury, dementia). As such, although an individual can go undiagnosed until adulthood, and then as an adult be diagnosed with ID, there must be significant and indisputable evidence of cognitive delay and adaptive functioning delay in the early developmental time period. Otherwise, an adult would not be diagnosed with ID.

13.6.2. What Are Specific Learning Disabilities?

A learning disorder is characterized by the inability or difficulty processing academic or functional information in our environment (APA, 2013). Despite an ability to cognitively achieve similar to peers, an individual is delayed in learning in a particular area. More specifically, academic tasks are challenging within one or more areas, which results in significant academic impairment (APA, 2013). Historically, we diagnosed LDs when there was a significant discrepancy between an individual’s cognitive/intellectual ability (as measured by an intelligence test) and their academic achievement (as measured by a standardized achievement test) as this was required by the DSM-IV-TR criteria. This method is referred to as the discrepancy model. While many still do this, and there is nothing in the DSM 5 that disallows this practice, the DSM 5 criteria were rewritten to allow for more flexibility. Ultimately, a discrepancy between one’s IQ and academic achievement is no longer required; however, there must be specific data that indicates an individual is performing significantly below what would be expected given their age.

In addition to significant academic deficits, there must be evidence that efforts (e.g., tutoring, increased and specialized instruction) to improve one’s abilities within the specific area have been made, before assigning a diagnosis of an LD. This is to ensure that an individual has had full access to educational material and support before a professional assigns a diagnosis to them. In school systems, tiered interventions have come into play (more on this in the Interventions section).

When considering LDs, there are three specific areas that are considered: reading, mathematics, and written expression. For example, a professional would diagnose an individual with a specific learning disorder with impairment in reading . An individual may have a diagnosis of only one LD, or multiple LDs.

Reading — This relates to an individual having difficulty in reading, may that be in comprehending material, reading fluently and quickly, or reading words accurately.

Mathematics — This may be related to simple calculation abilities such as math facts or more complex problem-solving and reasoning abilities.

Written expression — This may refer to the ability to accurately spell words or punctuate and use correct grammar, or it may include one’s ability or create written work that is well-organized and comprehendible.

13.6.2.1. Matters of dyslexia and dyscalculia. Technically, dyslexia and dyscalculia are not actual diagnoses in the DSM 5; rather they are alternative terms used to describe learning disorders in reading (dyslexia) and math (dyscalculia). Dyslexia is the presence of a significant deficit related to fluent word recognition, decoding, and spelling (APA, 2013). Dyscalculia is the presence of significant deficits related to “problems processing numerical information, learning arithmetic facts, and performing accurate or fluent calculations” (APA, 2013).  Although these two terms are used very frequently in school systems and by other professionals such as speech/language pathologists they are considered alternative terms in the DSM 5, not diagnoses, and as such psychologists cannot use these terms when diagnosing a patient. Instead, they assign a diagnosis of s pecific learning disorder with impairment in reading (for dyslexia) and a specific learning disorder with impairment in mathematics ( for dyscalculia). They can provide an explanation and rationale that the individual’s deficits are characteristic of the pattern of deficits seen in individuals with dyslexia or dyscalculia. This is an excellent example of how professionals sometimes will discuss the same phenomenon but use different terminology.

13.6.3. Differences and Similarities between ID and LD.

Although ID and LDs may seem very similar, it is important to not confuse the two as they are different. When thinking about both disorders, we have three different core areas to consider: adaptive functioning, cognitive/intellectual ability (IQ), and academic achievement. A rudimentarily way to think about this is — with ID we are concerned with adaptive functioning and IQ and with LD we are concerned with IQ (sort of) and academic achievement. Although IQ matters (sort of) in both disorders, the reason they are important vary slightly. However, because IQ is considered in both disorders, people often intertwine and confuse the two disorders.

Think about it like this: IQ essentially is what we are cognitively able to do — what we can do. Adaptive skills and academic achievement is what we are doing.

13.6.3.1 Intellectual disability. If we cannot perform in the average range on an IQ test and we are not performing daily living tasks appropriately (for our particular age — let’s not forget that we would not expect a 7-year-old to make their own doctor’s appointment. We would, however, expect a 7-year-old to know to dial 911 in an emergency), then this is indicative of an ID.

13.6.3.2. Learning disorders. If we can achieve an average level of skill (meaning our IQ is average), but we are not achieving an average level of academic achievement in an area, that leads us to be puzzled, right? If we can do something, but we are not , that does not make sense. But what if we cannot perform average (meaning our IQ is not average, but substantially below average)? Would we expect the individual to perform averagely on academic tasks? For example, if someone’s IQ is 65 ( cannot function typically on a cognitive task ) would we expect them to have an academic achievement score of 100 (remember, this is their “ is or is not doing/performing)? That is a 30-point jump from their ‘ can’ to their ‘ are doing’. We would not necessarily expect this, right? We would expect that if someone’s IQ is a 70 to have an academic score of around a 70. This isn’t necessarily an LD; it is reflective of low achievement due to low cognitive abilities resulting from ID. However, if that person’s IQ was 100 ( can ) and they scored a 70 ( is not performing) on an academic achievement task, we would be concerned about an LD because what they are doing is not matching and measuring up to what they, theoretically, can do.

13.6.3.3. LDs in the cognitively delayed and in the cognitively gifted. Individuals with extreme cognitive functioning abilities often get overlooked. For example, children that are gifted, but have a reading disorder, often go undiagnosed. Think about it, their weaknesses, although areas of deficit for themselves, look like average abilities to others around them. You might be asking yourself what I mean by this. An example should help.

A 2nd-grader with a high cognitive ability gets all As. She excels in math and writing. In fact, she is far past her peers in these areas. She has long learned her multiplication and division facts and is even working on some basic geometry skills. She has a great ability to write and has been drafting paragraphs with ease and has even started learning to write essays. She loves math and writing, but she dislikes reading. When in class, she reads just like her peers, no more advanced, but right on 2nd-grade-level expectations. She finds reading to be more difficult, though, and it does not come nearly as easy as math and writing. However, because she is on track compared to her peers, her teachers and parents do not recognize any issues — her grades are fine and her school standardized testing is not a problem.

What if I told you that her standardized math and writing scores matched her intellectual ability (meaning her can and is/are matched) but her reading score ( is/are ), although average, was well below what would be expected given her IQ ( can ) and is much lower than her math and writing scores (despite still being an acceptable score). Would you say she may have a reading disorder? If you said yes, you are right. If you said no, you may be right too. Fact is, this is a gray area. The old DSM would have made it easy to diagnose this child with an LD in reading. The new DSM makes it a bit tougher. However, one would be inclined, if this reading deficit (compared to her own abilities) caused impairment (internal distress, preventing her from advancing in math and writing because her reading abilities were lagging behind the other abilities), to diagnose her with an LD in reading. It is easy to see how this child would be missed and go undiagnosed for years.

Now let’s reverse the scenario. Let’s take a 2nd grade girl who has a diagnosis of an ID. She struggles in all academic areas but her math abilities are even more behind than her reading and writing. Do you think one could make a case for an LD in math? Theoretically, they could. But it takes a lot of careful documentation of intervention attempts (see RTI discussion) and standardized testing that makes it undoubtably clear that this is true (similar to the above example).

Essentially, when individuals have an IQ that falls to the extreme (low or high), their weaknesses are often missed. As such, providers and educators must be careful and mindful to not overlook potential LDs in these individuals.

13.6.4. Treatments for Intellectual Disability

13.6.4.1. Community supports and programs.  For individuals with ID, community supports may be critical during childhood, and even more so as the individual transitions to adulthood. Community supports may include organizations devoted to socialization and family support. For example, The Arc is an incredible organization that is devoted to serving individuals with developmental delays, including but not limited to ID. They often engage in advocacy efforts and offer training for the community and professionals. Moreover, they offer employment services for individuals with ID or other developmental delays. Local chapters will often host social gatherings and events for individuals and their families (The Arc, 2018). Typically, there is an Arc chapter in most major cities and areas. Other community supports may involve government-funded programming for living arrangements, supplemental income, etc.

As individuals’ transition to adulthood, some programming may need to be considered related to home/living arrangements. Historically, individuals with ID were often institutionalized. However, in recent years, a strong push to deinstitutionalize care, and provide group and community home options has occurred. As such, a more common and inclusive living option for individuals may be a group home in which multiple individuals live in a home-like setting and have constant supervision and medical care as well as transportation. Another option, often referred to as supported independent living, is a situation in which fewer, perhaps four individuals, live in an apartment or similar setting, and are provided constant supervision by one individual. This is a less restrictive environment than a group home, as only one supervising staff member is present, and a nurse and other medical staff are not readily available.  Moreover, individuals with ID are often capable of successful employment and these opportunities are provided in group and independent living home arrangements. Individuals with ID, depending on the severity of their intellectual impairment, may work in settings with routine tasks (e.g., assembling plasticware packets, bussing tables) in independent settings (e.g., employed independently within the community) or in ‘supervised workshops’ (i.e., settings where multiple individuals with disabilities are employed and provided significant help and supervision while working).   

13.6.4.2. Education. Individuals with an Intellectual Disability receive an Individualized Education Plan (IEP) at their school which is federally regulated, and implemented at the state level, through the Individuals with Disabilities Education Act (IDEA), established in 2004 (IDEA, n.d.). This was enacted to ensure fair and equal access to public education for all children. An IEP outlines specific accommodations and supports a child is entitled to in the educational setting so that they can access educational material to the fullest degree. Children with ID may receive typical academic instruction in an inclusion classroom, meaning they are in a general educational class. However, the more severe the disability, the more supports they may require. As such, this may mean the child is pulled out at periods of time to receive specialized instruction. Additionally, if the child’s disability is severe, they may be placed in a self-contained classroom which is a class with a small number of kids that all have a severe disability, oftentimes with several teachers/teacher aids. Supports and accommodations may include reduced workloads, extended time to master the material, increased instructional aid, etc. Additionally, supports may also go beyond specific academic areas. For example, social skills may be a focus of an intervention.

Individuals with severe deficits related to ID will eventually have to have a determination of diploma track or not. If an individual is not placed in a diploma track, they will receive a “certificate of completion” from high school, rather than a high school diploma. Non-diploma track supports might focus heavily on functional skills rather than traditional academics. For example, rather than worrying about mastering algebra, the individual’s education may focus on learning functional mathematics so that they will be able to successfully manage a grocery shopping trip/purchase.

Some college programs have been designed to allow individuals with developmental delays such as ID to access the college experience and receive specialized vocational instruction.  For example, Mississippi State University’s ACCESS program (which is an acronym for Academics, Campus Life, Community Involvement, Employment Opportunities, Socialization, and Self-Awareness) is 4-year, non-degree program designed for individuals that have a developmental delay, including ID. Students receive a “Certification of Completion” within a specific vocational area when they complete the program. They live on campus and are able to access the full college experience (MSU, n.d.).

13.6.4.3. Psychotherapy. Therapy is often underutilized in individuals with ID, despite beneficial impacts that research has shown when both behavioral and cognitive-behavioral therapies are utilized (Harris, 2006). Therapy often focuses on the emotional and behavioral impacts of ID, normalizing the individual’s experiences, and treating comorbid depression, anxiety, or other mental health conditions (Harris, 2006). Another area of strong focus may be increasing adaptive functioning skills. For example, helping the individual complete daily hygiene, chores, etc. and learn how to navigate their home and community safely, may be a focus of therapy.

13.6.4.4. Medication. Medications to manage emotional or behavioral concerns that are occurring comorbid with an individual’s ID diagnosis may be beneficial. For example, if an individual has ID and depression, an antidepressant may be beneficial to help resolve some symptoms of depression. However, medications are not utilized to “treat” ID.

13.6.5. Treatments for Learning Disorders

13.6.5.1. Education. Individuals with an LD receive an Individualized Education Plan (IEP) as well. Focus is placed on increasing instructional aids for the child. The child will often be pulled out for additional, one-on-one interventions in the academic area(s) of concern. Additionally, the child may receive additional supports such as extended time on tests and assignments, partial credit (when partial credit is not typically given in a particular class), and early access to study guides or access to study guides if a study guide is not regularly given in a particular class. A child may also be allowed to have tests read to them, especially on nonreading-related tests, such as history, when a reading impairment is noted. The reason for doing this is so that the child’s performance in the nonreading-subject (e.g., science, history) is not negatively impacted by their reading deficit. The child may also be able to verbally respond to test items and have a teacher write their answers. Moreover, the child may get opportunities to correct errors on tests for additional credit, etc. These are just examples of accommodations and are not an exhaustive list. The specific accommodations and supports that are implemented should be specific to the child, their deficits, and their current needs.

Tutoring, whether occurring in school or privately, is often useful as well. This simply increases exposure to material and provides additional support and intervention. Empirically-based tutoring methods are sometimes used, particularly for children with dyslexia.

13.6.5.2. Medication . Like ID, medicine is not utilized to ‘treat’ an LD. However, given that ADHD is highly comorbid with LDs, ADHD-related medications may be utilized and beneficial. As chronic underachievement in an academic area may lead to anxiety and depressive states for some children, prescription medication (or psychotherapy) may also be utilized and beneficial.  

Module Recap

And that’s it. We have now covered the cognitive process of learning across 13 modules. Our final topic was how we learn concepts that involved a multi-faceted discussion of cognitive development across the life span and the elements of cognition, and a few complementary cognitive processes including problem-solving and reasoning, as well as intelligence. I thought it important to at least raise your awareness of issues that can make learning more difficult for some among us. As such, we discussed intellectual and learning disabilities to finish out the module.

I hope you enjoyed our discussion in this module, and across the entire book. This concludes Part 6.

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Overview of the Problem-Solving Mental Process

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

learning concepts problem solving

Rachel Goldman, PhD FTOS, is a licensed psychologist, clinical assistant professor, speaker, wellness expert specializing in eating behaviors, stress management, and health behavior change.

learning concepts problem solving

  • Identify the Problem
  • Define the Problem
  • Form a Strategy
  • Organize Information
  • Allocate Resources
  • Monitor Progress
  • Evaluate the Results

Frequently Asked Questions

Problem-solving is a mental process that involves discovering, analyzing, and solving problems. The ultimate goal of problem-solving is to overcome obstacles and find a solution that best resolves the issue.

The best strategy for solving a problem depends largely on the unique situation. In some cases, people are better off learning everything they can about the issue and then using factual knowledge to come up with a solution. In other instances, creativity and insight are the best options.

It is not necessary to follow problem-solving steps sequentially, It is common to skip steps or even go back through steps multiple times until the desired solution is reached.

In order to correctly solve a problem, it is often important to follow a series of steps. Researchers sometimes refer to this as the problem-solving cycle. While this cycle is portrayed sequentially, people rarely follow a rigid series of steps to find a solution.

The following steps include developing strategies and organizing knowledge.

1. Identifying the Problem

While it may seem like an obvious step, identifying the problem is not always as simple as it sounds. In some cases, people might mistakenly identify the wrong source of a problem, which will make attempts to solve it inefficient or even useless.

Some strategies that you might use to figure out the source of a problem include :

  • Asking questions about the problem
  • Breaking the problem down into smaller pieces
  • Looking at the problem from different perspectives
  • Conducting research to figure out what relationships exist between different variables

2. Defining the Problem

After the problem has been identified, it is important to fully define the problem so that it can be solved. You can define a problem by operationally defining each aspect of the problem and setting goals for what aspects of the problem you will address

At this point, you should focus on figuring out which aspects of the problems are facts and which are opinions. State the problem clearly and identify the scope of the solution.

3. Forming a Strategy

After the problem has been identified, it is time to start brainstorming potential solutions. This step usually involves generating as many ideas as possible without judging their quality. Once several possibilities have been generated, they can be evaluated and narrowed down.

The next step is to develop a strategy to solve the problem. The approach used will vary depending upon the situation and the individual's unique preferences. Common problem-solving strategies include heuristics and algorithms.

  • Heuristics are mental shortcuts that are often based on solutions that have worked in the past. They can work well if the problem is similar to something you have encountered before and are often the best choice if you need a fast solution.
  • Algorithms are step-by-step strategies that are guaranteed to produce a correct result. While this approach is great for accuracy, it can also consume time and resources.

Heuristics are often best used when time is of the essence, while algorithms are a better choice when a decision needs to be as accurate as possible.

4. Organizing Information

Before coming up with a solution, you need to first organize the available information. What do you know about the problem? What do you not know? The more information that is available the better prepared you will be to come up with an accurate solution.

When approaching a problem, it is important to make sure that you have all the data you need. Making a decision without adequate information can lead to biased or inaccurate results.

5. Allocating Resources

Of course, we don't always have unlimited money, time, and other resources to solve a problem. Before you begin to solve a problem, you need to determine how high priority it is.

If it is an important problem, it is probably worth allocating more resources to solving it. If, however, it is a fairly unimportant problem, then you do not want to spend too much of your available resources on coming up with a solution.

At this stage, it is important to consider all of the factors that might affect the problem at hand. This includes looking at the available resources, deadlines that need to be met, and any possible risks involved in each solution. After careful evaluation, a decision can be made about which solution to pursue.

6. Monitoring Progress

After selecting a problem-solving strategy, it is time to put the plan into action and see if it works. This step might involve trying out different solutions to see which one is the most effective.

It is also important to monitor the situation after implementing a solution to ensure that the problem has been solved and that no new problems have arisen as a result of the proposed solution.

Effective problem-solvers tend to monitor their progress as they work towards a solution. If they are not making good progress toward reaching their goal, they will reevaluate their approach or look for new strategies .

7. Evaluating the Results

After a solution has been reached, it is important to evaluate the results to determine if it is the best possible solution to the problem. This evaluation might be immediate, such as checking the results of a math problem to ensure the answer is correct, or it can be delayed, such as evaluating the success of a therapy program after several months of treatment.

Once a problem has been solved, it is important to take some time to reflect on the process that was used and evaluate the results. This will help you to improve your problem-solving skills and become more efficient at solving future problems.

A Word From Verywell​

It is important to remember that there are many different problem-solving processes with different steps, and this is just one example. Problem-solving in real-world situations requires a great deal of resourcefulness, flexibility, resilience, and continuous interaction with the environment.

Get Advice From The Verywell Mind Podcast

Hosted by therapist Amy Morin, LCSW, this episode of The Verywell Mind Podcast shares how you can stop dwelling in a negative mindset.

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You can become a better problem solving by:

  • Practicing brainstorming and coming up with multiple potential solutions to problems
  • Being open-minded and considering all possible options before making a decision
  • Breaking down problems into smaller, more manageable pieces
  • Asking for help when needed
  • Researching different problem-solving techniques and trying out new ones
  • Learning from mistakes and using them as opportunities to grow

It's important to communicate openly and honestly with your partner about what's going on. Try to see things from their perspective as well as your own. Work together to find a resolution that works for both of you. Be willing to compromise and accept that there may not be a perfect solution.

Take breaks if things are getting too heated, and come back to the problem when you feel calm and collected. Don't try to fix every problem on your own—consider asking a therapist or counselor for help and insight.

If you've tried everything and there doesn't seem to be a way to fix the problem, you may have to learn to accept it. This can be difficult, but try to focus on the positive aspects of your life and remember that every situation is temporary. Don't dwell on what's going wrong—instead, think about what's going right. Find support by talking to friends or family. Seek professional help if you're having trouble coping.

Davidson JE, Sternberg RJ, editors.  The Psychology of Problem Solving .  Cambridge University Press; 2003. doi:10.1017/CBO9780511615771

Sarathy V. Real world problem-solving .  Front Hum Neurosci . 2018;12:261. Published 2018 Jun 26. doi:10.3389/fnhum.2018.00261

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Introduction to Problem Solving Skills

What is problem solving and why is it important.

Defining problem solving skills

The ability to solve problems is a basic life skill and is essential to our day-to-day lives, at home, at school, and at work. We solve problems every day without really thinking about how we solve them. For example: it’s raining and you need to go to the store. What do you do? There are lots of possible solutions. Take your umbrella and walk. If you don't want to get wet, you can drive, or take the bus. You might decide to call a friend for a ride, or you might decide to go to the store another day. There is no right way to solve this problem and different people will solve it differently.

Problem solving is the process of identifying a problem, developing possible solution paths, and taking the appropriate course of action.

Why is problem solving important? Good problem solving skills empower you not only in your personal life but are critical in your professional life. In the current fast-changing global economy, employers often identify everyday problem solving as crucial to the success of their organizations. For employees, problem solving can be used to develop practical and creative solutions, and to show independence and initiative to employers.

Throughout this case study you will be asked to jot down your thoughts in idea logs. These idea logs are used for reflection on concepts and for answering short questions. When you click on the "Next" button, your responses will be saved for that page. If you happen to close the webpage, you will lose your work on the page you were on, but previous pages will be saved. At the end of the case study, click on the "Finish and Export to PDF" button to acknowledge completion of the case study and receive a PDF document of your idea logs.

What Does Problem Solving Look Like?

IDEAL heuristic strategy for problem solving

The ability to solve problems is a skill, and just like any other skill, the more you practice, the better you get. So how exactly do you practice problem solving? Learning about different problem solving strategies and when to use them will give you a good start. Problem solving is a process. Most strategies provide steps that help you identify the problem and choose the best solution. There are two basic types of strategies: algorithmic and heuristic.

Algorithmic strategies are traditional step-by-step guides to solving problems. They are great for solving math problems (in algebra: multiply and divide, then add or subtract) or for helping us remember the correct order of things (a mnemonic such as “Spring Forward, Fall Back” to remember which way the clock changes for daylight saving time, or “Righty Tighty, Lefty Loosey” to remember what direction to turn bolts and screws). Algorithms are best when there is a single path to the correct solution.

But what do you do when there is no single solution for your problem? Heuristic methods are general guides used to identify possible solutions. A popular one that is easy to remember is IDEAL [ Bransford & Stein, 1993 ] :

  • I dentify the problem
  • D efine the context of the problem
  • E xplore possible strategies
  • A ct on best solution

IDEAL is just one problem solving strategy. Building a toolbox of problem solving strategies will improve your problem solving skills. With practice, you will be able to recognize and use multiple strategies to solve complex problems.

Watch the video

What is the best way to get a peanut out of a tube that cannot be moved? Watch a chimpanzee solve this problem in the video below [ Geert Stienissen, 2010 ].

[PDF transcript]

Describe the series of steps you think the chimpanzee used to solve this problem.

  • [Page 2: What does Problem Solving Look Like?] Describe the series of steps you think the chimpanzee used to solve this problem.

Think of an everyday problem you've encountered recently and describe your steps for solving it.

  • [Page 2: What does Problem Solving Look Like?] Think of an everyday problem you've encountered recently and describe your steps for solving it.

Developing Problem Solving Processes

Problem solving is a process that uses steps to solve problems. But what does that really mean? Let's break it down and start building our toolbox of problem solving strategies.

What is the first step of solving any problem? The first step is to recognize that there is a problem and identify the right cause of the problem. This may sound obvious, but similar problems can arise from different events, and the real issue may not always be apparent. To really solve the problem, it's important to find out what started it all. This is called identifying the root cause .

Example: You and your classmates have been working long hours on a project in the school's workshop. The next afternoon, you try to use your student ID card to access the workshop, but discover that your magnetic strip has been demagnetized. Since the card was a couple of years old, you chalk it up to wear and tear and get a new ID card. Later that same week you learn that several of your classmates had the same problem! After a little investigation, you discover that a strong magnet was stored underneath a workbench in the workshop. The magnet was the root cause of the demagnetized student ID cards.

The best way to identify the root cause of the problem is to ask questions and gather information. If you have a vague problem, investigating facts is more productive than guessing a solution. Ask yourself questions about the problem. What do you know about the problem? What do you not know? When was the last time it worked correctly? What has changed since then? Can you diagram the process into separate steps? Where in the process is the problem occurring? Be curious, ask questions, gather facts, and make logical deductions rather than assumptions.

Watch Adam Savage from Mythbusters, describe his problem solving process [ ForaTv, 2010 ]. As you watch this section of the video, try to identify the questions he asks and the different strategies he uses.

Adam Savage shared many of his problem solving processes. List the ones you think are the five most important. Your list may be different from other people in your class—that's ok!

  • [Page 3: Developing Problem Solving Processes] Adam Savage shared many of his problem solving processes. List the ones you think are the five most important.

“The ability to ask the right question is more than half the battle of finding the answer.” — Thomas J. Watson , founder of IBM

Voices From the Field: Solving Problems

In manufacturing facilities and machine shops, everyone on the floor is expected to know how to identify problems and find solutions. Today's employers look for the following skills in new employees: to analyze a problem logically, formulate a solution, and effectively communicate with others.

In this video, industry professionals share their own problem solving processes, the problem solving expectations of their employees, and an example of how a problem was solved.

Meet the Partners:

  • Taconic High School in Pittsfield, Massachusetts, is a comprehensive, fully accredited high school with special programs in Health Technology, Manufacturing Technology, and Work-Based Learning.
  • Berkshire Community College in Pittsfield, Massachusetts, prepares its students with applied manufacturing technical skills, providing hands-on experience at industrial laboratories and manufacturing facilities, and instructing them in current technologies.
  • H.C. Starck in Newton, Massachusetts, specializes in processing and manufacturing technology metals, such as tungsten, niobium, and tantalum. In almost 100 years of experience, they hold over 900 patents, and continue to innovate and develop new products.
  • Nypro Healthcare in Devens, Massachusetts, specializes in precision injection-molded healthcare products. They are committed to good manufacturing processes including lean manufacturing and process validation.

Making Decisions

Now that you have a couple problem solving strategies in your toolbox, let's practice. In this exercise, you are given a scenario and you will be asked to decide what steps you would take to identify and solve the problem.

Scenario: You are a new employee and have just finished your training. As your first project, you have been assigned the milling of several additional components for a regular customer. Together, you and your trainer, Bill, set up for the first run. Checking your paperwork, you gather the tools and materials on the list. As you are mounting the materials on the table, you notice that you didn't grab everything and hurriedly grab a few more items from one of the bins. Once the material is secured on the CNC table, you load tools into the tool carousel in the order listed on the tool list and set the fixture offsets.

Bill tells you that since this is a rerun of a job several weeks ago, the CAD/CAM model has already been converted to CNC G-code. Bill helps you download the code to the CNC machine. He gives you the go-ahead and leaves to check on another employee. You decide to start your first run.

What problems did you observe in the video?

  • [Page 5: Making Decisions] What problems did you observe in the video?
  • What do you do next?
  • Try to fix it yourself.
  • Ask your trainer for help.

As you are cleaning up, you think about what happened and wonder why it happened. You try to create a mental picture of what happened. You are not exactly sure what the end mill hit, but it looked like it might have hit the dowel pin. You wonder if you grabbed the correct dowel pins from the bins earlier.

You can think of two possible next steps. You can recheck the dowel pin length to make sure it is the correct length, or do a dry run using the CNC single step or single block function with the spindle empty to determine what actually happened.

screenshot of cnc problem

  • Check the dowel pins.
  • Use the single step/single block function to determine what happened.

You notice that your trainer, Bill, is still on the floor and decide to ask him for help. You describe the problem to him. Bill asks if you know what the end mill ran into. You explain that you are not sure but you think it was the dowel pin. Bill reminds you that it is important to understand what happened so you can fix the correct problem. He suggests that you start all over again and begin with a dry run using the single step/single block function, with the spindle empty, to determine what it hit. Or, since it happened at the end, he mentions that you can also check the G-code to make sure the Z-axis is raised before returning to the home position.

ask help from a more experienced person

  • Run the single step/single block function.
  • Edit the G-code to raise the Z-axis.

You finish cleaning up and check the CNC for any damage. Luckily, everything looks good. You check your paperwork and gather the components and materials again. You look at the dowel pins you used earlier, and discover that they are not the right length. As you go to grab the correct dowel pins, you have to search though several bins. For the first time, you are aware of the mess - it looks like the dowel pins and other items have not been put into the correctly labeled bins. You spend 30 minutes straightening up the bins and looking for the correct dowel pins.

Finally finding them, you finish setting up. You load tools into the tool carousel in the order listed on the tool list and set the fixture offsets. Just to make sure, you use the CNC single step/single block function, to do a dry run of the part. Everything looks good! You are ready to create your first part. The first component is done, and, as you admire your success, you notice that the part feels hotter than it should.

You wonder why? You go over the steps of the process to mentally figure out what could be causing the residual heat. You wonder if there is a problem with the CNC's coolant system or if the problem is in the G-code.

  • Look at the G-code.

After thinking about the problem, you decide that maybe there's something wrong with the setup. First, you clean up the damaged materials and remove the broken tool. You check the CNC machine carefully for any damage. Luckily, everything looks good. It is time to start over again from the beginning.

You again check your paperwork and gather the tools and materials on the setup sheet. After securing the new materials, you use the CNC single step/single block function with the spindle empty, to do a dry run of the part. You watch carefully to see if you can figure out what happened. It looks to you like the spindle barely misses hitting the dowel pin. You determine that the end mill was broken when it hit the dowel pin while returning to the start position.

idea at cnc machine

After conducting a dry run using the single step/single block function, you determine that the end mill was damaged when it hit the dowel pin on its return to the home position. You discuss your options with Bill. Together, you decide the best thing to do would be to edit the G-code and raise the Z-axis before returning to home. You open the CNC control program and edit the G-code. Just to make sure, you use the CNC single step/single block function, to do another dry run of the part. You are ready to create your first part. It works. You first part is completed. Only four more to go.

software or hardware problem

As you are cleaning up, you notice that the components are hotter than you expect and the end mill looks more worn than it should be. It dawns on you that while you were milling the component, the coolant didn't turn on. You wonder if it is a software problem in the G-code or hardware problem with the CNC machine.

It's the end of the day and you decide to finish the rest of the components in the morning.

  • You decide to look at the G-code in the morning.
  • You leave a note on the machine, just in case.

You decide that the best thing to do would be to edit the G-code and raise the Z-axis of the spindle before it returns to home. You open the CNC control program and edit the G-code.

While editing the G-code to raise the Z-axis, you notice that the coolant is turned off at the beginning of the code and at the end of the code. The coolant command error caught your attention because your coworker, Mark, mentioned having a similar issue during lunch. You change the coolant command to turn the mist on.

  • You decide to talk with your supervisor.
  • You discuss what happened with a coworker over lunch.

As you reflect on the residual heat problem, you think about the machining process and the factors that could have caused the issue. You try to think of anything and everything that could be causing the issue. Are you using the correct tool for the specified material? Are you using the specified material? Is it running at the correct speed? Is there enough coolant? Are there chips getting in the way?

Wait, was the coolant turned on? As you replay what happened in your mind, you wonder why the coolant wasn't turned on. You decide to look at the G-code to find out what is going on.

From the milling machine computer, you open the CNC G-code. You notice that there are no coolant commands. You add them in and on the next run, the coolant mist turns on and the residual heat issues is gone. Now, its on to creating the rest of the parts.

Have you ever used brainstorming to solve a problem? Chances are, you've probably have, even if you didn't realize it.

You notice that your trainer, Bill, is on the floor and decide to ask him for help. You describe the problem with the end mill breaking, and how you discovered that items are not being returned to the correctly labeled bins. You think this caused you to grab the incorrect length dowel pins on your first run. You have sorted the bins and hope that the mess problem is fixed. You then go on to tell Bill about the residual heat issue with the completed part.

Together, you go to the milling machine. Bill shows you how to check the oil and coolant levels. Everything looks good at the machine level. Next, on the CNC computer, you open the CNC G-code. While looking at the code, Bill points out that there are no coolant commands. Bill adds them in and when you rerun the program, it works.

Bill is glad you mentioned the problem to him. You are the third worker to mention G-code issues over the last week. You noticed the coolant problems in your G-code, John noticed a Z-axis issue in his G-code, and Sam had issues with both the Z-axis and the coolant. Chances are, there is a bigger problem and Bill will need to investigate the root cause .

Talking with Bill, you discuss the best way to fix the problem. Bill suggests editing the G-code to raise the Z-axis of the spindle before it returns to its home position. You open the CNC control program and edit the G-code. Following the setup sheet, you re-setup the job and use the CNC single step/single block function, to do another dry run of the part. Everything looks good, so you run the job again and create the first part. It works. Since you need four of each component, you move on to creating the rest of them before cleaning up and leaving for the day.

It's a new day and you have new components to create. As you are setting up, you go in search of some short dowel pins. You discover that the bins are a mess and components have not been put away in the correctly labeled bins. You wonder if this was the cause of yesterday's problem. As you reorganize the bins and straighten up the mess, you decide to mention the mess issue to Bill in your afternoon meeting.

You describe the bin mess and using the incorrect length dowels to Bill. He is glad you mentioned the problem to him. You are not the first person to mention similar issues with tools and parts not being put away correctly. Chances are there is a bigger safety issue here that needs to be addressed in the next staff meeting.

In any workplace, following proper safety and cleanup procedures is always important. This is especially crucial in manufacturing where people are constantly working with heavy, costly and sometimes dangerous equipment. When issues and problems arise, it is important that they are addressed in an efficient and timely manner. Effective communication is an important tool because it can prevent problems from recurring, avoid injury to personnel, reduce rework and scrap, and ultimately, reduce cost, and save money.

You now know that the end mill was damaged when it hit the dowel pin. It seems to you that the easiest thing to do would be to edit the G-code and raise the Z-axis position of the spindle before it returns to the home position. You open the CNC control program and edit the G-code, raising the Z-axis. Starting over, you follow the setup sheet and re-setup the job. This time, you use the CNC single step/single block function, to do another dry run of the part. Everything looks good, so you run the job again and create the first part.

At the end of the day, you are reviewing your progress with your trainer, Bill. After you describe the day's events, he reminds you to always think about safety and the importance of following work procedures. He decides to bring the issue up in the next morning meeting as a reminder to everyone.

In any workplace, following proper procedures (especially those that involve safety) is always important. This is especially crucial in manufacturing where people are constantly working with heavy, costly, and sometimes dangerous equipment. When issues and problems arise, it is important that they are addressed in an efficient and timely manner. Effective communication is an important tool because it can prevent problems from recurring, avoid injury to personnel, reduce rework and scrap, and ultimately, reduce cost, and save money. One tool to improve communication is the morning meeting or huddle.

The next morning, you check the G-code to determine what is wrong with the coolant. You notice that the coolant is turned off at the beginning of the code and also at the end of the code. This is strange. You change the G-code to turn the coolant on at the beginning of the run and off at the end. This works and you create the rest of the parts.

Throughout the day, you keep wondering what caused the G-code error. At lunch, you mention the G-code error to your coworker, John. John is not surprised. He said that he encountered a similar problem earlier this week. You decide to talk with your supervisor the next time you see him.

You are in luck. You see your supervisor by the door getting ready to leave. You hurry over to talk with him. You start off by telling him about how you asked Bill for help. Then you tell him there was a problem and the end mill was damaged. You describe the coolant problem in the G-code. Oh, and by the way, John has seen a similar problem before.

Your supervisor doesn't seem overly concerned, errors happen. He tells you "Good job, I am glad you were able to fix the issue." You are not sure whether your supervisor understood your explanation of what happened or that it had happened before.

The challenge of communicating in the workplace is learning how to share your ideas and concerns. If you need to tell your supervisor that something is not going well, it is important to remember that timing, preparation, and attitude are extremely important.

It is the end of your shift, but you want to let the next shift know that the coolant didn't turn on. You do not see your trainer or supervisor around. You decide to leave a note for the next shift so they are aware of the possible coolant problem. You write a sticky note and leave it on the monitor of the CNC control system.

How effective do you think this solution was? Did it address the problem?

In this scenario, you discovered several problems with the G-code that need to be addressed. When issues and problems arise, it is important that they are addressed in an efficient and timely manner. Effective communication is an important tool because it can prevent problems from recurring and avoid injury to personnel. The challenge of communicating in the workplace is learning how and when to share your ideas and concerns. If you need to tell your co-workers or supervisor that there is a problem, it is important to remember that timing and the method of communication are extremely important.

You are able to fix the coolant problem in the G-code. While you are glad that the problem is fixed, you are worried about why it happened in the first place. It is important to remember that if a problem keeps reappearing, you may not be fixing the right problem. You may only be addressing the symptoms.

You decide to talk to your trainer. Bill is glad you mentioned the problem to him. You are the third worker to mention G-code issues over the last week. You noticed the coolant problems in your G-code, John noticed a Z-axis issue in his G-code, and Sam had issues with both the Z-axis and the coolant. Chances are, there is a bigger problem and Bill will need to investigate the root cause .

Over lunch, you ask your coworkers about the G-code problem and what may be causing the error. Several people mention having similar problems but do not know the cause.

You have now talked to three coworkers who have all experienced similar coolant G-code problems. You make a list of who had the problem, when they had the problem, and what each person told you.

When you see your supervisor later that afternoon, you are ready to talk with him. You describe the problem you had with your component and the damaged bit. You then go on to tell him about talking with Bill and discovering the G-code issue. You show him your notes on your coworkers' coolant issues, and explain that you think there might be a bigger problem.

You supervisor thanks you for your initiative in identifying this problem. It sounds like there is a bigger problem and he will need to investigate the root cause. He decides to call a team huddle to discuss the issue, gather more information, and talk with the team about the importance of communication.

Root Cause Analysis

flower root cause of a problem

Root cause analysis ( RCA ) is a method of problem solving that identifies the underlying causes of an issue. Root cause analysis helps people answer the question of why the problem occurred in the first place. RCA uses clear cut steps in its associated tools, like the "5 Whys Analysis" and the "Cause and Effect Diagram," to identify the origin of the problem, so that you can:

  • Determine what happened.
  • Determine why it happened.
  • Fix the problem so it won’t happen again.

RCA works under the idea that systems and events are connected. An action in one area triggers an action in another, and another, and so on. By tracing back these actions, you can discover where the problem started and how it developed into the problem you're now facing. Root cause analysis can prevent problems from recurring, reduce injury to personnel, reduce rework and scrap, and ultimately, reduce cost and save money. There are many different RCA techniques available to determine the root cause of a problem. These are just a few:

  • Root Cause Analysis Tools
  • 5 Whys Analysis
  • Fishbone or Cause and Effect Diagram
  • Pareto Analysis

5 whys diagram root cause

How Huddles Work

group huddle discussion meeting

Communication is a vital part of any setting where people work together. Effective communication helps employees and managers form efficient teams. It builds trusts between employees and management, and reduces unnecessary competition because each employee knows how their part fits in the larger goal.

One tool that management can use to promote communication in the workplace is the huddle . Just like football players on the field, a huddle is a short meeting where everyone is standing in a circle. A daily team huddle ensures that team members are aware of changes to the schedule, reiterated problems and safety issues, and how their work impacts one another. When done right, huddles create collaboration, communication, and accountability to results. Impromptu huddles can be used to gather information on a specific issue and get each team member's input.

The most important thing to remember about huddles is that they are short, lasting no more than 10 minutes, and their purpose is to communicate and identify. In essence, a huddle’s purpose is to identify priorities, communicate essential information, and discover roadblocks to productivity.

Who uses huddles? Many industries and companies use daily huddles. At first thought, most people probably think of hospitals and their daily patient update meetings, but lots of managers use daily meetings to engage their employees. Here are a few examples:

  • Brian Scudamore, CEO of 1-800-Got-Junk? , uses the daily huddle as an operational tool to take the pulse of his employees and as a motivational tool. Watch a morning huddle meeting .
  • Fusion OEM, an outsourced manufacturing and production company. What do employees take away from the daily huddle meeting .
  • Biz-Group, a performance consulting group. Tips for a successful huddle .

Brainstorming

brainstorming small lightbulbs combined become a big idea

One tool that can be useful in problem solving is brainstorming . Brainstorming is a creativity technique designed to generate a large number of ideas for the solution to a problem. The method was first popularized in 1953 by Alex Faickney Osborn in the book Applied Imagination . The goal is to come up with as many ideas as you can in a fixed amount of time. Although brainstorming is best done in a group, it can be done individually. Like most problem solving techniques, brainstorming is a process.

  • Define a clear objective.
  • Have an agreed a time limit.
  • During the brainstorming session, write down everything that comes to mind, even if the idea sounds crazy.
  • If one idea leads to another, write down that idea too.
  • Combine and refine ideas into categories of solutions.
  • Assess and analyze each idea as a potential solution.

When used during problem solving, brainstorming can offer companies new ways of encouraging staff to think creatively and improve production. Brainstorming relies on team members' diverse experiences, adding to the richness of ideas explored. This means that you often find better solutions to the problems. Team members often welcome the opportunity to contribute ideas and can provide buy-in for the solution chosen—after all, they are more likely to be committed to an approach if they were involved in its development. What's more, because brainstorming is fun, it helps team members bond.

  • Watch Peggy Morgan Collins, a marketing executive at Power Curve Communications discuss How to Stimulate Effective Brainstorming .
  • Watch Kim Obbink, CEO of Filter Digital, a digital content company, and her team share their top five rules for How to Effectively Generate Ideas .

Importance of Good Communication and Problem Description

talking too much when describing a problem

Communication is one of the most frequent activities we engage in on a day-to-day basis. At some point, we have all felt that we did not effectively communicate an idea as we would have liked. The key to effective communication is preparation. Rather than attempting to haphazardly improvise something, take a few minutes and think about what you want say and how you will say it. If necessary, write yourself a note with the key points or ideas in the order you want to discuss them. The notes can act as a reminder or guide when you talk to your supervisor.

Tips for clear communication of an issue:

  • Provide a clear summary of your problem. Start at the beginning, give relevant facts, timelines, and examples.
  • Avoid including your opinion or personal attacks in your explanation.
  • Avoid using words like "always" or "never," which can give the impression that you are exaggerating the problem.
  • If this is an ongoing problem and you have collected documentation, give it to your supervisor once you have finished describing the problem.
  • Remember to listen to what's said in return; communication is a two-way process.

Not all communication is spoken. Body language is nonverbal communication that includes your posture, your hands and whether you make eye contact. These gestures can be subtle or overt, but most importantly they communicate meaning beyond what is said. When having a conversation, pay attention to how you stand. A stiff position with arms crossed over your chest may imply that you are being defensive even if your words state otherwise. Shoving your hands in your pockets when speaking could imply that you have something to hide. Be wary of using too many hand gestures because this could distract listeners from your message.

The challenge of communicating in the workplace is learning how and when to share your ideas or concerns. If you need to tell your supervisor or co-worker about something that is not going well, keep in mind that good timing and good attitude will go a long way toward helping your case.

Like all skills, effective communication needs to be practiced. Toastmasters International is perhaps the best known public speaking organization in the world. Toastmasters is open to anyone who wish to improve their speaking skills and is willing to put in the time and effort to do so. To learn more, visit Toastmasters International .

Methods of Communication

different ways to communicate

Communication of problems and issues in any workplace is important, particularly when safety is involved. It is therefore crucial in manufacturing where people are constantly working with heavy, costly, and sometimes dangerous equipment. As issues and problems arise, they need to be addressed in an efficient and timely manner. Effective communication is an important skill because it can prevent problems from recurring, avoid injury to personnel, reduce rework and scrap, and ultimately, reduce cost and save money.

There are many different ways to communicate: in person, by phone, via email, or written. There is no single method that fits all communication needs, each one has its time and place.

In person: In the workplace, face-to-face meetings should be utilized whenever possible. Being able to see the person you need to speak to face-to-face gives you instant feedback and helps you gauge their response through their body language. Be careful of getting sidetracked in conversation when you need to communicate a problem.

Email: Email has become the communication standard for most businesses. It can be accessed from almost anywhere and is great for things that don’t require an immediate response. Email is a great way to communicate non-urgent items to large amounts of people or just your team members. One thing to remember is that most people's inboxes are flooded with emails every day and unless they are hyper vigilant about checking everything, important items could be missed. For issues that are urgent, especially those around safety, email is not always be the best solution.

Phone: Phone calls are more personal and direct than email. They allow us to communicate in real time with another person, no matter where they are. Not only can talking prevent miscommunication, it promotes a two-way dialogue. You don’t have to worry about your words being altered or the message arriving on time. However, mobile phone use and the workplace don't always mix. In particular, using mobile phones in a manufacturing setting can lead to a variety of problems, cause distractions, and lead to serious injury.

Written: Written communication is appropriate when detailed instructions are required, when something needs to be documented, or when the person is too far away to easily speak with over the phone or in person.

There is no "right" way to communicate, but you should be aware of how and when to use the appropriate form of communication for your situation. When deciding the best way to communicate with a co-worker or manager, put yourself in their shoes, and think about how you would want to learn about the issue. Also, consider what information you would need to know to better understand the issue. Use your good judgment of the situation and be considerate of your listener's viewpoint.

Did you notice any other potential problems in the previous exercise?

  • [Page 6:] Did you notice any other potential problems in the previous exercise?

Summary of Strategies

In this exercise, you were given a scenario in which there was a problem with a component you were creating on a CNC machine. You were then asked how you wanted to proceed. Depending on your path through this exercise, you might have found an easy solution and fixed it yourself, asked for help and worked with your trainer, or discovered an ongoing G-code problem that was bigger than you initially thought.

When issues and problems arise, it is important that they are addressed in an efficient and timely manner. Communication is an important tool because it can prevent problems from recurring, avoid injury to personnel, reduce rework and scrap, and ultimately, reduce cost, and save money. Although, each path in this exercise ended with a description of a problem solving tool for your toolbox, the first step is always to identify the problem and define the context in which it happened.

There are several strategies that can be used to identify the root cause of a problem. Root cause analysis (RCA) is a method of problem solving that helps people answer the question of why the problem occurred. RCA uses a specific set of steps, with associated tools like the “5 Why Analysis" or the “Cause and Effect Diagram,” to identify the origin of the problem, so that you can:

Once the underlying cause is identified and the scope of the issue defined, the next step is to explore possible strategies to fix the problem.

If you are not sure how to fix the problem, it is okay to ask for help. Problem solving is a process and a skill that is learned with practice. It is important to remember that everyone makes mistakes and that no one knows everything. Life is about learning. It is okay to ask for help when you don’t have the answer. When you collaborate to solve problems you improve workplace communication and accelerates finding solutions as similar problems arise.

One tool that can be useful for generating possible solutions is brainstorming . Brainstorming is a technique designed to generate a large number of ideas for the solution to a problem. The method was first popularized in 1953 by Alex Faickney Osborn in the book Applied Imagination. The goal is to come up with as many ideas as you can, in a fixed amount of time. Although brainstorming is best done in a group, it can be done individually.

Depending on your path through the exercise, you may have discovered that a couple of your coworkers had experienced similar problems. This should have been an indicator that there was a larger problem that needed to be addressed.

In any workplace, communication of problems and issues (especially those that involve safety) is always important. This is especially crucial in manufacturing where people are constantly working with heavy, costly, and sometimes dangerous equipment. When issues and problems arise, it is important that they be addressed in an efficient and timely manner. Effective communication is an important tool because it can prevent problems from recurring, avoid injury to personnel, reduce rework and scrap, and ultimately, reduce cost and save money.

One strategy for improving communication is the huddle . Just like football players on the field, a huddle is a short meeting with everyone standing in a circle. A daily team huddle is a great way to ensure that team members are aware of changes to the schedule, any problems or safety issues are identified and that team members are aware of how their work impacts one another. When done right, huddles create collaboration, communication, and accountability to results. Impromptu huddles can be used to gather information on a specific issue and get each team member's input.

To learn more about different problem solving strategies, choose an option below. These strategies accompany the outcomes of different decision paths in the problem solving exercise.

  • View Problem Solving Strategies Select a strategy below... Root Cause Analysis How Huddles Work Brainstorming Importance of Good Problem Description Methods of Communication

Communication is one of the most frequent activities we engage in on a day-to-day basis. At some point, we have all felt that we did not effectively communicate an idea as we would have liked. The key to effective communication is preparation. Rather than attempting to haphazardly improvise something, take a few minutes and think about what you want say and how you will say it. If necessary, write yourself a note with the key points or ideas in the order you want to discuss them. The notes can act as a reminder or guide during your meeting.

  • Provide a clear summary of the problem. Start at the beginning, give relevant facts, timelines, and examples.

In person: In the workplace, face-to-face meetings should be utilized whenever possible. Being able to see the person you need to speak to face-to-face gives you instant feedback and helps you gauge their response in their body language. Be careful of getting sidetracked in conversation when you need to communicate a problem.

There is no "right" way to communicate, but you should be aware of how and when to use the appropriate form of communication for the situation. When deciding the best way to communicate with a co-worker or manager, put yourself in their shoes, and think about how you would want to learn about the issue. Also, consider what information you would need to know to better understand the issue. Use your good judgment of the situation and be considerate of your listener's viewpoint.

"Never try to solve all the problems at once — make them line up for you one-by-one.” — Richard Sloma

Problem Solving: An Important Job Skill

Problem solving improves efficiency and communication on the shop floor. It increases a company's efficiency and profitability, so it's one of the top skills employers look for when hiring new employees. Recent industry surveys show that employers consider soft skills, such as problem solving, as critical to their business’s success.

The 2011 survey, "Boiling Point? The skills gap in U.S. manufacturing ," polled over a thousand manufacturing executives who reported that the number one skill deficiency among their current employees is problem solving, which makes it difficult for their companies to adapt to the changing needs of the industry.

In this video, industry professionals discuss their expectations and present tips for new employees joining the manufacturing workforce.

Quick Summary

  • [Quick Summary: Question1] What are two things you learned in this case study?
  • What question(s) do you still have about the case study?
  • [Quick Summary: Question2] What question(s) do you still have about the case study?
  • Is there anything you would like to learn more about with respect to this case study?
  • [Quick Summary: Question3] Is there anything you would like to learn more about with respect to this case study?

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Problem-Based Learning (PBL)

What is Problem-Based Learning (PBL)? PBL is a student-centered approach to learning that involves groups of students working to solve a real-world problem, quite different from the direct teaching method of a teacher presenting facts and concepts about a specific subject to a classroom of students. Through PBL, students not only strengthen their teamwork, communication, and research skills, but they also sharpen their critical thinking and problem-solving abilities essential for life-long learning.

See also: Just-in-Time Teaching

Problem-Based Learning (PBL)

In implementing PBL, the teaching role shifts from that of the more traditional model that follows a linear, sequential pattern where the teacher presents relevant material, informs the class what needs to be done, and provides details and information for students to apply their knowledge to a given problem. With PBL, the teacher acts as a facilitator; the learning is student-driven with the aim of solving the given problem (note: the problem is established at the onset of learning opposed to being presented last in the traditional model). Also, the assignments vary in length from relatively short to an entire semester with daily instructional time structured for group work.

Pbl

By working with PBL, students will:

  • Become engaged with open-ended situations that assimilate the world of work
  • Participate in groups to pinpoint what is known/ not known and the methods of finding information to help solve the given problem.
  • Investigate a problem; through critical thinking and problem solving, brainstorm a list of unique solutions.
  • Analyze the situation to see if the real problem is framed or if there are other problems that need to be solved.

How to Begin PBL

  • Establish the learning outcomes (i.e., what is it that you want your students to really learn and to be able to do after completing the learning project).
  • Find a real-world problem that is relevant to the students; often the problems are ones that students may encounter in their own life or future career.
  • Discuss pertinent rules for working in groups to maximize learning success.
  • Practice group processes: listening, involving others, assessing their work/peers.
  • Explore different roles for students to accomplish the work that needs to be done and/or to see the problem from various perspectives depending on the problem (e.g., for a problem about pollution, different roles may be a mayor, business owner, parent, child, neighboring city government officials, etc.).
  • Determine how the project will be evaluated and assessed. Most likely, both self-assessment and peer-assessment will factor into the assignment grade.

Designing Classroom Instruction

See also: Inclusive Teaching Strategies

  • Take the curriculum and divide it into various units. Decide on the types of problems that your students will solve. These will be your objectives.
  • Determine the specific problems that most likely have several answers; consider student interest.
  • Arrange appropriate resources available to students; utilize other teaching personnel to support students where needed (e.g., media specialists to orientate students to electronic references).
  • Decide on presentation formats to communicate learning (e.g., individual paper, group PowerPoint, an online blog, etc.) and appropriate grading mechanisms (e.g., rubric).
  • Decide how to incorporate group participation (e.g., what percent, possible peer evaluation, etc.).

How to Orchestrate a PBL Activity

  • Explain Problem-Based Learning to students: its rationale, daily instruction, class expectations, grading.
  • Serve as a model and resource to the PBL process; work in-tandem through the first problem
  • Help students secure various resources when needed.
  • Supply ample class time for collaborative group work.
  • Give feedback to each group after they share via the established format; critique the solution in quality and thoroughness. Reinforce to the students that the prior thinking and reasoning process in addition to the solution are important as well.

Teacher’s Role in PBL

See also: Flipped teaching

As previously mentioned, the teacher determines a problem that is interesting, relevant, and novel for the students. It also must be multi-faceted enough to engage students in doing research and finding several solutions. The problems stem from the unit curriculum and reflect possible use in future work situations.

  • Determine a problem aligned with the course and your students. The problem needs to be demanding enough that the students most likely cannot solve it on their own. It also needs to teach them new skills. When sharing the problem with students, state it in a narrative complete with pertinent background information without excessive information. Allow the students to find out more details as they work on the problem.
  • Place students in groups, well-mixed in diversity and skill levels, to strengthen the groups. Help students work successfully. One way is to have the students take on various roles in the group process after they self-assess their strengths and weaknesses.
  • Support the students with understanding the content on a deeper level and in ways to best orchestrate the various stages of the problem-solving process.

The Role of the Students

See also: ADDIE model

The students work collaboratively on all facets of the problem to determine the best possible solution.

  • Analyze the problem and the issues it presents. Break the problem down into various parts. Continue to read, discuss, and think about the problem.
  • Construct a list of what is known about the problem. What do your fellow students know about the problem? Do they have any experiences related to the problem? Discuss the contributions expected from the team members. What are their strengths and weaknesses? Follow the rules of brainstorming (i.e., accept all answers without passing judgment) to generate possible solutions for the problem.
  • Get agreement from the team members regarding the problem statement.
  • Put the problem statement in written form.
  • Solicit feedback from the teacher.
  • Be open to changing the written statement based on any new learning that is found or feedback provided.
  • Generate a list of possible solutions. Include relevant thoughts, ideas, and educated guesses as well as causes and possible ways to solve it. Then rank the solutions and select the solution that your group is most likely to perceive as the best in terms of meeting success.
  • Include what needs to be known and done to solve the identified problems.
  • Prioritize the various action steps.
  • Consider how the steps impact the possible solutions.
  • See if the group is in agreement with the timeline; if not, decide how to reach agreement.
  • What resources are available to help (e.g., textbooks, primary/secondary sources, Internet).
  • Determine research assignments per team members.
  • Establish due dates.
  • Determine how your group will present the problem solution and also identify the audience. Usually, in PBL, each group presents their solutions via a team presentation either to the class of other students or to those who are related to the problem.
  • Both the process and the results of the learning activity need to be covered. Include the following: problem statement, questions, data gathered, data analysis, reasons for the solution(s) and/or any recommendations reflective of the data analysis.
  • A well-stated problem and conclusion.
  • The process undertaken by the group in solving the problem, the various options discussed, and the resources used.
  • Your solution’s supporting documents, guests, interviews and their purpose to be convincing to your audience.
  • In addition, be prepared for any audience comments and questions. Determine who will respond and if your team doesn’t know the answer, admit this and be open to looking into the question at a later date.
  • Reflective thinking and transfer of knowledge are important components of PBL. This helps the students be more cognizant of their own learning and teaches them how to ask appropriate questions to address problems that need to be solved. It is important to look at both the individual student and the group effort/delivery throughout the entire process. From here, you can better determine what was learned and how to improve. The students should be asked how they can apply what was learned to a different situation, to their own lives, and to other course projects.

See also: Kirkpatrick Model: Four Levels of Learning Evaluation

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I am a professor of Educational Technology. I have worked at several elite universities. I hold a PhD degree from the University of Illinois and a master's degree from Purdue University.

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Thinking and Intelligence

Introduction to thinking and problem-solving, what you’ll learn to do: describe cognition and problem-solving strategies.

A man sitting down in "The Thinker" pose.

Imagine all of your thoughts as if they were physical entities, swirling rapidly inside your mind. How is it possible that the brain is able to move from one thought to the next in an organized, orderly fashion? The brain is endlessly perceiving, processing, planning, organizing, and remembering—it is always active. Yet, you don’t notice most of your brain’s activity as you move throughout your daily routine. This is only one facet of the complex processes involved in cognition. Simply put, cognition is thinking, and it encompasses the processes associated with perception, knowledge, problem solving, judgment, language, and memory. Scientists who study cognition are searching for ways to understand how we integrate, organize, and utilize our conscious cognitive experiences without being aware of all of the unconscious work that our brains are doing (for example, Kahneman, 2011).

Learning Objectives

  • Distinguish between concepts and prototypes
  • Explain the difference between natural and artificial concepts
  • Describe problem solving strategies, including algorithms and heuristics
  • Explain some common roadblocks to effective problem solving

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7 Thinking, Language, and Problem Solving

Three different artistic portrayals of a person in thought are shown. From left to right, a painting of a woman with an open book, a sculpture of a man hunched over, head on chin, and a ink painting of a man sitting cross-legged holding his head.

What is the best way to solve a problem? How does a person who has never seen or touched snow in real life develop an understanding of the concept of snow? How do young children acquire the ability to learn language with no formal instruction? Psychologists who study thinking explore questions like these and are called cognitive psychologists.

In other chapters, we discussed the cognitive processes of perception, learning, and memory. In this chapter, we will focus on high-level cognitive processes. As a part of this discussion, we will consider thinking and briefly explore the development and use of language. We will also discuss problem solving and creativity. After finishing this chapter, you will have a greater appreciation of the higher-level cognitive processes that contribute to our distinctiveness as a species.

Table of Contents

7.1 What is Cognition? 7.2 Language 7.3 Problem Solving

7.1 What is Cognition?

Learning Objectives

By the end of this section, you will be able to:

  • Describe cognition
  • Distinguish concepts and prototypes
  • Explain the difference between natural and artificial concepts
  • Describe how schemata are organized and constructed

Imagine all of your thoughts as if they were physical entities, swirling rapidly inside your mind. How is it possible that the brain is able to move from one thought to the next in an organized, orderly fashion? The brain is endlessly perceiving, processing, planning, organizing, and remembering—it is always active. Yet, you don’t notice most of your brain’s activity as you move throughout your daily routine. This is only one facet of the complex processes involved in cognition . Simply put,  cognition  is thinking, and it encompasses the processes associated with perception, knowledge, problem solving, judgment, language, and memory. Scientists who study cognition are searching for ways to understand how we integrate, organize, and utilize our conscious cognitive experiences without being aware of all of the unconscious work that our brains are doing (for example, Kahneman, 2011).

Upon waking each morning, you begin thinking—contemplating the tasks that you must complete that day. In what order should you run your errands? Should you go to the bank, the cleaners, or the grocery store first? Can you get these things done before you head to class or will they need to wait until school is done? These thoughts are one example of cognition at work. Exceptionally complex, cognition is an essential feature of human consciousness, yet not all aspects of cognition are consciously experienced.

Cognitive psychology  is the field of psychology dedicated to examining how people think. It attempts to explain how and why we think the way we do by studying the interactions among human thinking, emotion, creativity, language, and problem solving, in addition to other cognitive processes. Cognitive psychologists strive to determine and measure different types of intelligence, why some people are better at problem solving than others, and how emotional intelligence affects success in the workplace, among countless other topics. They also sometimes focus on how we organize thoughts and information gathered from our environments into meaningful categories of thought, which will be discussed later.

Concepts and Prototypes

The human nervous system is capable of handling endless streams of information. The senses serve as the interface between the mind and the external environment, receiving stimuli and translating it into nervous impulses that are transmitted to the brain. The brain then processes this information and uses the relevant pieces to create thoughts, which can then be expressed through language or stored in memory for future use. To make this process more complex, the brain does not gather information from external environments only. When thoughts are formed, the mind synthesizes information from emotions and memories ( Figure 7.2 ). Emotion and memory are powerful influences on both our thoughts and behaviors.

A flow chart is overlaid on a drawing of a head with a ponytail. The flowchart reads: Information, sensations (arrow) emotions, memories (arrow) thoughts (arrow) behavior. Thoughts is also connected to Emotions, memories via a feedback arrow.

Concepts are informed by our semantic memory (you will learn more about semantic memory in a later chapter) and are present in every aspect of our lives; however, one of the easiest places to notice concepts is inside a classroom, where they are discussed explicitly. When you study United States history, for example, you learn about more than just individual events that have happened in America’s past. You absorb a large quantity of information by listening to and participating in discussions, examining maps, and reading first-hand accounts of people’s lives. Your brain analyzes these details and develops an overall understanding of American history. In the process, your brain gathers details that inform and refine your understanding of related concepts like democracy, power, and freedom.

Concepts can be complex and abstract, like justice, or more concrete, like types of birds. Some concepts, like tolerance, are agreed upon by many people, because they have been used in various ways over many years. Other concepts, like the characteristics of your ideal friend or your family’s birthday traditions, are personal and individualized. In this way, concepts touch every aspect of our lives, from our many daily routines to the guiding principles behind the way governments function.

Another technique used by your brain to organize information is the identification of prototypes for the concepts you have developed. A  prototype  is the best example or representation of a concept. For example, what comes to your mind when you think of a dog? Most likely your early experiences with dogs will shape what you imagine. If your first pet was a Golden Retriever, there is a good chance that this would be your prototype for the category of dogs.

Natural and Artificial Concepts

In psychology, concepts can be divided into two categories, natural and artificial. Natural concepts  are created “naturally” through your experiences and can be developed from either direct or indirect experiences. For example, if you live in Essex Junction, Vermont, you have probably had a lot of direct experience with snow. You’ve watched it fall from the sky, you’ve seen lightly falling snow that barely covers the windshield of your car, and you’ve shoveled out 18 inches of fluffy white snow as you’ve thought, “This is perfect for skiing.” You’ve thrown snowballs at your best friend and gone sledding down the steepest hill in town. In short, you know snow. You know what it looks like, smells like, tastes like, and feels like. If, however, you’ve lived your whole life on the island of Saint Vincent in the Caribbean, you may never have actually seen snow, much less tasted, smelled, or touched it. You know snow from the indirect experience of seeing pictures of falling snow—or from watching films that feature snow as part of the setting. Either way, snow is a natural concept because you can construct an understanding of it through direct observations, experiences with snow, or indirect knowledge (such as from films or books) ( Figure 7.3 ).

Two images labeled a and b. A depicts a snowy field on a sunny day. B depicts a sphere, rectangular prism, and triangular prism.

An  artificial concept , on the other hand, is a concept that is defined by a specific set of characteristics. Various properties of geometric shapes, like squares and triangles, serve as useful examples of artificial concepts. A triangle always has three angles and three sides. A square always has four equal sides and four right angles. Mathematical formulas, like the equation for area (length × width) are artificial concepts defined by specific sets of characteristics that are always the same. Artificial concepts can enhance the understanding of a topic by building on one another. For example, before learning the concept of “area of a square” (and the formula to find it), you must understand what a square is. Once the concept of “area of a square” is understood, an understanding of area for other geometric shapes can be built upon the original understanding of area. The use of artificial concepts to define an idea is crucial to communicating with others and engaging in complex thought. According to Goldstone and Kersten (2003), concepts act as building blocks and can be connected in countless combinations to create complex thoughts.

A  schema (plural: schemata)  is a mental construct consisting of a cluster or collection of related concepts (Bartlett, 1932). There are many different types of schemata, and they all have one thing in common: schemata are a method of organizing information that allows the brain to work more efficiently. When a schema is activated, the brain makes immediate assumptions about the person or object being observed.

There are several types of schemata. A  role schema  makes assumptions about how individuals in certain roles will behave (Callero, 1994). For example, imagine you meet someone who introduces himself as a firefighter. When this happens, your brain automatically activates the “firefighter schema” and begins making assumptions that this person is brave, selfless, and community-oriented. Despite not knowing this person, already you have unknowingly made judgments about him. Schemata also help you fill in gaps in the information you receive from the world around you. While schemata allow for more efficient information processing, there can be problems with schemata, regardless of whether they are accurate: Perhaps this particular firefighter is not brave, he just works as a firefighter to pay the bills while studying to become a children’s librarian.

An  event schema , also known as a  cognitive script , is a set of behaviors that can feel like a routine. Think about what you do when you walk into an elevator ( Figure 7.4 ). First, the doors open and you wait to let exiting passengers leave the elevator car. Then, you step into the elevator and turn around to face the doors, looking for the correct button to push. You never face the back of the elevator, do you? And when you’re riding in a crowded elevator and you can’t face the front, it feels uncomfortable, doesn’t it? Interestingly, event schemata can vary widely among different cultures and countries. For example, while it is quite common for people to greet one another with a handshake in the United States, in Tibet, you greet someone by sticking your tongue out at them, and in Belize, you bump fists (Cairns Regional Council, n.d.)

A crowded elevator.

Because event schemata are automatic, they can be difficult to change. Imagine that you are driving home from work or school. This event schema involves getting in the car, shutting the door, and buckling your seatbelt before putting the key in the ignition. You might perform this script two or three times each day. As you drive home, you hear your phone’s ring tone. Typically, the event schema that occurs when you hear your phone ringing involves locating the phone and answering it or responding to your latest text message. So without thinking, you reach for your phone, which could be in your pocket, in your bag, or on the passenger seat of the car. This powerful event schema is informed by your pattern of behavior and the pleasurable stimulation that a phone call or text message gives your brain. Because it is a schema, it is extremely challenging for us to stop reaching for the phone, even though we know that we endanger our own lives and the lives of others while we do it (Neyfakh, 2013) ( Figure 7.5 ).

A hand holds a cellphone in front of a steering wheel and front-shield window of a car. The car is on a road.

Remember the elevator? It feels almost impossible to walk in and  not  face the door. Our powerful event schema dictates our behavior in the elevator, and it is no different with our phones. Current research suggests that it is the habit, or event schema, of checking our phones in many different situations that makes refraining from checking them while driving especially difficult (Bayer & Campbell, 2012). Because texting and driving has become a dangerous epidemic in recent years, psychologists are looking at ways to help people interrupt the “phone schema” while driving. Event schemata like these are the reason why many habits are difficult to break once they have been acquired. As we continue to examine thinking, keep in mind how powerful the forces of concepts and schemata are to our understanding of the world.

7.2 LAnguage

  • Define language and demonstrate familiarity with the components of language
  • Understand the development of language
  • Explain the relationship between language and thinking

Language  is a communication system that involves using words and systematic rules to organize those words to transmit information from one individual to another. While language is a form of communication, not all communication is language. Many species communicate with one another through their postures, movements, odors, or vocalizations. This communication is crucial for species that need to interact and develop social relationships with their conspecifics. However, many people have asserted that it is language that makes humans unique among all of the animal species (Corballis & Suddendorf, 2007; Tomasello & Rakoczy, 2003). This section will focus on what distinguishes language as a special form of communication, how the use of language develops, and how language affects the way we think.

Components of Language

Language, be it spoken, signed, or written, has specific components: a lexicon and lexicon grammar .  Lexicon  refers to the words of a given language. Thus, lexicon is a language’s vocabulary.  Grammar  refers to the set of rules that are used to convey meaning through the use of the lexicon (Fernández & Cairns, 2011). For instance, English grammar dictates that most verbs receive an “-ed” at the end to indicate past tense.

Words are formed by combining the various phonemes that make up the language. A  phoneme  (e.g., the sounds “ah” vs. “eh”) is a basic sound unit of a given language, and different languages have different sets of phonemes. For example, the phoneme English speakers associate with the letter ‘L’ is not used in the Japanese language. Similarly, many Southern African languages use phonemes, sometimes referred to as ‘click consonants’ that are not used in English.

Phonemes are combined to form  morphemes , which are the smallest units of language that convey some type of meaning. Some words are morphemes, but not all morphemes are words.  For example, “-ed” is a morpheme used to convey the past-tense in English, but it is not a word. The word “review” contains two morphemes: re- (meaning to do something again) and view (to see). Finally, some words like “I” and “a” are both a phonemes and morphemes.

We use semantics and syntax to construct language. Semantics and syntax are part of a language’s grammar.  Semantics  refers to the process by which we derive meaning from morphemes and words by connecting those morphemes and words to stored concepts.  Syntax  refers to the way words are organized into sentences (Chomsky, 1965; Fernández & Cairns, 2011). For example, you would never say “the dog walked I today” to let someone know you took your dog for a walk–that sentence does not obey English syntax and is therefore difficult to make sense of.

We apply the rules of grammar to organize the lexicon in novel and creative ways, which allow us to communicate information about both concrete and abstract concepts. We can talk about our immediate and observable surroundings as well as the surface of unseen planets. We can share our innermost thoughts, our plans for the future, and debate the value of a college education. We can provide detailed instructions for cooking a meal, fixing a car, or building a fire. Through our use of words and language, we are able to form, organize, and express ideas, schema, and artificial concepts.

Language Development

Given the remarkable complexity of a language, one might expect that mastering a language would be an especially arduous task; indeed, for those of us trying to learn a second language as adults, this might seem to be true. However, young children master language very quickly with relative ease. B. F.  Skinner  (1957) proposed that language is learned through reinforcement. Noam  Chomsky  (1965) criticized this behaviorist approach, asserting instead that the mechanisms underlying language acquisition are biologically determined. The use of language develops in the absence of formal instruction and appears to follow a very similar pattern in children from vastly different cultures and backgrounds. It would seem, therefore, that we are born with a biological predisposition to acquire a language (Chomsky, 1965; Fernández & Cairns, 2011). Moreover, it appears that there is a critical period for language acquisition, such that this proficiency at acquiring language is maximal early in life; generally, as people age, the ease with which they acquire and master new languages diminishes (Johnson & Newport, 1989; Lenneberg, 1967; Singleton, 1995).

Children begin to learn about language from a very early age ( Table 7.1 ). In fact, it appears that this is occurring even before we are born. Newborns show preference for their mother’s voice and appear to be able to discriminate between the language spoken by their mother and other languages. Babies are also attuned to the languages being used around them and show preferences for videos of faces that are moving in synchrony with the audio of spoken language versus videos that do not synchronize with the audio (Blossom & Morgan, 2006; Pickens, 1994; Spelke & Cortelyou, 1981).

DIG DEEPER: The Case of Genie

In the fall of 1970, a social worker in the Los Angeles area found a 13-year-old girl who was being raised in extremely neglectful and abusive conditions. The girl, who came to be known as Genie, had lived most of her life tied to a potty chair or confined to a crib in a small room that was kept closed with the curtains drawn. For a little over a decade, Genie had virtually no social interaction and no access to the outside world. As a result of these conditions, Genie was unable to stand up, chew solid food, or speak (Fromkin, Krashen, Curtiss, Rigler, & Rigler, 1974; Rymer, 1993). The police took Genie into protective custody.

Genie’s abilities improved dramatically following her removal from her abusive environment, and early on, it appeared she was acquiring language—much later than would be predicted by critical period hypotheses that had been posited at the time (Fromkin et al., 1974). Genie managed to amass an impressive vocabulary in a relatively short amount of time. However, she never developed a mastery of the grammatical aspects of language (Curtiss, 1981). Perhaps being deprived of the opportunity to learn language during a critical period impeded Genie’s ability to fully acquire and use language.

You may recall that each language has its own set of phonemes that are used to generate morphemes, words, and so on. Babies can discriminate among the sounds that make up a language (for example, they can tell the difference between the “s” in vision and the “ss” in fission); early on, they can differentiate between the sounds of all human languages, even those that do not occur in the languages that are used in their environments. However, by the time that they are about 1 year old, they can only discriminate among those phonemes that are used in the language or languages in their environments (Jensen, 2011; Werker & Lalonde, 1988; Werker & Tees, 1984).

After the first few months of life, babies enter what is known as the babbling stage, during which time they tend to produce single syllables that are repeated over and over. As time passes, more variations appear in the syllables that they produce. During this time, it is unlikely that the babies are trying to communicate; they are just as likely to babble when they are alone as when they are with their caregivers (Fernández & Cairns, 2011). Interestingly, babies who are raised in environments in which sign language is used will also begin to show babbling in the gestures of their hands during this stage (Petitto, Holowka, Sergio, Levy, & Ostry, 2004).

Generally, a child’s first word is uttered sometime between the ages of 1 year to 18 months, and for the next few months, the child will remain in the “one word” stage of language development. During this time, children know a number of words, but they only produce one-word utterances. The child’s early vocabulary is limited to familiar objects or events, often nouns. Although children in this stage only make one-word utterances, these words often carry larger meaning (Fernández & Cairns, 2011). So, for example, a child saying “cookie” could be identifying a cookie or asking for a cookie.

As a child’s lexicon grows, she begins to utter simple sentences and to acquire new vocabulary at a very rapid pace. In addition, children begin to demonstrate a clear understanding of the specific rules that apply to their language(s). Even the mistakes that children sometimes make provide evidence of just how much they understand about those rules. This is sometimes seen in the form of  overgeneralization . In this context, overgeneralization refers to an extension of a language rule to an exception to the rule. For example, in English, it is usually the case that an “s” is added to the end of a word to indicate plurality. For example, we speak of one dog versus two dogs. Young children will overgeneralize this rule to cases that are exceptions to the “add an s to the end of the word” rule and say things like “those two gooses” or “three mouses.” Clearly, the rules of the language are understood, even if the exceptions to the rules are still being learned (Moskowitz, 1978).

Language and Thought

When we speak one language, we agree that words are representations of ideas, people, places, and events. The given language that children learn is connected to their culture and surroundings. But can words themselves shape the way we think about things? Psychologists have long investigated the question of whether language shapes thoughts and actions, or whether our thoughts and beliefs shape our language. Two researchers, Edward Sapir and Benjamin Lee Whorf, began this investigation in the 1940s. They wanted to understand how the language habits of a community encourage members of that community to interpret language in a particular manner (Sapir, 1941/1964). Sapir and Whorf proposed that language determines thought. For example, in some languages there are many different words for love. However, in English we use the word love for all types of love. Does this affect how we think about love depending on the language that we speak (Whorf, 1956)? Researchers have since identified this view as too absolute, pointing out a lack of empiricism behind what Sapir and Whorf proposed (Abler, 2013; Boroditsky, 2011; van Troyer, 1994). Today, psychologists continue to study and debate the relationship between language and thought.

WHAT DO YOU THINK? The Meaning of Language

Think about what you know of other languages; perhaps you even speak multiple languages. Imagine for a moment that your closest friend fluently speaks more than one language. Do you think that friend thinks differently, depending on which language is being spoken? You may know a few words that are not translatable from their original language into English. For example, the Portuguese word  saudade  originated during the 15th century, when Portuguese sailors left home to explore the seas and travel to Africa or Asia. Those left behind described the emptiness and fondness they felt as  saudade  ( Figure 7.6 ) .  The word came to express many meanings, including loss, nostalgia, yearning, warm memories, and hope. There is no single word in English that includes all of those emotions in a single description. Do words such as  saudade  indicate that different languages produce different patterns of thought in people? What do you think??

Two paintings are depicted in a and b. A depicts a young boy leaning on a trunk. He looks forlornly past the viewer. B depicts a woman wrapped in a black shawl standing near a window. She reads a letter while holding the shawl to her mouth.

One group of researchers who wanted to investigate how language influences thought compared how English speakers and the Dani people of Papua New Guinea think and speak about color. The Dani have two words for color: one word for  light  and one word for  dark . In contrast, the English language has 11 color words. Researchers hypothesized that the number of color terms could limit the ways that the Dani people conceptualized color. However, the Dani were able to distinguish colors with the same ability as English speakers, despite having fewer words at their disposal (Berlin & Kay, 1969). A recent review of research aimed at determining how language might affect something like color perception suggests that language can influence perceptual phenomena, especially in the left hemisphere of the brain. You may recall from earlier chapters that the left hemisphere is associated with language for most people. However, the right (less linguistic hemisphere) of the brain is less affected by linguistic influences on perception (Regier & Kay, 2009)

7.3 Problem Solving

  • Describe problem solving strategies
  • Define algorithm and heuristic
  • Explain some common roadblocks to effective problem solving and decision making

People face problems every day—usually, multiple problems throughout the day. Sometimes these problems are straightforward: To double a recipe for pizza dough, for example, all that is required is that each ingredient in the recipe be doubled. Sometimes, however, the problems we encounter are more complex. For example, say you have a work deadline, and you must mail a printed copy of a report to your supervisor by the end of the business day. The report is time-sensitive and must be sent overnight. You finished the report last night, but your printer will not work today. What should you do? First, you need to identify the problem and then apply a strategy for solving the problem.

Problem-Solving Strategies

When you are presented with a problem—whether it is a complex mathematical problem or a broken printer, how do you solve it? Before finding a solution to the problem, the problem must first be clearly identified. After that, one of many problem solving strategies can be applied, hopefully resulting in a solution.

A  problem-solving strategy  is a plan of action used to find a solution. Different strategies have different action plans associated with them ( Table 7.2 ). For example, a well-known strategy is  trial and error . The old adage, “If at first you don’t succeed, try, try again” describes trial and error. In terms of your broken printer, you could try checking the ink levels, and if that doesn’t work, you could check to make sure the paper tray isn’t jammed. Or maybe the printer isn’t actually connected to your laptop. When using trial and error, you would continue to try different solutions until you solved your problem. Although trial and error is not typically one of the most time-efficient strategies, it is a commonly used one.

Another type of strategy is an algorithm. An  algorithm  is a problem-solving formula that provides you with step-by-step instructions used to achieve a desired outcome (Kahneman, 2011). You can think of an algorithm as a recipe with highly detailed instructions that produce the same result every time they are performed. Algorithms are used frequently in our everyday lives, especially in computer science. When you run a search on the Internet, search engines like Google use algorithms to decide which entries will appear first in your list of results. Facebook also uses algorithms to decide which posts to display on your newsfeed. Can you identify other situations in which algorithms are used?

A heuristic is another type of problem solving strategy. While an algorithm must be followed exactly to produce a correct result, a  heuristic  is a general problem-solving framework (Tversky & Kahneman, 1974). You can think of these as mental shortcuts that are used to solve problems. A “rule of thumb” is an example of a heuristic. Such a rule saves the person time and energy when making a decision, but despite its time-saving characteristics, it is not always the best method for making a rational decision. Different types of heuristics are used in different types of situations, but the impulse to use a heuristic occurs when one of five conditions is met (Pratkanis, 1989):

  • When one is faced with too much information
  • When the time to make a decision is limited
  • When the decision to be made is unimportant
  • When there is access to very little information to use in making the decision
  • When an appropriate heuristic happens to come to mind in the same moment

Working backwards  is a useful heuristic in which you begin solving the problem by focusing on the end result. Consider this example: You live in Washington, D.C. and have been invited to a wedding at 4 PM on Saturday in Philadelphia. Knowing that Interstate 95 tends to back up any day of the week, you need to plan your route and time your departure accordingly. If you want to be at the wedding service by 3:30 PM, and it takes 2.5 hours to get to Philadelphia without traffic, what time should you leave your house? You use the working backwards heuristic to plan the events of your day on a regular basis, probably without even thinking about it.

Another useful heuristic is the practice of accomplishing a large goal or task by breaking it into a series of smaller steps. Students often use this common method to complete a large research project or long essay for school. For example, students typically brainstorm, develop a thesis or main topic, research the chosen topic, organize their information into an outline, write a rough draft, revise and edit the rough draft, develop a final draft, organize the references list, and proofread their work before turning in the project. The large task becomes less overwhelming when it is broken down into a series of small steps.

EVERYDAY CONNECTION: Solving Puzzles

Problem-solving abilities can improve with practice. Many people challenge themselves every day with puzzles and other mental exercises to sharpen their problem-solving skills. Sudoku puzzles appear daily in most newspapers. Typically, a sudoku puzzle is a 9×9 grid. The simple sudoku below ( Figure 7.7 ) is a 4×4 grid. To solve the puzzle, fill in the empty boxes with a single digit: 1, 2, 3, or 4. Here are the rules: The numbers must total 10 in each bolded box, each row, and each column; however, each digit can only appear once in a bolded box, row, and column. Time yourself as you solve this puzzle and compare your time with a classmate.

A sudoku puzzle is pictured. The puzzle is a 4x4 square with each sub-square also divided into four. Inside the top left square, the numbers are 3, blank, blank, 4 from left-to-right and top-to-bottom. In the top right square, the numbers are blank, two, one, blank. In the bottom left square, the numbers are blank, 3, four, blank; and the bottom right square contains 2, blank, blank, 1.

Here is another popular type of puzzle ( Figure 7.8 ) that challenges your spatial reasoning skills. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper:

Nine dots are arrayed in three rows of three.

Not all problems are successfully solved, however. What challenges stop us from successfully solving a problem? Albert Einstein once said, “Insanity is doing the same thing over and over again and expecting a different result.” Imagine a person in a room that has four doorways. One doorway that has always been open in the past is now locked. The person, accustomed to exiting the room by that particular doorway, keeps trying to get out through the same doorway even though the other three doorways are open. The person is stuck—but she just needs to go to another doorway, instead of trying to get out through the locked doorway. A  mental set  is where you persist in approaching a problem in a way that has worked in the past but is clearly not working now.

The top figure shows a book of matches, a box of tacks, and a candle. The bottom figure shows the box tacked to the wall with the candle standing in the box.

Functional fixedness  is a type of mental set where you cannot perceive an object being used for something other than what it was designed for. Duncker (1945) conducted foundational research on functional fixedness. He created an experiment in which participants were given a candle, a book of matches, and a box of thumbtacks. They were instructed to use those items to attach the candle to the wall so that it did not drip wax onto the table below. Participants had to use functional fixedness to solve the problem ( Figure 7.10 ). During the  Apollo 13  mission to the moon, NASA engineers at Mission Control had to overcome functional fixedness to save the lives of the astronauts aboard the spacecraft. An explosion in a module of the spacecraft damaged multiple systems. The astronauts were in danger of being poisoned by rising levels of carbon dioxide because of problems with the carbon dioxide filters. The engineers found a way for the astronauts to use spare plastic bags, tape, and air hoses to create a makeshift air filter, which saved the lives of the astronauts.

Researchers have investigated whether functional fixedness is affected by culture. In one experiment, individuals from the Shuar group in Ecuador were asked to use an object for a purpose other than that for which the object was originally intended. For example, the participants were told a story about a bear and a rabbit that were separated by a river and asked to select among various objects, including a spoon, a cup, erasers, and so on, to help the animals. The spoon was the only object long enough to span the imaginary river, but if the spoon was presented in a way that reflected its normal usage, it took participants longer to choose the spoon to solve the problem. (German & Barrett, 2005). The researchers wanted to know if exposure to highly specialized tools, as occurs with individuals in industrialized nations, affects their ability to transcend functional fixedness. It was determined that functional fixedness is experienced in both industrialized and nonindustrialized cultures (German & Barrett, 2005).

In order to make good decisions, we use our knowledge and our reasoning. Often, this knowledge and reasoning is sound and solid. Sometimes, however, we are swayed by biases or by others manipulating a situation. For example, let’s say you and three friends wanted to rent a house and had a combined target budget of $1,600. The realtor shows you only very run-down houses for $1,600 and then shows you a very nice house for $2,000. Might you ask each person to pay more in rent to get the $2,000 home? Why would the realtor show you the run-down houses and the nice house? The realtor may be challenging your anchoring bias. An  anchoring bias  occurs when you focus on one piece of information when making a decision or solving a problem. In this case, you’re so focused on the amount of money you are willing to spend that you may not recognize what kinds of houses are available at that price point.

The  confirmation bias  is the tendency to focus on information that confirms your existing beliefs. For example, if you think that your professor is not very nice, you notice all of the instances of rude behavior exhibited by the professor while ignoring the countless pleasant interactions he is involved in on a daily basis.  Hindsight bias  leads you to believe that the event you just experienced was predictable, even though it really wasn’t. In other words, you knew all along that things would turn out the way they did.  Representative bias  describes a faulty way of thinking, in which you unintentionally stereotype someone or something; for example, you may assume that your professors spend their free time reading books and engaging in intellectual conversation, because the idea of them spending their time playing volleyball or visiting an amusement park does not fit in with your stereotypes of professors.

Finally, the  availability heuristic  is a heuristic in which you make a decision based on an example, information, or recent experience that is that readily available to you, even though it may not be the best example to inform your decision .  Biases tend to “preserve that which is already established—to maintain our preexisting knowledge, beliefs, attitudes, and hypotheses” (Aronson, 1995; Kahneman, 2011). These biases are summarized in  Table 7.3 .

Were you able to determine how many marbles are needed to balance the scales in  Figure 7.9 ? You need nine. Were you able to solve the problems in  Figure 7.7  and  Figure 7.8 ? Here are the answers ( Figure 7.11 ).

image

Chapter Summary

7.1 what is cognition.

In this section, you were introduced to cognitive psychology, which is the study of cognition, or the brain’s ability to think, perceive, plan, analyze, and remember. Concepts and their corresponding prototypes help us quickly organize our thinking by creating categories into which we can sort new information. We also develop schemata, which are clusters of related concepts. Some schemata involve routines of thought and behavior, and these help us function properly in various situations without having to “think twice” about them. Schemata show up in social situations and routines of daily behavior.

7.2 Language

Language is a communication system that has both a lexicon and a system of grammar. Language acquisition occurs naturally and effortlessly during the early stages of life, and this acquisition occurs in a predictable sequence for individuals around the world. Language has a strong influence on thought, and the concept of how language may influence cognition remains an area of study and debate in psychology.

Many different strategies exist for solving problems. Typical strategies include trial and error, applying algorithms, and using heuristics. To solve a large, complicated problem, it often helps to break the problem into smaller steps that can be accomplished individually, leading to an overall solution. Roadblocks to problem solving include a mental set, functional fixedness, and various biases that can cloud decision making skills.

thinking; or, all of the processes associated with perception, knowledge, problem solving, judgement, language, and memory.

A modern school of psychological thought that empirically examines mental processes such as perception, memory, language, and judgement.

a category or grouping of linguistic information, images, ideas or memories, such as life experiences.

knowledge about words, concepts, and language-based knowledge and facts

the best example or representation of a concept, specific to an individual

concepts developed through direct or indirect experiences with the world

a concept defined by a specific set of characteristics.

a mental construct consisting of a cluster of related concepts

a set of ideas relating to how individuals in certain roles will behave.

also known as a cognitive script; a set of behaviors associated with a particular place or event

also known as an event schema; a set of behaviors associated with a particular place or event

a communication system that involves using words and systematic rules to organize those words to transmit information from one individual to another.

the words of a language

the rules of a language used to convey meaning through the use of the lexicon

the basic sounds that make up a language

the smallest unit of language that conveys meaning

the process by which we derive meaning from morphemes and words

the rules guiding the organization of morphemes into words and words into sentences.

Psychology 2e Copyright © 2020 by Openstax is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

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Problem-Based Learning

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What is Problem-Based Learning

Problem-based learning & the classroom, the problem-based learning process, problem-based learning & the common core, project example: a better community, project example: preserving appalachia, project example: make an impact.

All Toolkits

A Learning is Open toolkit written by the New Learning Institute.

Problem-based learning (PBL) challenges students to identify and examine real problems, then work together to address and solve those problems through advocacy and by mobilizing resources. Importantly, every aspect of the problem solving process involves students in real work—work that is a reflection of the range of expertise required to solve issues in the world outside of school.

While problem-based learning can use any type of problem as its basis, the approach described here is deliberately focused on local ones. Local problems allow students to have a meaningful voice, and be instrumental in a process where real, recognizable change results. It also gives students opportunities to source and interact with a variety of local experts.

In many classrooms teachers give students information and then ask them to solve problems at the culmination of a unit. Problem-based learning turns this on its head by challenging students to define the problem before finding the resources necessary to address or solve it. In this approach, teachers are facilitators: they set the context for the problem, ask questions to propel students’ interests and learning forward, help students locate necessary resources and experts, and provide multiple opportunities to critique students’ process and progress. In some cases, the teacher may identify a problem that is connected to existing curriculum; in others the teacher may assign a larger topic and challenge the students to identify a specific problem they are interested in addressing.

This approach is interdisciplinary and provides natural opportunities for integrating a variety of required content areas. Because recognizing and making relationships between content areas is a necessary part of the problem-solving process—as it is in the real world—students are building skills to prepare them for life, work, and civic participation. Problem-based learning gives students a variety of ways to address and tackle a problem. It encourages everyone to contribute and rewards different kinds of success. This builds confidence in students who have not always been successful in school. With the changing needs of today’s world, there is a growing urgency for people who are competent in a range of areas including the ability to apply critical thinking to complex problems, collaborate, network and gather resources, and communicate and persuade others to actively take up a cause.

Problem-based learning builds agency & independence

Although students work collaboratively throughout the process, applying a wide range of skills to new tasks requires them to develop their own specialties that lead to greater confidence and competency. And because the process is student-driven, students are challenged to define the problem, conduct comprehensive research, sort through multiple solutions and present the one that allows them best move forward. This reinforces a sense of self-agency and independence.

Problem-based learning promotes adaptability & flexibility

Investigating and solving problems requires students to work with many different types of people and encounter many unknowns throughout the process. These experiences help students learn to be adaptable and flexible during periods of uncertainty. From an academic standpoint, this flexible mindset is an opportunity for students to develop a range of communication aptitudes and styles. For example, in the beginning research phases, students must gather multiple perspectives and gain a clear understanding of their various audiences. As they move into the later project phases they must develop more nuanced ways to communicate with each audience, from clearly presenting information to persuasion to defending the merits of a new idea.

Problem-based learning is persistent

Educators recognize that when students are working towards a real goal they care about, they show increased investment and willingness to persist through challenges. Problem-based learning requires students to navigate many variables including the diverse personalities on a project team, the decisions and perspectives of stakeholders, challenging and rigorous content, and real world deadlines. Students will experience frustration and failure, but they will learn that working though that by trying new things will be its own reward. And this is a critical lesson that will be carried on into life and work.

Problem-based learning is civically engaged

Because problem-based learning focuses on using local issues as jumping off points it gives students a meaningful context in which to voice their opinions and take the initiative to find solutions. Problems within schools and communities also provide opportunities for students to work directly with stakeholders (i.e. the school principal or a town council member) and experts (i.e. local residents, professionals, and business owners). These local connections make it more likely that students will successfully implement some aspect of their plan and gives students firsthand experience with civic processes.

A problem well put is half solved. – John Dewey

The problem-based learning process described in this toolkit has been refined and tested through the Model Classroom Program, a project of the New Learning Institute. Educators throughout the United States participated in this program by designing, implementing, and documenting projects. The resulting problem-based learning approach provides a clear process and diverse set of tools to support problem-based learning.

The problem-based learning process can help students define problems in new ways, explore multiple perspectives, challenge their thinking, and develop the real-world skills needed for planning and carrying out a project. Beyond this, because the approach emphasizes local and community-based issues, this process develops student drive and motivation as they work towards a tangible end result with the potential to impact their community.

Make it Real

The world is full of unsolved problems and opportunities just waiting to be addressed. The Make It Real phase is about identifying a real problem within the local community, then conducting further investigation to define the problem.

Identify what you do and don’t know about the problem Brainstorm what is known about the problem. What do you know about it at the local level? Is this problem globally relevant? How? What questions would you investigate further?

Discover the problem’s root causes and impacts on the community While it’s easy to find a problem, it’s much harder to understand it. Investigate how the problem impacts different people and places. As a result of these investigations, students will gain a clearer understanding of the problem.

Make it Relevant

Problems are everywhere, but it can often be difficult to convince people that a specific problem should matter to them. The word relevant is from the Latin root meaning “to raise” or “to lift up.” To Make It Relevant, elevate the problem so that people in the community and beyond will take interest and become invested in its resolution. Make important connections in order to begin a plan to address the problem.

Field Studies

Collect as much information as possible on the problem. Conduct the kind of research experts in the field—scientists and historians—conduct. While online and library research is a good starting point, it’s important that students get out into the real world to conduct their own original research! This includes using methods such as surveys, interviews, photo and video documentation, collection of evidence (such as science related activities), and working with a variety of experts and viewpoints.

Develop an action-plan Have students analyze their field studies data and create charts, graphs, and other visual representations to understand their findings. After analyzing, students will have the information needed to develop a plan of action. Importantly, they’ll need to consider how best to meet the needs of all stakeholders, which will include a diverse community such as local businesses, community members, experts, and even the natural world.

Make an Impact

Make An Impact with a creative implementation based on the best research-supported ideas. In many cases, making an impact is about solving the problem. Sometimes it’s about addressing it, making representations to stakeholders, or presenting a possible solution for future implementation. At the most rigorous level, students will implement a project that has lasting impact on their community.

Put your plan into action See the hard work of researching and analyzing the problem pay off as students begin implementing their plans. In so doing, they’ll act as part of a team creating a product to share. Depending on the problem, purpose, and audience, their products might be anything from a website to an art installation to the planning of a community-wide event.

Share your findings and make an impact Share results with important stakeholders and the larger community. Depending on the project, this effort may include awareness campaigns, a persuasive presentation to stakeholders, an action-oriented campaign, a community-wide event, or a re-designed program. In many cases this “final” act leads to the beginning of another project!

With the Common Core implementation, teachers have found different strategies and resources to help align their practice to the standards. Indeed, many schools and districts have discovered a variety of solutions. When considering Common Core alignment, the opportunity presented by methods like problem-based learning hinges on a belief in the art of teaching and the importance of developing students’ passion and love of learning. In short, with the ultimate goal of making students college-, career-, and life-ready, it’s essential that educators put students in the driver’s seat to collaboratively solve real problems.

The Common Core ELA standards draw a portrait of a college- and career-ready student. This portrait includes characteristics such as independence, the ability to adapt communication to different audiences and purposes, the ability to comprehend and critique, appreciation for the value of evidence (when reading and when creating their own work), and the capability to make strategic use of digital media. Developing creative solutions to complex problems provides students with multiple opportunities to develop all of these skills.

Independence

Students are challenged to define the problem and conduct comprehensive research, then present solutions. This student-driven process requires students to find multiple answers and think critically about the best way to act, ultimately building confidence and independence.

Adapting Communication to Different Audiences and Purposes

In the initial research phases, students must gather multiple perspectives and gain a clear understanding of who those audiences are. As they move into the later project phases, they must communicate in a variety of ways (including informative and persuasive methods) to reach diverse audiences.

Comprehending and Critiquing

In examining multiple perspectives, students must summarize various viewpoints, addressing their strengths and critiquing their weaknesses. Furthermore, as students develop solutions they must analyze each idea for its potential success, which compels them to critique their own work in addition to the work of others.

Valuing Evidence

Collecting evidence is essential to the process, whether through visual documentation of a problem, uncovering key facts, or collecting narratives from the community.

Strategic Use of Digital Media

The use of digital media is naturally integrated throughout the entire process. The problem-based learning approach not only builds the specific 21st century skills called for by the Common Core, it also embraces practices supported by hundreds of years of educational theory. This is not the next new thing – problem-based learning is one example of how vetted best educational practices will meet the needs of a future economy and society; and, more immediately, the new Common Core Standards.

Language Arts

The Key Design Considerations for the English Language Arts standards describe an integrated literacy model in which all communication processes are closely connected. Likewise, the problem-based learning approach expects students to read, write, and speak about the issue (whether through interviews or speeches) in a variety of ways (expository, persuasive). In addition, the Key Design Considerations describe how literacy is a shared responsibility across subject areas. Because problem-based learning is rooted in real issues, these naturally connect to science content areas (environmental sciences, engineering and design, innovation and invention), social studies (community history, geography/land forms), math (including operations such as graphing, statistics, economics, and mathematical modeling), and art. As part of this interdisciplinary model, problem-based learning follows a process that touches on key ELA skill areas including research, a variety of writing styles and formats (both reading and writing in these formats), publishing, and integration of digital media.

It’s also important to note that the Common Core calls for an increase in informational and nonfiction text. This objective is easily met through examining real problems. Quite simply, informational and nonfiction text is everywhere – in newspaper articles, public surveys, government documents, etc. Very often, when reading out of context, many students struggle to work through and comprehend these types of complex texts. Because problem-based learning authentically integrates a real purpose with reading informational text, students work harder to comprehend and apply their reading.

Note: Each project has the potential to meet many additional standards. The standards outlined here are only a sampling of those addressed by this approach.

Reading Standards

CCSS.ELA-Literacy.CCRA.R.6 Assess how point of view or purpose shapes the content and style of a text. In the early phases of problem-based learning, students investigate the topic by reading a range of informational and persuasive texts, and by talking to a variety of experts and community members. As an essential component to these investigations on multiple perspectives, students must be able to understand the purpose of the text, the intended audience, and the individual’s position on the issue (if applicable).

CCSS.ELA-Literacy.CCRA.R.7 Integrate and evaluate content presented in diverse media and formats, including visually and quantitatively, as well as in words. As students consider multiple perspectives on their identified problem, they naturally will seek a wide range of print materials, media resources (videos, presentations), and formats (research studies, opinion pieces). Comparing and contrasting the viewpoints of these various texts will help students shape a more holistic view of the problem.

Writing Standards

CCSS.ELA-Literacy.CCRA.W.1 Write arguments to support claims in an analysis of substantive topics or texts using valid reasoning and relevant and sufficient evidence. As students analyze the problem, multiple opportunities for persuasive writing emerge. In the early project phases, students might summarize their perspective on the problem using key evidence from a variety of research (online, community polling, and discussions with experts). In the later project phases, students might develop a proposal or presentation to persuade others to change personal habits or consider a larger change in the community.

Speaking & Listening Standards

CCSS.ELA-Literacy.CCRA.SL.1 Prepare for and participate effectively in a range of conversations and collaborations with diverse partners, building on others’ ideas and expressing their own clearly and persuasively. Multiple perspectives are an essential component to any problem-based project. As students investigate, they must seek a wide range of opinions and personal stories on the issues. Furthermore, this process is collaborative. Students must trust and work with each other, they must trust and work with key experts, and, in some cases, they must convince others to collaborate with them around a shared purpose or cause.

CCSS.ELA-Literacy.CCRA.SL.5 Make strategic use of digital media and visual displays of data to express information and enhance understanding of presentations. Because each problem-based project requires students to analyze information, share their findings with others, and collaborate on a variety of levels, digital media is naturally integrated into these tasks. Students might create charts, graphs, or other illustrative/photo/video displays to communicate their research results. Students might use a variety of digital formats including graphic posters, video public service announcements (PSAs), and digital presentations to mobilize the community to their cause. Inherent to these processes is special consideration of how images, videos, and other media support key ideas and key evidence and further the effectiveness of their presentation on the intended audience.

Mathematics

Simply put, math is problem solving. Problem-based learning provides multiple opportunities for students to apply and develop their understanding of various mathematical concepts within real contexts. Through the various stages of problem-based learning, students engage in the same dispositions encouraged by the Standards for Mathematical Practice

CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them. Problem-based learning is all about problem solving. An essential first step is understanding the problem as deeply as possible, rather than rushing to solve it. This is a process that takes time and perseverance, both individually and in collaborative student groups.

CCSS.Math.Practice.MP3 Construct viable arguments and critique the reasoning of others. As students understand and deconstruct a problem, they must begin to form solutions. As part of this process, they must have evidence (including visual and mathematical evidence) to support their position. They must also understand other perspectives to solving the problem, and they must be prepared to critique those other perspectives based on verbal and mathematical reasoning.

CCSS.Math.Practice.MP4 Model with mathematics. Throughout the process, students must analyze information and data using a variety of mathematical models. These range from charts and graphs to 3-D modeling used in science or engineering projects.

CCSS.Math.Practice.MP5 Use appropriate tools strategically. According to the Common Core Math Practices standard, “Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software.” In addition to providing opportunities to use these tools, problem-based learning asks students to make effective use of digital and mobile media as they collect information, document the issue, share their findings, and mobilize others to their cause.

School Name | Big Horn Elementary Location | Big Horn, Wyoming Total Time | 1 year Subjects | English Language Arts, Social Studies, Math, Science Grade Level | 3rd Grade Number of Participants | 40 students in two classrooms

Students informed the school about the importance of recycling, developed systems to improve recycling options and implemented a school-wide recycling program that involved all students, other teachers, school principals, school custodians, and the county recycling center.

While investigating their local county history, students were challenged to recognize their role in the community and ultimately realize the importance of stewardship for the county’s land, history and culture. Students began by researching their local history through many first hand experiences including museum visits, local resident interviews and visits to places representing the current culture.

Challenged to find ways to make “A Better Community”, students chose to investigate recycling.

They conducted hands-on research to determine the need for a recycling program through a school survey, town trash pickup and visit to the local Landfill and Recycling Center.

Students then developed a proposal for a school-wide recycling program, interviewed the principal to address their concerns and began to carry out their plan.

Students designed recycling bins for each classroom and worked with school janitors to develop a plan for collection.

Students visited each classroom to distribute the recycling bins and describe how to use them. Students developed a schedule for collecting bins and sorting materials. The program continues beyond the initial school-year; students continue to expand their efforts.

School Name | Bates Middle School Location | Danville, Kentucky Total Time | 8 weeks Subjects | English Language Arts Grade Level | 6th Grade Number of Participants |25 students

Students created Project Playhouse, a live production for the local community. Audience members included community members, parents, and other students. In addition, students designed a quilt sharing Appalachian history, and recorded their work on a community website.

Appalachia has a rich culture full of unique traditions and an impressive heritage, yet many negative stereotypes persist. 6th grade students brainstormed existing stereotypes and their consequences on the community.

Students discussions led them to realize that, in their region, stereotypes were preventing people from overcoming adversity. They set about to conduct further research demonstrating the strengths of Appalachian heritage.

Students investigated Appalachian culture by working with local experts like Tammy Horn, professor at Eastern Kentucky University and specialist in Appalachian cultural traditions; taking a field trip to Logan Hubble Park to explore the natural region; talking with a “coon” hunter and other local Appalachians including quilters, cooks, artists, and writers.

Students developed a plan to curate an exhibition and live production for the local community. Finally, students connected virtually with museum expert Rebecca Kasemeyer, Associate Director of Education at the Smithsonian National Portrait Gallery to discuss exhibition design.

For their final projects students produced a series of works exhibiting Appalachian life, work, play and community structure including a quilt, a theatrical performance and a website.

Students invited the community to view their exhibit and theatrical performance.

School Name | Northwestern High School Location | Rock Hill, South Carolina Total Time | One Semester Subjects | Engineering Grade Level | High School Number of Participants | 20 students

Engineering teacher Bryan Coburn presented a scenario to his students inspired by the community’s very real drought, a drought so bad that cars could only be washed on specific days. Students identified and examined environmental issues related to water scarcity in their community.

Based on initial brainstorming, students divided into teams based on specific problems related to a water shortage. These included topics like watering gardens and lawns, watering cars, drinking water to name a few.

Based on their topic, students conducted online research on existing solutions to their specific problem.

Students analyzed their research to develop their own prototypes and plans for addressing the problem. Throughout the planning phase students received peer and teacher feedback on the viability of their prototypes, resulting in many edits before final designs were selected for creation.

Students created online portfolios showcasing their research, 3D designs, and multimedia presentations marketing their designs. Student portfolios included documentation of each stage of the design process, a design brief, decision matrix, a prototype using Autodesk Inventor 3D professional modeling tool, and a final presentation.

Students shared their presentations and portfolios in a public forum, pitching their proposed solution to a review committee consisting of local engineers from the community, the city water manager and the school principal.

Plan Your PBL Experience

Resources to help you plan.

Problem-based learning projects are inspired by students’ real world experiences and the pressing issues and concerns they want to address. Problem-based learning projects benefit teachers by increasing student motivation and engagement, while deepening knowledge and improving essential skills. In spite of the inherent value problem-based learning brings to any educational setting, planning a large project can be an overwhelming task.

Through the New Learning Institute’s Model Classroom, a range of problem-based learning planning tools have been developed and tested in a variety of educational settings. These tools make the planning process more manageable by supporting teachers in establishing the context and/or problem for a project, planning for and procuring the necessary resources for a real-world project (including community organizations, expert involvement, and tools needed for communicating, creating and sharing), and facilitating students through the project phases.

Here are some initial considerations when planning a problem-based learning project. (More detailed tips and planning tools follow.) These questions can help you determine where to begin your project planning. Once you have a clear idea, the problem-based learning planning tools will guide you through the process.

Are you starting from the curriculum? It’s probably tempting to jump in and define a problem for students based on the unit of study. And time constraints may make a teacher-defined problem necessary. If time permits, a problem-based learning project will be more successful if time is built-in for students to define a problem they’d like to address. Do this by building in topic exploration time, and then challenging students to define a problem based on their findings. Including this extra time will allow students to develop their own interests and questions about the topic, deepening engagement and ensuring that students are investigating a problem they’re invested in—all while covering curriculum requirements.

Are you starting from student interest? Perhaps your students want to solve a problem in the school, such as bullying or lack of recycling. Perhaps they’re concerned about a larger community problem, such as a contested piece of parkland that is up for development or a pollution problem in your local waterways. Starting with student interest can help ensure students’ investment and motivation. However, this starting point provides less direct navigation than existing projects or curriculum materials. When taking on a project of this nature, be sure to identify natural intersections with your curriculum. It also helps to enlist community or expert support.

Start Small – Focus on Practices as Entry Points

If you’re new to problem-based learning it makes sense to start small. Many teachers new to this approach report that starting with the smaller practices—such as integrating research methods or having students define a specific problem within a unit of study—ultimately sets the stage for larger projects and more easily leads them to implement a problem-based learning project.

Opportunities to address and solve problems are everywhere. Just look in your own backyard or schoolyard. Better yet, ask students to identify problems within the school community or based on a topic of interest within a unit of study. As you progress through the project, find natural opportunities for research and problem solving by working with the people who are affected by the issue and invested in solving it. Finally, make sure students share their work with an authentic audience who cares about the problem and its resolution.

Be Honest About Project Constraints

When you’re new to problem-based learning, the most important consideration is your project constraints. For example, perhaps you’re required to cover a designated set of standards and content. Or perhaps you have limited time for this project experience. Whatever the constraints, determine them in advance then plan backwards to determine the length and depth of your project.

Identify Intersections With Your Curriculum

Problem-based learning projects are interdisciplinary and have the ability to meet a range of standards. Identify where these intersections naturally occur with the topic students have selected, then design some activities or project requirements to ensure these content areas are covered.

Turn Limitations Into Opportunities

Many educators work in schools with pre-defined curriculum or schedule constraints that make implementing larger projects difficult. In these cases, it may help to find small windows of opportunity during the school day or after school to implement problem-based learning. For example, some teachers implement problem-based learning in special subject courses which have a more flexible curriculum. Others host afterschool “Genius Hour” programs that challenge students to explore and investigate their interests. Whatever opportunity you find, make the work highly visible to staff and parents. Make it an intention to get the school community exploring and designing possibilities of integrating these practices more holistically.

Take Risks and Model Perseverance

The problem-based learning process is messy and full of opportunities to fail, just like real life and real jobs. Many educators share that this is incredibly difficult for their students and themselves. Despite the initial letdown that comes with small failures, it’s important that students see the value in learning from failure and persevering through these challenges. Model risk taking for your students and when you make a mistake or face a challenge, welcome it with open arms by demonstrating what you’ve learned and what you’ll do differently next time around. Let students know that it’s okay to make mistakes; that mistakes are a welcome opportunity to learn and try something new.

Be Less Helpful

A key to building problem-solving and critical thinking capacities is to be less helpful. Let students figure things out on their own. In classroom implementation, teachers repeatedly share that handing over control to the students and “being less helpful” makes for a big mindshift. This shift is often described as becoming a facilitator, which means knowing when to stand back and knowing when to step-in and offer extra support.

Be Flexible

Recognize that there is no one-size-fits-all answer to any problem. Understanding this and being able to identify unique challenges will help students understand that an initial failure is just a bump in the road. Being flexible also helps students focus on the importance of process over product.

Experts are Everywhere

Experts are everywhere; their differing perspectives and expertise help bring learning to life. But think outside the box about who experts are and integrate multiple opportunities for their involvement. Parents and community members who are not often thought of as experts can speak to life, work, and lived historical experiences. Beyond that, the people usually thought of as experts—researchers, scientists, museum professionals, business professionals, university professors—are more available than many teachers think. It’s often just a matter of asking. And don’t take sole responsibility for finding experts! Seek your students’ help in identifying and securing expert or community support. And when trying to locate experts, don’t forget: students can also be experts.

Maintain a List of Your Support Networks

Some schools have brought the practice of working with the community and outside experts to scale by building databases of parent and community expertise and their interest in working with students. See if a school administrative assistant, student intern, or parent helper can take the lead in developing and maintaining this list for your school community.

Encourage Original Research

Online research is often a great starting point. It can be a way to identify a knowledge base, locate experts, and even find interest-based communities for the topic being approached. While online research is literally right at students’ fingertips, make sure your students spend time offline as well. Original research methods include student-conducted surveys, interviewing experts, and working alongside experts in the field.

This Learning is Open toolkit includes a number of tools and resources that may be helpful as you plan and reflect on your project.

Brainstorming Project Details (Google Presentation) This tool is designed to aid teachers as they brainstorm a project from a variety of starting-points. It’s a helpful tool for independent brainstorming, and would also make a useful workshop tool for teachers who are designing problem-based learning experiences.

Guide to Writing a Problem Statement (PDF) You’ve got to start somewhere. Finding—and defining—a problem is a great place to begin. This guide is a useful tool for teachers and students alike. It will walk you through the process of identifying a problem by providing inspiration on where to look. Then it will support you through the process of defining that problem clearly.

Project Planning Templates (PDF) Need a place to plan out each project phase? Use this project planner to record your ideas in one place. This template is great used alone or in tandem with the other problem-based learning tools.

Ladder of Real World Learning Experiences (PDF) Want to determine if your project is “real” enough? This ladder can be used to help teachers assess their project design based on the real world nature of the project’s learning context, type of activities, and the application of digital tools.

Digital Toolkit (Google Doc) This toolkit was developed in collaboration with teachers and continues to be a community-edited document. The toolkit provides extensive information on digital tools that can be used for planning, brainstorming, collaborating, creating, and sharing work.

Assessing student learning is a crucial part of any dynamic, nonlinear problem-based learning project. Problem-based projects have many parts to them. It’s important to understand each project as a whole as well as each individual component. This section of the toolkit will help you understand problem-based learning assessments and help you develop assessment tools for your problem-based learning experiences.

Because the subject of assessments is so complex, it may be helpful to define how it is approached here.

Portfolio-based Assessment

Each phase of problem-based learning has important tasks and outcomes associated with it. Assessing each phase of the process allows students to receive on-time feedback about their process and associated products and gives them the opportunity to refine and revise their work throughout the process.

Feedback-based Assessment

Problem-based learning emphasizes collaboration with classmates and a range of experts. Assessment should include multiple opportunities for peer feedback, teacher feedback, and expert feedback.

Assessment as a System of Interrelated Feedback Tools

These tools may include rubrics, checklists, observation, portfolios, or quizzes. Whatever the matrix of carefully selected tools, they should optimize the feedback that students receive about what and how they are learning and growing.

Assessment Tools

One way to approach developing assessment tools for your students’ specific problem-based learning project is to deconstruct the learning experience into various categories. Together, these categories make up a simple system through which students may receive feedback on their learning.

Assessing Process

Many students and teachers alike have been conditioned to emphasize and evaluate the end product. While problem-based learning projects often result in impressive end products, it’s important to emphasize each stage of the process with students.

Each phase of problem-based learning process emphasizes important skills, from research and data gathering in the early phases to problem solving, collaboration, and persuasion in the later phases. There are many opportunities to assess student understanding and skill throughout the process. The tools here provide many methods for students to self-assess their process, get feedback from peers, and get feedback from their teachers and other adults.

The Process Portfolio Tool (PDF) provides a place for students to collect their work, define their problem and goals, and reflect throughout the process. Use this as a self-assessment tool, as well as a place to organize the materials for student portfolios.

Driving & Reflection Questioning Guidelines (PDF) is a simple tool for teachers who are integrating problem-based learning into the learning process. The tool highlights the two types of questions teachers/facilitators should consider with students: driving questions and reflection questions. Driving questions push students in their thinking, challenging them to build upon ideas and try new ways to solve problems. Reflection questions ask students to reflect on a process phase once it’s complete, challenging them to think about how they think.

The Peer Feedback Guidelines (PDF) will help students frame how they provide feedback to their peers. The guide includes tips on how and when to use these guidelines in different types of forums (i.e. whole group, gallery-style, and peer-to-peer).

The Buck Institute has also developed a series of rubrics that address various project phases. Their Collaboration Rubric (PDF) can help students be better teammates. (Being an effective teammate is critical to the problem-based learning process.) Their Presentation Rubric (PDF) can help students, adult mentors, and outside experts evaluate final presentations. Final presentations are often one of the most exciting parts of a project.

Assessing Subject Matter and Content

A common concern that emerges in any problem-based learning design is whether projects are able to meet all required subject matter content targets. Because many students are required to learn specific content, there is often tension around the student-directed nature of problem-based learning. While teachers acknowledge that students go deeper into specific content during problem-based learning experiences, teachers also want to ensure that their students are meeting all content goals.

Many teachers in the New Learning Institute’s Model Classroom Program addressed this issue directly by carefully examining their curriculum requirements throughout the planning and implementation phases. Begin by planning activities and real world explorations that address core content. As the project evolves, revisit content standards to mark off and record additional standards met and create a contingency plan for those that have not been addressed.

The Buck Institute’s Rubric for Rubrics (DOC) is an excellent source for designing a rubric to fit your needs. Developing a rubric can be the most simple and effective tool for planning a project around required content targets.

Blended learning is another emerging trend that educators are moving towards as a way to both address individualized skill needs and to create space for real world project strategies, like problem-based learning. In these learning environments, students address skill acquisition through blended experiences and then apply their skills through projects and other real world applications. To learn more about blended models, visit Blend My Learning .

Assessing Mindsets and Skills

In addition to assessing process and subject matter content, it may be helpful to consider the other important mindsets and skills that the problem-based learning project experience fosters. These include persistence, problem solving, collaboration, and adaptability. While problem-based learning supports the development of a large suite of 21st century mindsets and skills, it may be helpful to focus assessments on one or two issues that are most relevant. Some helpful tools may include:

The Buck Institute offers rubrics for Critical Thinking (PDF), Collaboration (PDF), and Creativity and Innovation (PDF) that are aligned to the Common Core State Standards. These can be used as is or tailored to your specific needs.

The Character Growth Card (PDF) from the CharacterLab at Kipp is designed for school assessments more than it is for project assessment, but the list of skills and character traits are relevant to design thinking. With the inclusion of a more relevant, effective scale, these can easily be turned into a rubric, especially when paired with the Buck Institute’s Rubric for Rubrics tool.

Host a Teacher Workshop

Teachers are instrumental in sharing and spreading best practices and innovative strategies to other teachers. Once you’re confident in your conceptual and practical grasp of problem-based learning, share your knowledge and expertise with others.

The downloadable presentation decks below (PowerPoint) are adaptable tools for helping you spread the word to other educators. The presentations vary in length and depth. A 90-minute presentation introduces problem-based learning and provides a hands-on opportunity to complete an activity. The half-day and full day presentations provide in-depth opportunities to explore projects and consider their classroom applications. While this series is structured in a way that each presentation builds on the previous one, each one can also be used individually as appropriate. Each is designed to be interactive and participatory.

Getting Started with Problem-based Learning (PPT) A presentation deck for introducing educators to the Learning is Open problem-based learning process during a 90-minute peer workshop.

Dig Deeper with Problem-based Learning – Half-day (PPT) A presentation deck for training educators on the Learning is Open problem-based learning process during a half-day peer workshop.

Dig Deeper with Problem-based Learning – Full day (PPT) A presentation deck for training educators on the Learning is Open problem-based learning process during a full day peer workshop.

Related Links

Problem-based learning: detailed case studies from the model classroom.

For three years, the New Learning Institute’s Model Classroom program worked with teachers to design and implement projects. This report details the work and provides extensive case studies.

Title: Model Classroom: 3-Year Report (PDF) Type: PDF Source: New Learning Institute

Setting up Learning Experiences Using Real Problems

This New York Times Learning Blog article explores how projects can be set-up with real problems, providing many examples and suggestions for this approach.

Title: “ Guest Lesson | For Authentic Learning Start with Real Problems ” Type: Article Source: Suzie Boss. New York Times Learning Blog

Guest Lesson: Recycling as a Focus for Project-based Learning

There are many ways to set-up a project with a real world problem. This article describes the problem of recycling, providing multiple examples of student projects addressing the issue.

Title: “ Guest Lesson | Recycling as a Focus for Project-Based Learning ” Type: Article Source: Suzie Boss. New York Times Learning Blog

Problem-based Learning: Professional Development Inspires Classroom Project

This video features how the Model Classroom professional development workshop model worked in practice, challenging teachers to collaboratively problem-solve using real world places and experts. It also shows how one workshop participant used her experience to design a yearlong problem-based learning project for first-graders called the “Streamkeepers Project.”

Title: Mission Possible: the Model Classroom Type: Video Source: New Learning Institute

Problem-based Learning in an Engineering Class: Solutions to a Water Shortage

Engineering teacher Bryan Coburn used the problem of a local water shortage to inspire his students to conduct research and design solutions.

Title: “ National Project Aims to Inspire the Model Classroom ” Type: Article Source: eSchool News

Making Project-based Learning More Meaningful

This article provides great tips on how to design projects to be relevant and purposeful for students. While it addresses the larger umbrella of project-based learning, the suggestions and tips provided apply to problem-based learning.

Title: “ How to Reinvent Project-Based Learning to Make it More Meaningful ” Type: Article Source: KQED Mindshift

PBL Downloads

Guide to Writing a Problem Statement (PDF)

A walk-through guide for identifying and defining a problem.

Project Planning Templates (PDF)

A planning template for standalone use or to be used along with other problem-based learning tools.

Process Portfolio Tool (PDF)

A self-assessment tool to support students as they collect their work, define their problem and goals, and make reflections throughout the process.

More PBL Downloads

Getting Started with Problem-based Learning (PPT)

A presentation deck for introducing educators to the Project MASH problem-based learning process during a 90-minute peer workshop.

Dig Deeper with Problem-based Learning – Half-day (PPT)

A presentation deck for training educators on the PBL process during a half-day peer workshop.

Dig Deeper with Problem-based Learning – Full day (PPT)

A presentation deck for training educators on the PBL process during a full day peer workshop.

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Fluency, Reasoning and Problem Solving: What This Looks Like In Every Math Lesson

Neil almond.

Fluency, reasoning and problem solving are central strands of mathematical competency, as recognized by the National Council of Teachers of Mathematics (NCTM) and the National Research Council’s report ‘Adding It Up’.

They are key components to the Standards of Mathematical Practice, standards that are interwoven into every mathematics lesson. Here we look at how these three approaches or elements of math can be interwoven in a child’s math education through elementary and middle school.

We look at what fluency, reasoning and problem solving are, how to teach them, and how to know how a child is progressing in each – as well as what to do when they’re not, and what to avoid.

The hope is that this blog will help elementary and middle school teachers think carefully about their practice and the pedagogical choices they make around the teaching of what the common core refers to as ‘mathematical practices’, and reasoning and problem solving in particular.

Before we can think about what this would look like in Common Core math examples and other state-specific math frameworks, we need to understand the background to these terms.

The Ultimate Guide to Problem Solving Techniques

Develop problem solving skills in the classroom with this free, downloadable worksheet

What is fluency in math?

Fluency in math is a fairly broad concept. The basics of mathematical fluency – as defined by the Common Core State Standards for math – involve knowing key mathematical skills and being able to carry them out flexibly, accurately and efficiently.

But true fluency in math (at least up to middle school) means being able to apply the same skill to multiple contexts, and being able to choose the most appropriate method for a particular task.

Fluency in math lessons means we teach the content using a range of representations, to ensure that all students understand and have sufficient time to practice what is taught.

Read more: How the best schools develop math fluency

What is reasoning in math?

Reasoning in math is the process of applying logical thinking to a situation to derive the correct problem solving strategy for a given question, and using this method to develop and describe a solution.

Put more simply, mathematical reasoning is the bridge between fluency and problem solving. It allows students to use the former to accurately carry out the latter.

Read more: Developing math reasoning: the mathematical skills required and how to teach them .

What is problem solving in math?

It’s sometimes easier to start off with what problem solving is not. Problem solving is not necessarily just about answering word problems in math. If a child already has a readily available method to solve this sort of problem, problem solving has not occurred. Problem solving in math is finding a way to apply knowledge and skills you have to answer unfamiliar types of problems.

Read more: Math problem solving: strategies and resources for primary school teachers .

We are all problem solvers

First off, problem solving should not be seen as something that some students can do and some cannot. Every single person is born with an innate level of problem-solving ability.

Early on as a species on this planet, we solved problems like recognizing faces we know, protecting ourselves against other species, and as babies the problem of getting food (by crying relentlessly until we were fed).

All these scenarios are a form of what the evolutionary psychologist David Geary (1995) calls biologically primary knowledge. We have been solving these problems for millennia and they are so ingrained in our DNA that we learn them without any specific instruction.

image of baby crying used to illustrate ingrained problem solving skills.

Why then, if we have this innate ability, does actually teaching problem solving seem so hard?

Mathematical problem solving is a learned skill

As you might have guessed, the domain of mathematics is far from innate. Math doesn’t just happen to us; we need to learn it. It needs to be passed down from experts that have the knowledge to novices who do not.

This is what Geary calls biologically secondary knowledge. Solving problems (within the domain of math) is a mixture of both primary and secondary knowledge.

The issue is that problem solving in domains that are classified as biologically secondary knowledge (like math) can only be improved by practicing elements of that domain.

So there is no generic problem-solving skill that can be taught in isolation and transferred to other areas.

This will have important ramifications for pedagogical choices, which I will go into more detail about later on in this blog.

The educationalist Dylan Wiliam had this to say on the matter: ‘for…problem solving, the idea that students can learn these skills in one context and apply them in another is essentially wrong.’ (Wiliam, 2018) So what is the best method of teaching problem solving to elementary and middle school math students?

The answer is that we teach them plenty of domain specific biological secondary knowledge – in this case, math. Our ability to successfully problem solve requires us to have a deep understanding of content and fluency of facts and mathematical procedures.

Here is what cognitive psychologist Daniel Willingham (2010) has to say:

‘Data from the last thirty years leads to a conclusion that is not scientifically challengeable: thinking well requires knowing facts, and that’s true not simply because you need something to think about.

The very processes that teachers care about most—critical thinking processes such as reasoning and problem solving—are intimately intertwined with factual knowledge that is stored in long-term memory (not just found in the environment).’

Colin Foster (2019), a reader in Mathematics Education in the Mathematics Education Center at Loughborough University, UK, says, ‘I think of fluency and mathematical reasoning, not as ends in themselves, but as means to support students in the most important goal of all: solving problems.’

In that paper he produces this pyramid:

pyramid diagram showing the link between fluency, reasoning and problem solving

This is important for two reasons:

1)    It splits up reasoning skills and problem solving into two different entities

2)    It demonstrates that fluency is not something to be rushed through to get to the ‘problem solving’ stage but is rather the foundation of problem solving.

In my own work I adapt this model and turn it into a cone shape, as education seems to have a problem with pyramids and gross misinterpretation of them (think Bloom’s taxonomy).

conical diagram showing the link between fluency, reasoning skills and problem solving

Notice how we need plenty of fluency of facts, concepts, procedures and mathematical language.

Having this fluency will help with improving logical reasoning skills, which will then lend themselves to solving mathematical problems – but only if it is truly learnt and there is systematic retrieval of this information carefully planned across the curriculum.

Performance vs learning: what to avoid when teaching fluency, reasoning, and problem solving

I mean to make no sweeping generalization here; this was my experience both at university when training and from working in schools.

At some point, schools become obsessed with the ridiculous notion of moving students through content at an accelerated rate. I have heard it used in all manner of educational contexts while training and being a teacher. ‘You will need to show ‘accelerated progress in math’ in this lesson,’ ‘School officials will be looking for ‘accelerated progress’ etc.

I have no doubt that all of this came from a good place and from those wanting the best possible outcomes – but it is misguided.

I remember being told that we needed to get students onto the problem solving questions as soon as possible to demonstrate this mystical ‘accelerated progress’.

This makes sense; you have a group of students and you have taken them from not knowing something to working out pretty sophisticated 2-step or multi-step word problems within an hour. How is that not ‘accelerated progress?’

This was a frequent feature of my lessons up until last academic year: teach a mathematical procedure; get the students to do about 10 of them in their books; mark these and if the majority were correct, model some reasoning/problem solving questions from the same content as the fluency content; give the students some reasoning and word problem questions and that was it.

I wondered if I was the only one who had been taught this while at university so I did a quick poll on Twitter and found that was not the case.

twitter poll regarding teaching of problem solving techniques in primary school

I know these numbers won’t be big enough for a representative sample but it still shows that others are familiar with this approach.

The issue with the lesson framework I mentioned above is that it does not take into account ‘performance vs learning.’

What IS ‘performance vs learning’?

The premise is that performance in a lesson is not a good proxy for learning.

Yes, those students were performing well after I had modeled a mathematical procedure for them, and managed to get questions correct.

But if problem solving depends on a deep knowledge of mathematics, this approach to lesson structure is going to be very ineffective.

As mentioned earlier, the reasoning and problem solving questions were based on the same math content as the fluency exercises, making it more likely that students would solve problems correctly whether they fully understood them or not.

Chances are that all they’d need to do is find the numbers in the questions and use the same method they used in the fluency section to get their answers (a process referred to as “number plucking”) – not exactly high level problem solving skills.

Teaching to “cover the curriculum” hinders development of strong problem solving skills.

This is one of my worries with ‘math mastery schemes’ that block content so that, in some circumstances, it is not looked at again until the following year (and with new objectives).

The pressure for teachers to ‘get through the curriculum’ results in many opportunities to revisit content being missed in the classroom.

Students are unintentionally forced to skip ahead in the fluency, reasoning, problem solving chain without proper consolidation of the earlier processes.

As David Didau (2019) puts it, ‘When novices face a problem for which they do not have a conveniently stored solution, they have to rely on the costlier means-end analysis.

This is likely to lead to cognitive overload because it involves trying to work through and hold in mind multiple possible solutions.

It’s a bit like trying to juggle five objects at once without previous practice. Solving problems is an inefficient way to get better at problem solving.’

Fluency and reasoning – Best practice in a lesson, a unit, and a semester

By now I hope you have realized that when it comes to problem solving, fluency is king. As such we should look to mastery math based teaching to ensure that the fluency that students need is there.

The answer to what fluency looks like will obviously depend on many factors, including the content being taught and the grade you find yourself teaching.

But we should not consider rushing them on to problem solving or logical reasoning in the early stages of this new content as it has not been learnt, only performed.

I would say that in the early stages of learning, content that requires the end goal of being fluent should take up the majority of lesson time – approximately 60%. The rest of the time should be spent rehearsing and retrieving other knowledge that is at risk of being forgotten about.

This blog on mental math strategies students should learn at each grade level is a good place to start when thinking about the core aspects of fluency that students should achieve.

Little and often is a good mantra when we think about fluency, particularly when revisiting the key mathematical skills of number bond fluency or multiplication fluency. So when it comes to what fluency could look like throughout the day, consider all the opportunities to get students practicing.

They could chant multiplication facts when transitioning. If a lesson in another subject has finished earlier than expected, use that time to quiz students on number bonds. Have fluency exercises as part of the morning work.

Read more: How to teach multiplication for instant recall

What about best practice over a longer period?

Thinking about what fluency could look like across a unit of work would again depend on the unit itself.

Look at this unit below from a popular scheme of work.

example scheme of work

They recommend 20 days to cover 9 objectives. One of these specifically mentions problem solving so I will forget about that one at the moment – so that gives 8 objectives.

I would recommend that the fluency of this unit look something like this:

example first lesson of a unit of work targeted towards fluency

This type of structure is heavily borrowed from Mark McCourt’s phased learning idea from his book ‘Teaching for Mastery.’

This should not be seen as something set in stone; it would greatly depend on the needs of the class in front of you. But it gives an idea of what fluency could look like across a unit of lessons – though not necessarily all math lessons.

When we think about a semester, we can draw on similar ideas to the one above except that your lessons could also pull on content from previous units from that semester.

So lesson one may focus 60% on the new unit and 40% on what was learnt in the previous unit.

The structure could then follow a similar pattern to the one above.

Best practice for problem solving in a lesson, a unit, and a semester 

When an adult first learns something new, we cannot solve a problem with it straight away. We need to become familiar with the idea and practice before we can make connections, reason and problem solve with it.

The same is true for students. Indeed, it could take up to two years ‘between the mathematics a student can use in imitative exercises and that they have sufficiently absorbed and connected to use autonomously in non-routine problem solving.’ (Burkhardt, 2017).

Practice with facts that are secure

So when we plan for reasoning and problem solving, we need to be looking at content from 2 years ago to base these questions on.

You could get students in 3rd grade to solve complicated place value problems with the numbers they should know from 1st or 2nd grade. This would lessen the cognitive load , freeing up valuable working memory so they can actually focus on solving the problems using content they are familiar with.

Increase complexity gradually

Once they practice solving these types of problems, they can draw on this knowledge later when solving problems with more difficult numbers.

This is what Mark McCourt calls the ‘Behave’ phase. In his book he writes:

‘Many teachers find it an uncomfortable – perhaps even illogical – process to plan the ‘Behave’ phase as one that relates to much earlier learning rather than the new idea, but it is crucial to do so if we want to bring about optimal gains in learning, understanding and long term recall.’  (Mark McCourt, 2019)

This just shows the fallacy of ‘accelerated progress’; in the space of 20 minutes some teachers are taught to move students from fluency through to non-routine problem solving, or we are somehow not catering to the needs of the child.

When considering what problem solving lessons could look like, here’s an example structure based on the objectives above.

example lesson of a unit using fluency and reasoning to embed problem solving

Fluency, Reasoning and Problem Solving should NOT be taught by rote 

It is important to reiterate that this is not something that should be set in stone. Key to getting the most out of this teaching for mastery approach is ensuring your students (across abilities) are interested and engaged in their work.

Depending on the previous attainment and abilities of the children in your class, you may find that a few have come across some of the mathematical ideas you have been teaching, and so they are able to problem solve effectively with these ideas.

Equally likely is encountering students on the opposite side of the spectrum, who may not have fully grasped the concept of place value and will need to go further back than 2 years and solve even simpler problems.

In order to have the greatest impact on class performance, you will have to account for these varying experiences in your lessons.

Read more: 

  • Math Mastery Toolkit : A Practical Guide To Mastery Teaching And Learning
  • Problem Solving and Reasoning Questions and Answers
  • Get to Grips with Math Problem Solving For Elementary Students
  • Mixed Ability Teaching for Mastery: Classroom How To
  • 21 Math Challenges To Really Stretch Your More Able Students
  • Why You Should Be Incorporating Stem Sentences Into Your Elementary Math Teaching

Do you have students who need extra support in math? Give your students more opportunities to consolidate learning and practice skills through personalized math tutoring with their own dedicated online math tutor. Each student receives differentiated instruction designed to close their individual learning gaps, and scaffolded learning ensures every student learns at the right pace. Lessons are aligned with your state’s standards and assessments, plus you’ll receive regular reports every step of the way. Personalized one-on-one math tutoring programs are available for: – 2nd grade tutoring – 3rd grade tutoring – 4th grade tutoring – 5th grade tutoring – 6th grade tutoring – 7th grade tutoring – 8th grade tutoring Why not learn more about how it works ?

The content in this article was originally written by primary school lead teacher Neil Almond and has since been revised and adapted for US schools by elementary math teacher Jaclyn Wassell.

Ultimate Guide to Metacognition [FREE]

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Check out this guide featuring practical examples, tips and strategies to successfully embed metacognition across your school to accelerate math growth.

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7 Module 7: Thinking, Reasoning, and Problem-Solving

This module is about how a solid working knowledge of psychological principles can help you to think more effectively, so you can succeed in school and life. You might be inclined to believe that—because you have been thinking for as long as you can remember, because you are able to figure out the solution to many problems, because you feel capable of using logic to argue a point, because you can evaluate whether the things you read and hear make sense—you do not need any special training in thinking. But this, of course, is one of the key barriers to helping people think better. If you do not believe that there is anything wrong, why try to fix it?

The human brain is indeed a remarkable thinking machine, capable of amazing, complex, creative, logical thoughts. Why, then, are we telling you that you need to learn how to think? Mainly because one major lesson from cognitive psychology is that these capabilities of the human brain are relatively infrequently realized. Many psychologists believe that people are essentially “cognitive misers.” It is not that we are lazy, but that we have a tendency to expend the least amount of mental effort necessary. Although you may not realize it, it actually takes a great deal of energy to think. Careful, deliberative reasoning and critical thinking are very difficult. Because we seem to be successful without going to the trouble of using these skills well, it feels unnecessary to develop them. As you shall see, however, there are many pitfalls in the cognitive processes described in this module. When people do not devote extra effort to learning and improving reasoning, problem solving, and critical thinking skills, they make many errors.

As is true for memory, if you develop the cognitive skills presented in this module, you will be more successful in school. It is important that you realize, however, that these skills will help you far beyond school, even more so than a good memory will. Although it is somewhat useful to have a good memory, ten years from now no potential employer will care how many questions you got right on multiple choice exams during college. All of them will, however, recognize whether you are a logical, analytical, critical thinker. With these thinking skills, you will be an effective, persuasive communicator and an excellent problem solver.

The module begins by describing different kinds of thought and knowledge, especially conceptual knowledge and critical thinking. An understanding of these differences will be valuable as you progress through school and encounter different assignments that require you to tap into different kinds of knowledge. The second section covers deductive and inductive reasoning, which are processes we use to construct and evaluate strong arguments. They are essential skills to have whenever you are trying to persuade someone (including yourself) of some point, or to respond to someone’s efforts to persuade you. The module ends with a section about problem solving. A solid understanding of the key processes involved in problem solving will help you to handle many daily challenges.

7.1. Different kinds of thought

7.2. Reasoning and Judgment

7.3. Problem Solving

READING WITH PURPOSE

Remember and understand.

By reading and studying Module 7, you should be able to remember and describe:

  • Concepts and inferences (7.1)
  • Procedural knowledge (7.1)
  • Metacognition (7.1)
  • Characteristics of critical thinking:  skepticism; identify biases, distortions, omissions, and assumptions; reasoning and problem solving skills  (7.1)
  • Reasoning:  deductive reasoning, deductively valid argument, inductive reasoning, inductively strong argument, availability heuristic, representativeness heuristic  (7.2)
  • Fixation:  functional fixedness, mental set  (7.3)
  • Algorithms, heuristics, and the role of confirmation bias (7.3)
  • Effective problem solving sequence (7.3)

By reading and thinking about how the concepts in Module 6 apply to real life, you should be able to:

  • Identify which type of knowledge a piece of information is (7.1)
  • Recognize examples of deductive and inductive reasoning (7.2)
  • Recognize judgments that have probably been influenced by the availability heuristic (7.2)
  • Recognize examples of problem solving heuristics and algorithms (7.3)

Analyze, Evaluate, and Create

By reading and thinking about Module 6, participating in classroom activities, and completing out-of-class assignments, you should be able to:

  • Use the principles of critical thinking to evaluate information (7.1)
  • Explain whether examples of reasoning arguments are deductively valid or inductively strong (7.2)
  • Outline how you could try to solve a problem from your life using the effective problem solving sequence (7.3)

7.1. Different kinds of thought and knowledge

  • Take a few minutes to write down everything that you know about dogs.
  • Do you believe that:
  • Psychic ability exists?
  • Hypnosis is an altered state of consciousness?
  • Magnet therapy is effective for relieving pain?
  • Aerobic exercise is an effective treatment for depression?
  • UFO’s from outer space have visited earth?

On what do you base your belief or disbelief for the questions above?

Of course, we all know what is meant by the words  think  and  knowledge . You probably also realize that they are not unitary concepts; there are different kinds of thought and knowledge. In this section, let us look at some of these differences. If you are familiar with these different kinds of thought and pay attention to them in your classes, it will help you to focus on the right goals, learn more effectively, and succeed in school. Different assignments and requirements in school call on you to use different kinds of knowledge or thought, so it will be very helpful for you to learn to recognize them (Anderson, et al. 2001).

Factual and conceptual knowledge

Module 5 introduced the idea of declarative memory, which is composed of facts and episodes. If you have ever played a trivia game or watched Jeopardy on TV, you realize that the human brain is able to hold an extraordinary number of facts. Likewise, you realize that each of us has an enormous store of episodes, essentially facts about events that happened in our own lives. It may be difficult to keep that in mind when we are struggling to retrieve one of those facts while taking an exam, however. Part of the problem is that, in contradiction to the advice from Module 5, many students continue to try to memorize course material as a series of unrelated facts (picture a history student simply trying to memorize history as a set of unrelated dates without any coherent story tying them together). Facts in the real world are not random and unorganized, however. It is the way that they are organized that constitutes a second key kind of knowledge, conceptual.

Concepts are nothing more than our mental representations of categories of things in the world. For example, think about dogs. When you do this, you might remember specific facts about dogs, such as they have fur and they bark. You may also recall dogs that you have encountered and picture them in your mind. All of this information (and more) makes up your concept of dog. You can have concepts of simple categories (e.g., triangle), complex categories (e.g., small dogs that sleep all day, eat out of the garbage, and bark at leaves), kinds of people (e.g., psychology professors), events (e.g., birthday parties), and abstract ideas (e.g., justice). Gregory Murphy (2002) refers to concepts as the “glue that holds our mental life together” (p. 1). Very simply, summarizing the world by using concepts is one of the most important cognitive tasks that we do. Our conceptual knowledge  is  our knowledge about the world. Individual concepts are related to each other to form a rich interconnected network of knowledge. For example, think about how the following concepts might be related to each other: dog, pet, play, Frisbee, chew toy, shoe. Or, of more obvious use to you now, how these concepts are related: working memory, long-term memory, declarative memory, procedural memory, and rehearsal? Because our minds have a natural tendency to organize information conceptually, when students try to remember course material as isolated facts, they are working against their strengths.

One last important point about concepts is that they allow you to instantly know a great deal of information about something. For example, if someone hands you a small red object and says, “here is an apple,” they do not have to tell you, “it is something you can eat.” You already know that you can eat it because it is true by virtue of the fact that the object is an apple; this is called drawing an  inference , assuming that something is true on the basis of your previous knowledge (for example, of category membership or of how the world works) or logical reasoning.

Procedural knowledge

Physical skills, such as tying your shoes, doing a cartwheel, and driving a car (or doing all three at the same time, but don’t try this at home) are certainly a kind of knowledge. They are procedural knowledge, the same idea as procedural memory that you saw in Module 5. Mental skills, such as reading, debating, and planning a psychology experiment, are procedural knowledge, as well. In short, procedural knowledge is the knowledge how to do something (Cohen & Eichenbaum, 1993).

Metacognitive knowledge

Floyd used to think that he had a great memory. Now, he has a better memory. Why? Because he finally realized that his memory was not as great as he once thought it was. Because Floyd eventually learned that he often forgets where he put things, he finally developed the habit of putting things in the same place. (Unfortunately, he did not learn this lesson before losing at least 5 watches and a wedding ring.) Because he finally realized that he often forgets to do things, he finally started using the To Do list app on his phone. And so on. Floyd’s insights about the real limitations of his memory have allowed him to remember things that he used to forget.

All of us have knowledge about the way our own minds work. You may know that you have a good memory for people’s names and a poor memory for math formulas. Someone else might realize that they have difficulty remembering to do things, like stopping at the store on the way home. Others still know that they tend to overlook details. This knowledge about our own thinking is actually quite important; it is called metacognitive knowledge, or  metacognition . Like other kinds of thinking skills, it is subject to error. For example, in unpublished research, one of the authors surveyed about 120 General Psychology students on the first day of the term. Among other questions, the students were asked them to predict their grade in the class and report their current Grade Point Average. Two-thirds of the students predicted that their grade in the course would be higher than their GPA. (The reality is that at our college, students tend to earn lower grades in psychology than their overall GPA.) Another example: Students routinely report that they thought they had done well on an exam, only to discover, to their dismay, that they were wrong (more on that important problem in a moment). Both errors reveal a breakdown in metacognition.

The Dunning-Kruger Effect

In general, most college students probably do not study enough. For example, using data from the National Survey of Student Engagement, Fosnacht, McCormack, and Lerma (2018) reported that first-year students at 4-year colleges in the U.S. averaged less than 14 hours per week preparing for classes. The typical suggestion is that you should spend two hours outside of class for every hour in class, or 24 – 30 hours per week for a full-time student. Clearly, students in general are nowhere near that recommended mark. Many observers, including some faculty, believe that this shortfall is a result of students being too busy or lazy. Now, it may be true that many students are too busy, with work and family obligations, for example. Others, are not particularly motivated in school, and therefore might correctly be labeled lazy. A third possible explanation, however, is that some students might not think they need to spend this much time. And this is a matter of metacognition. Consider the scenario that we mentioned above, students thinking they had done well on an exam only to discover that they did not. Justin Kruger and David Dunning examined scenarios very much like this in 1999. Kruger and Dunning gave research participants tests measuring humor, logic, and grammar. Then, they asked the participants to assess their own abilities and test performance in these areas. They found that participants in general tended to overestimate their abilities, already a problem with metacognition. Importantly, the participants who scored the lowest overestimated their abilities the most. Specifically, students who scored in the bottom quarter (averaging in the 12th percentile) thought they had scored in the 62nd percentile. This has become known as the  Dunning-Kruger effect . Many individual faculty members have replicated these results with their own student on their course exams, including the authors of this book. Think about it. Some students who just took an exam and performed poorly believe that they did well before seeing their score. It seems very likely that these are the very same students who stopped studying the night before because they thought they were “done.” Quite simply, it is not just that they did not know the material. They did not know that they did not know the material. That is poor metacognition.

In order to develop good metacognitive skills, you should continually monitor your thinking and seek frequent feedback on the accuracy of your thinking (Medina, Castleberry, & Persky 2017). For example, in classes get in the habit of predicting your exam grades. As soon as possible after taking an exam, try to find out which questions you missed and try to figure out why. If you do this soon enough, you may be able to recall the way it felt when you originally answered the question. Did you feel confident that you had answered the question correctly? Then you have just discovered an opportunity to improve your metacognition. Be on the lookout for that feeling and respond with caution.

concept :  a mental representation of a category of things in the world

Dunning-Kruger effect : individuals who are less competent tend to overestimate their abilities more than individuals who are more competent do

inference : an assumption about the truth of something that is not stated. Inferences come from our prior knowledge and experience, and from logical reasoning

metacognition :  knowledge about one’s own cognitive processes; thinking about your thinking

Critical thinking

One particular kind of knowledge or thinking skill that is related to metacognition is  critical thinking (Chew, 2020). You may have noticed that critical thinking is an objective in many college courses, and thus it could be a legitimate topic to cover in nearly any college course. It is particularly appropriate in psychology, however. As the science of (behavior and) mental processes, psychology is obviously well suited to be the discipline through which you should be introduced to this important way of thinking.

More importantly, there is a particular need to use critical thinking in psychology. We are all, in a way, experts in human behavior and mental processes, having engaged in them literally since birth. Thus, perhaps more than in any other class, students typically approach psychology with very clear ideas and opinions about its subject matter. That is, students already “know” a lot about psychology. The problem is, “it ain’t so much the things we don’t know that get us into trouble. It’s the things we know that just ain’t so” (Ward, quoted in Gilovich 1991). Indeed, many of students’ preconceptions about psychology are just plain wrong. Randolph Smith (2002) wrote a book about critical thinking in psychology called  Challenging Your Preconceptions,  highlighting this fact. On the other hand, many of students’ preconceptions about psychology are just plain right! But wait, how do you know which of your preconceptions are right and which are wrong? And when you come across a research finding or theory in this class that contradicts your preconceptions, what will you do? Will you stick to your original idea, discounting the information from the class? Will you immediately change your mind? Critical thinking can help us sort through this confusing mess.

But what is critical thinking? The goal of critical thinking is simple to state (but extraordinarily difficult to achieve): it is to be right, to draw the correct conclusions, to believe in things that are true and to disbelieve things that are false. We will provide two definitions of critical thinking (or, if you like, one large definition with two distinct parts). First, a more conceptual one: Critical thinking is thinking like a scientist in your everyday life (Schmaltz, Jansen, & Wenckowski, 2017).  Our second definition is more operational; it is simply a list of skills that are essential to be a critical thinker. Critical thinking entails solid reasoning and problem solving skills; skepticism; and an ability to identify biases, distortions, omissions, and assumptions. Excellent deductive and inductive reasoning, and problem solving skills contribute to critical thinking. So, you can consider the subject matter of sections 7.2 and 7.3 to be part of critical thinking. Because we will be devoting considerable time to these concepts in the rest of the module, let us begin with a discussion about the other aspects of critical thinking.

Let’s address that first part of the definition. Scientists form hypotheses, or predictions about some possible future observations. Then, they collect data, or information (think of this as making those future observations). They do their best to make unbiased observations using reliable techniques that have been verified by others. Then, and only then, they draw a conclusion about what those observations mean. Oh, and do not forget the most important part. “Conclusion” is probably not the most appropriate word because this conclusion is only tentative. A scientist is always prepared that someone else might come along and produce new observations that would require a new conclusion be drawn. Wow! If you like to be right, you could do a lot worse than using a process like this.

A Critical Thinker’s Toolkit 

Now for the second part of the definition. Good critical thinkers (and scientists) rely on a variety of tools to evaluate information. Perhaps the most recognizable tool for critical thinking is  skepticism (and this term provides the clearest link to the thinking like a scientist definition, as you are about to see). Some people intend it as an insult when they call someone a skeptic. But if someone calls you a skeptic, if they are using the term correctly, you should consider it a great compliment. Simply put, skepticism is a way of thinking in which you refrain from drawing a conclusion or changing your mind until good evidence has been provided. People from Missouri should recognize this principle, as Missouri is known as the Show-Me State. As a skeptic, you are not inclined to believe something just because someone said so, because someone else believes it, or because it sounds reasonable. You must be persuaded by high quality evidence.

Of course, if that evidence is produced, you have a responsibility as a skeptic to change your belief. Failure to change a belief in the face of good evidence is not skepticism; skepticism has open mindedness at its core. M. Neil Browne and Stuart Keeley (2018) use the term weak sense critical thinking to describe critical thinking behaviors that are used only to strengthen a prior belief. Strong sense critical thinking, on the other hand, has as its goal reaching the best conclusion. Sometimes that means strengthening your prior belief, but sometimes it means changing your belief to accommodate the better evidence.

Many times, a failure to think critically or weak sense critical thinking is related to a  bias , an inclination, tendency, leaning, or prejudice. Everybody has biases, but many people are unaware of them. Awareness of your own biases gives you the opportunity to control or counteract them. Unfortunately, however, many people are happy to let their biases creep into their attempts to persuade others; indeed, it is a key part of their persuasive strategy. To see how these biases influence messages, just look at the different descriptions and explanations of the same events given by people of different ages or income brackets, or conservative versus liberal commentators, or by commentators from different parts of the world. Of course, to be successful, these people who are consciously using their biases must disguise them. Even undisguised biases can be difficult to identify, so disguised ones can be nearly impossible.

Here are some common sources of biases:

  • Personal values and beliefs.  Some people believe that human beings are basically driven to seek power and that they are typically in competition with one another over scarce resources. These beliefs are similar to the world-view that political scientists call “realism.” Other people believe that human beings prefer to cooperate and that, given the chance, they will do so. These beliefs are similar to the world-view known as “idealism.” For many people, these deeply held beliefs can influence, or bias, their interpretations of such wide ranging situations as the behavior of nations and their leaders or the behavior of the driver in the car ahead of you. For example, if your worldview is that people are typically in competition and someone cuts you off on the highway, you may assume that the driver did it purposely to get ahead of you. Other types of beliefs about the way the world is or the way the world should be, for example, political beliefs, can similarly become a significant source of bias.
  • Racism, sexism, ageism and other forms of prejudice and bigotry.  These are, sadly, a common source of bias in many people. They are essentially a special kind of “belief about the way the world is.” These beliefs—for example, that women do not make effective leaders—lead people to ignore contradictory evidence (examples of effective women leaders, or research that disputes the belief) and to interpret ambiguous evidence in a way consistent with the belief.
  • Self-interest.  When particular people benefit from things turning out a certain way, they can sometimes be very susceptible to letting that interest bias them. For example, a company that will earn a profit if they sell their product may have a bias in the way that they give information about their product. A union that will benefit if its members get a generous contract might have a bias in the way it presents information about salaries at competing organizations. (Note that our inclusion of examples describing both companies and unions is an explicit attempt to control for our own personal biases). Home buyers are often dismayed to discover that they purchased their dream house from someone whose self-interest led them to lie about flooding problems in the basement or back yard. This principle, the biasing power of self-interest, is likely what led to the famous phrase  Caveat Emptor  (let the buyer beware) .  

Knowing that these types of biases exist will help you evaluate evidence more critically. Do not forget, though, that people are not always keen to let you discover the sources of biases in their arguments. For example, companies or political organizations can sometimes disguise their support of a research study by contracting with a university professor, who comes complete with a seemingly unbiased institutional affiliation, to conduct the study.

People’s biases, conscious or unconscious, can lead them to make omissions, distortions, and assumptions that undermine our ability to correctly evaluate evidence. It is essential that you look for these elements. Always ask, what is missing, what is not as it appears, and what is being assumed here? For example, consider this (fictional) chart from an ad reporting customer satisfaction at 4 local health clubs.

learning concepts problem solving

Clearly, from the results of the chart, one would be tempted to give Club C a try, as customer satisfaction is much higher than for the other 3 clubs.

There are so many distortions and omissions in this chart, however, that it is actually quite meaningless. First, how was satisfaction measured? Do the bars represent responses to a survey? If so, how were the questions asked? Most importantly, where is the missing scale for the chart? Although the differences look quite large, are they really?

Well, here is the same chart, with a different scale, this time labeled:

learning concepts problem solving

Club C is not so impressive any more, is it? In fact, all of the health clubs have customer satisfaction ratings (whatever that means) between 85% and 88%. In the first chart, the entire scale of the graph included only the percentages between 83 and 89. This “judicious” choice of scale—some would call it a distortion—and omission of that scale from the chart make the tiny differences among the clubs seem important, however.

Also, in order to be a critical thinker, you need to learn to pay attention to the assumptions that underlie a message. Let us briefly illustrate the role of assumptions by touching on some people’s beliefs about the criminal justice system in the US. Some believe that a major problem with our judicial system is that many criminals go free because of legal technicalities. Others believe that a major problem is that many innocent people are convicted of crimes. The simple fact is, both types of errors occur. A person’s conclusion about which flaw in our judicial system is the greater tragedy is based on an assumption about which of these is the more serious error (letting the guilty go free or convicting the innocent). This type of assumption is called a value assumption (Browne and Keeley, 2018). It reflects the differences in values that people develop, differences that may lead us to disregard valid evidence that does not fit in with our particular values.

Oh, by the way, some students probably noticed this, but the seven tips for evaluating information that we shared in Module 1 are related to this. Actually, they are part of this section. The tips are, to a very large degree, set of ideas you can use to help you identify biases, distortions, omissions, and assumptions. If you do not remember this section, we strongly recommend you take a few minutes to review it.

skepticism :  a way of thinking in which you refrain from drawing a conclusion or changing your mind until good evidence has been provided

bias : an inclination, tendency, leaning, or prejudice

  • Which of your beliefs (or disbeliefs) from the Activate exercise for this section were derived from a process of critical thinking? If some of your beliefs were not based on critical thinking, are you willing to reassess these beliefs? If the answer is no, why do you think that is? If the answer is yes, what concrete steps will you take?

7.2 Reasoning and Judgment

  • What percentage of kidnappings are committed by strangers?
  • Which area of the house is riskiest: kitchen, bathroom, or stairs?
  • What is the most common cancer in the US?
  • What percentage of workplace homicides are committed by co-workers?

An essential set of procedural thinking skills is  reasoning , the ability to generate and evaluate solid conclusions from a set of statements or evidence. You should note that these conclusions (when they are generated instead of being evaluated) are one key type of inference that we described in Section 7.1. There are two main types of reasoning, deductive and inductive.

Deductive reasoning

Suppose your teacher tells you that if you get an A on the final exam in a course, you will get an A for the whole course. Then, you get an A on the final exam. What will your final course grade be? Most people can see instantly that you can conclude with certainty that you will get an A for the course. This is a type of reasoning called  deductive reasoning , which is defined as reasoning in which a conclusion is guaranteed to be true as long as the statements leading to it are true. The three statements can be listed as an  argument , with two beginning statements and a conclusion:

Statement 1: If you get an A on the final exam, you will get an A for the course

Statement 2: You get an A on the final exam

Conclusion: You will get an A for the course

This particular arrangement, in which true beginning statements lead to a guaranteed true conclusion, is known as a  deductively valid argument . Although deductive reasoning is often the subject of abstract, brain-teasing, puzzle-like word problems, it is actually an extremely important type of everyday reasoning. It is just hard to recognize sometimes. For example, imagine that you are looking for your car keys and you realize that they are either in the kitchen drawer or in your book bag. After looking in the kitchen drawer, you instantly know that they must be in your book bag. That conclusion results from a simple deductive reasoning argument. In addition, solid deductive reasoning skills are necessary for you to succeed in the sciences, philosophy, math, computer programming, and any endeavor involving the use of logic to persuade others to your point of view or to evaluate others’ arguments.

Cognitive psychologists, and before them philosophers, have been quite interested in deductive reasoning, not so much for its practical applications, but for the insights it can offer them about the ways that human beings think. One of the early ideas to emerge from the examination of deductive reasoning is that people learn (or develop) mental versions of rules that allow them to solve these types of reasoning problems (Braine, 1978; Braine, Reiser, & Rumain, 1984). The best way to see this point of view is to realize that there are different possible rules, and some of them are very simple. For example, consider this rule of logic:

therefore q

Logical rules are often presented abstractly, as letters, in order to imply that they can be used in very many specific situations. Here is a concrete version of the of the same rule:

I’ll either have pizza or a hamburger for dinner tonight (p or q)

I won’t have pizza (not p)

Therefore, I’ll have a hamburger (therefore q)

This kind of reasoning seems so natural, so easy, that it is quite plausible that we would use a version of this rule in our daily lives. At least, it seems more plausible than some of the alternative possibilities—for example, that we need to have experience with the specific situation (pizza or hamburger, in this case) in order to solve this type of problem easily. So perhaps there is a form of natural logic (Rips, 1990) that contains very simple versions of logical rules. When we are faced with a reasoning problem that maps onto one of these rules, we use the rule.

But be very careful; things are not always as easy as they seem. Even these simple rules are not so simple. For example, consider the following rule. Many people fail to realize that this rule is just as valid as the pizza or hamburger rule above.

if p, then q

therefore, not p

Concrete version:

If I eat dinner, then I will have dessert

I did not have dessert

Therefore, I did not eat dinner

The simple fact is, it can be very difficult for people to apply rules of deductive logic correctly; as a result, they make many errors when trying to do so. Is this a deductively valid argument or not?

Students who like school study a lot

Students who study a lot get good grades

Jane does not like school

Therefore, Jane does not get good grades

Many people are surprised to discover that this is not a logically valid argument; the conclusion is not guaranteed to be true from the beginning statements. Although the first statement says that students who like school study a lot, it does NOT say that students who do not like school do not study a lot. In other words, it may very well be possible to study a lot without liking school. Even people who sometimes get problems like this right might not be using the rules of deductive reasoning. Instead, they might just be making judgments for examples they know, in this case, remembering instances of people who get good grades despite not liking school.

Making deductive reasoning even more difficult is the fact that there are two important properties that an argument may have. One, it can be valid or invalid (meaning that the conclusion does or does not follow logically from the statements leading up to it). Two, an argument (or more correctly, its conclusion) can be true or false. Here is an example of an argument that is logically valid, but has a false conclusion (at least we think it is false).

Either you are eleven feet tall or the Grand Canyon was created by a spaceship crashing into the earth.

You are not eleven feet tall

Therefore the Grand Canyon was created by a spaceship crashing into the earth

This argument has the exact same form as the pizza or hamburger argument above, making it is deductively valid. The conclusion is so false, however, that it is absurd (of course, the reason the conclusion is false is that the first statement is false). When people are judging arguments, they tend to not observe the difference between deductive validity and the empirical truth of statements or conclusions. If the elements of an argument happen to be true, people are likely to judge the argument logically valid; if the elements are false, they will very likely judge it invalid (Markovits & Bouffard-Bouchard, 1992; Moshman & Franks, 1986). Thus, it seems a stretch to say that people are using these logical rules to judge the validity of arguments. Many psychologists believe that most people actually have very limited deductive reasoning skills (Johnson-Laird, 1999). They argue that when faced with a problem for which deductive logic is required, people resort to some simpler technique, such as matching terms that appear in the statements and the conclusion (Evans, 1982). This might not seem like a problem, but what if reasoners believe that the elements are true and they happen to be wrong; they will would believe that they are using a form of reasoning that guarantees they are correct and yet be wrong.

deductive reasoning :  a type of reasoning in which the conclusion is guaranteed to be true any time the statements leading up to it are true

argument :  a set of statements in which the beginning statements lead to a conclusion

deductively valid argument :  an argument for which true beginning statements guarantee that the conclusion is true

Inductive reasoning and judgment

Every day, you make many judgments about the likelihood of one thing or another. Whether you realize it or not, you are practicing  inductive reasoning   on a daily basis. In inductive reasoning arguments, a conclusion is likely whenever the statements preceding it are true. The first thing to notice about inductive reasoning is that, by definition, you can never be sure about your conclusion; you can only estimate how likely the conclusion is. Inductive reasoning may lead you to focus on Memory Encoding and Recoding when you study for the exam, but it is possible the instructor will ask more questions about Memory Retrieval instead. Unlike deductive reasoning, the conclusions you reach through inductive reasoning are only probable, not certain. That is why scientists consider inductive reasoning weaker than deductive reasoning. But imagine how hard it would be for us to function if we could not act unless we were certain about the outcome.

Inductive reasoning can be represented as logical arguments consisting of statements and a conclusion, just as deductive reasoning can be. In an inductive argument, you are given some statements and a conclusion (or you are given some statements and must draw a conclusion). An argument is  inductively strong   if the conclusion would be very probable whenever the statements are true. So, for example, here is an inductively strong argument:

  • Statement #1: The forecaster on Channel 2 said it is going to rain today.
  • Statement #2: The forecaster on Channel 5 said it is going to rain today.
  • Statement #3: It is very cloudy and humid.
  • Statement #4: You just heard thunder.
  • Conclusion (or judgment): It is going to rain today.

Think of the statements as evidence, on the basis of which you will draw a conclusion. So, based on the evidence presented in the four statements, it is very likely that it will rain today. Will it definitely rain today? Certainly not. We can all think of times that the weather forecaster was wrong.

A true story: Some years ago psychology student was watching a baseball playoff game between the St. Louis Cardinals and the Los Angeles Dodgers. A graphic on the screen had just informed the audience that the Cardinal at bat, (Hall of Fame shortstop) Ozzie Smith, a switch hitter batting left-handed for this plate appearance, had never, in nearly 3000 career at-bats, hit a home run left-handed. The student, who had just learned about inductive reasoning in his psychology class, turned to his companion (a Cardinals fan) and smugly said, “It is an inductively strong argument that Ozzie Smith will not hit a home run.” He turned back to face the television just in time to watch the ball sail over the right field fence for a home run. Although the student felt foolish at the time, he was not wrong. It was an inductively strong argument; 3000 at-bats is an awful lot of evidence suggesting that the Wizard of Ozz (as he was known) would not be hitting one out of the park (think of each at-bat without a home run as a statement in an inductive argument). Sadly (for the die-hard Cubs fan and Cardinals-hating student), despite the strength of the argument, the conclusion was wrong.

Given the possibility that we might draw an incorrect conclusion even with an inductively strong argument, we really want to be sure that we do, in fact, make inductively strong arguments. If we judge something probable, it had better be probable. If we judge something nearly impossible, it had better not happen. Think of inductive reasoning, then, as making reasonably accurate judgments of the probability of some conclusion given a set of evidence.

We base many decisions in our lives on inductive reasoning. For example:

Statement #1: Psychology is not my best subject

Statement #2: My psychology instructor has a reputation for giving difficult exams

Statement #3: My first psychology exam was much harder than I expected

Judgment: The next exam will probably be very difficult.

Decision: I will study tonight instead of watching Netflix.

Some other examples of judgments that people commonly make in a school context include judgments of the likelihood that:

  • A particular class will be interesting/useful/difficult
  • You will be able to finish writing a paper by next week if you go out tonight
  • Your laptop’s battery will last through the next trip to the library
  • You will not miss anything important if you skip class tomorrow
  • Your instructor will not notice if you skip class tomorrow
  • You will be able to find a book that you will need for a paper
  • There will be an essay question about Memory Encoding on the next exam

Tversky and Kahneman (1983) recognized that there are two general ways that we might make these judgments; they termed them extensional (i.e., following the laws of probability) and intuitive (i.e., using shortcuts or heuristics, see below). We will use a similar distinction between Type 1 and Type 2 thinking, as described by Keith Stanovich and his colleagues (Evans and Stanovich, 2013; Stanovich and West, 2000). Type 1 thinking is fast, automatic, effortful, and emotional. In fact, it is hardly fair to call it reasoning at all, as judgments just seem to pop into one’s head. Type 2 thinking , on the other hand, is slow, effortful, and logical. So obviously, it is more likely to lead to a correct judgment, or an optimal decision. The problem is, we tend to over-rely on Type 1. Now, we are not saying that Type 2 is the right way to go for every decision or judgment we make. It seems a bit much, for example, to engage in a step-by-step logical reasoning procedure to decide whether we will have chicken or fish for dinner tonight.

Many bad decisions in some very important contexts, however, can be traced back to poor judgments of the likelihood of certain risks or outcomes that result from the use of Type 1 when a more logical reasoning process would have been more appropriate. For example:

Statement #1: It is late at night.

Statement #2: Albert has been drinking beer for the past five hours at a party.

Statement #3: Albert is not exactly sure where he is or how far away home is.

Judgment: Albert will have no difficulty walking home.

Decision: He walks home alone.

As you can see in this example, the three statements backing up the judgment do not really support it. In other words, this argument is not inductively strong because it is based on judgments that ignore the laws of probability. What are the chances that someone facing these conditions will be able to walk home alone easily? And one need not be drunk to make poor decisions based on judgments that just pop into our heads.

The truth is that many of our probability judgments do not come very close to what the laws of probability say they should be. Think about it. In order for us to reason in accordance with these laws, we would need to know the laws of probability, which would allow us to calculate the relationship between particular pieces of evidence and the probability of some outcome (i.e., how much likelihood should change given a piece of evidence), and we would have to do these heavy math calculations in our heads. After all, that is what Type 2 requires. Needless to say, even if we were motivated, we often do not even know how to apply Type 2 reasoning in many cases.

So what do we do when we don’t have the knowledge, skills, or time required to make the correct mathematical judgment? Do we hold off and wait until we can get better evidence? Do we read up on probability and fire up our calculator app so we can compute the correct probability? Of course not. We rely on Type 1 thinking. We “wing it.” That is, we come up with a likelihood estimate using some means at our disposal. Psychologists use the term heuristic to describe the type of “winging it” we are talking about. A  heuristic   is a shortcut strategy that we use to make some judgment or solve some problem (see Section 7.3). Heuristics are easy and quick, think of them as the basic procedures that are characteristic of Type 1.  They can absolutely lead to reasonably good judgments and decisions in some situations (like choosing between chicken and fish for dinner). They are, however, far from foolproof. There are, in fact, quite a lot of situations in which heuristics can lead us to make incorrect judgments, and in many cases the decisions based on those judgments can have serious consequences.

Let us return to the activity that begins this section. You were asked to judge the likelihood (or frequency) of certain events and risks. You were free to come up with your own evidence (or statements) to make these judgments. This is where a heuristic crops up. As a judgment shortcut, we tend to generate specific examples of those very events to help us decide their likelihood or frequency. For example, if we are asked to judge how common, frequent, or likely a particular type of cancer is, many of our statements would be examples of specific cancer cases:

Statement #1: Andy Kaufman (comedian) had lung cancer.

Statement #2: Colin Powell (US Secretary of State) had prostate cancer.

Statement #3: Bob Marley (musician) had skin and brain cancer

Statement #4: Sandra Day O’Connor (Supreme Court Justice) had breast cancer.

Statement #5: Fred Rogers (children’s entertainer) had stomach cancer.

Statement #6: Robin Roberts (news anchor) had breast cancer.

Statement #7: Bette Davis (actress) had breast cancer.

Judgment: Breast cancer is the most common type.

Your own experience or memory may also tell you that breast cancer is the most common type. But it is not (although it is common). Actually, skin cancer is the most common type in the US. We make the same types of misjudgments all the time because we do not generate the examples or evidence according to their actual frequencies or probabilities. Instead, we have a tendency (or bias) to search for the examples in memory; if they are easy to retrieve, we assume that they are common. To rephrase this in the language of the heuristic, events seem more likely to the extent that they are available to memory. This bias has been termed the  availability heuristic   (Kahneman and Tversky, 1974).

The fact that we use the availability heuristic does not automatically mean that our judgment is wrong. The reason we use heuristics in the first place is that they work fairly well in many cases (and, of course that they are easy to use). So, the easiest examples to think of sometimes are the most common ones. Is it more likely that a member of the U.S. Senate is a man or a woman? Most people have a much easier time generating examples of male senators. And as it turns out, the U.S. Senate has many more men than women (74 to 26 in 2020). In this case, then, the availability heuristic would lead you to make the correct judgment; it is far more likely that a senator would be a man.

In many other cases, however, the availability heuristic will lead us astray. This is because events can be memorable for many reasons other than their frequency. Section 5.2, Encoding Meaning, suggested that one good way to encode the meaning of some information is to form a mental image of it. Thus, information that has been pictured mentally will be more available to memory. Indeed, an event that is vivid and easily pictured will trick many people into supposing that type of event is more common than it actually is. Repetition of information will also make it more memorable. So, if the same event is described to you in a magazine, on the evening news, on a podcast that you listen to, and in your Facebook feed; it will be very available to memory. Again, the availability heuristic will cause you to misperceive the frequency of these types of events.

Most interestingly, information that is unusual is more memorable. Suppose we give you the following list of words to remember: box, flower, letter, platypus, oven, boat, newspaper, purse, drum, car. Very likely, the easiest word to remember would be platypus, the unusual one. The same thing occurs with memories of events. An event may be available to memory because it is unusual, yet the availability heuristic leads us to judge that the event is common. Did you catch that? In these cases, the availability heuristic makes us think the exact opposite of the true frequency. We end up thinking something is common because it is unusual (and therefore memorable). Yikes.

The misapplication of the availability heuristic sometimes has unfortunate results. For example, if you went to K-12 school in the US over the past 10 years, it is extremely likely that you have participated in lockdown and active shooter drills. Of course, everyone is trying to prevent the tragedy of another school shooting. And believe us, we are not trying to minimize how terrible the tragedy is. But the truth of the matter is, school shootings are extremely rare. Because the federal government does not keep a database of school shootings, the Washington Post has maintained their own running tally. Between 1999 and January 2020 (the date of the most recent school shooting with a death in the US at of the time this paragraph was written), the Post reported a total of 254 people died in school shootings in the US. Not 254 per year, 254 total. That is an average of 12 per year. Of course, that is 254 people who should not have died (particularly because many were children), but in a country with approximately 60,000,000 students and teachers, this is a very small risk.

But many students and teachers are terrified that they will be victims of school shootings because of the availability heuristic. It is so easy to think of examples (they are very available to memory) that people believe the event is very common. It is not. And there is a downside to this. We happen to believe that there is an enormous gun violence problem in the United States. According the the Centers for Disease Control and Prevention, there were 39,773 firearm deaths in the US in 2017. Fifteen of those deaths were in school shootings, according to the Post. 60% of those deaths were suicides. When people pay attention to the school shooting risk (low), they often fail to notice the much larger risk.

And examples like this are by no means unique. The authors of this book have been teaching psychology since the 1990’s. We have been able to make the exact same arguments about the misapplication of the availability heuristics and keep them current by simply swapping out for the “fear of the day.” In the 1990’s it was children being kidnapped by strangers (it was known as “stranger danger”) despite the facts that kidnappings accounted for only 2% of the violent crimes committed against children, and only 24% of kidnappings are committed by strangers (US Department of Justice, 2007). This fear overlapped with the fear of terrorism that gripped the country after the 2001 terrorist attacks on the World Trade Center and US Pentagon and still plagues the population of the US somewhat in 2020. After a well-publicized, sensational act of violence, people are extremely likely to increase their estimates of the chances that they, too, will be victims of terror. Think about the reality, however. In October of 2001, a terrorist mailed anthrax spores to members of the US government and a number of media companies. A total of five people died as a result of this attack. The nation was nearly paralyzed by the fear of dying from the attack; in reality the probability of an individual person dying was 0.00000002.

The availability heuristic can lead you to make incorrect judgments in a school setting as well. For example, suppose you are trying to decide if you should take a class from a particular math professor. You might try to make a judgment of how good a teacher she is by recalling instances of friends and acquaintances making comments about her teaching skill. You may have some examples that suggest that she is a poor teacher very available to memory, so on the basis of the availability heuristic you judge her a poor teacher and decide to take the class from someone else. What if, however, the instances you recalled were all from the same person, and this person happens to be a very colorful storyteller? The subsequent ease of remembering the instances might not indicate that the professor is a poor teacher after all.

Although the availability heuristic is obviously important, it is not the only judgment heuristic we use. Amos Tversky and Daniel Kahneman examined the role of heuristics in inductive reasoning in a long series of studies. Kahneman received a Nobel Prize in Economics for this research in 2002, and Tversky would have certainly received one as well if he had not died of melanoma at age 59 in 1996 (Nobel Prizes are not awarded posthumously). Kahneman and Tversky demonstrated repeatedly that people do not reason in ways that are consistent with the laws of probability. They identified several heuristic strategies that people use instead to make judgments about likelihood. The importance of this work for economics (and the reason that Kahneman was awarded the Nobel Prize) is that earlier economic theories had assumed that people do make judgments rationally, that is, in agreement with the laws of probability.

Another common heuristic that people use for making judgments is the  representativeness heuristic (Kahneman & Tversky 1973). Suppose we describe a person to you. He is quiet and shy, has an unassuming personality, and likes to work with numbers. Is this person more likely to be an accountant or an attorney? If you said accountant, you were probably using the representativeness heuristic. Our imaginary person is judged likely to be an accountant because he resembles, or is representative of the concept of, an accountant. When research participants are asked to make judgments such as these, the only thing that seems to matter is the representativeness of the description. For example, if told that the person described is in a room that contains 70 attorneys and 30 accountants, participants will still assume that he is an accountant.

inductive reasoning :  a type of reasoning in which we make judgments about likelihood from sets of evidence

inductively strong argument :  an inductive argument in which the beginning statements lead to a conclusion that is probably true

heuristic :  a shortcut strategy that we use to make judgments and solve problems. Although they are easy to use, they do not guarantee correct judgments and solutions

availability heuristic :  judging the frequency or likelihood of some event type according to how easily examples of the event can be called to mind (i.e., how available they are to memory)

representativeness heuristic:   judging the likelihood that something is a member of a category on the basis of how much it resembles a typical category member (i.e., how representative it is of the category)

Type 1 thinking : fast, automatic, and emotional thinking.

Type 2 thinking : slow, effortful, and logical thinking.

  • What percentage of workplace homicides are co-worker violence?

Many people get these questions wrong. The answers are 10%; stairs; skin; 6%. How close were your answers? Explain how the availability heuristic might have led you to make the incorrect judgments.

  • Can you think of some other judgments that you have made (or beliefs that you have) that might have been influenced by the availability heuristic?

7.3 Problem Solving

  • Please take a few minutes to list a number of problems that you are facing right now.
  • Now write about a problem that you recently solved.
  • What is your definition of a problem?

Mary has a problem. Her daughter, ordinarily quite eager to please, appears to delight in being the last person to do anything. Whether getting ready for school, going to piano lessons or karate class, or even going out with her friends, she seems unwilling or unable to get ready on time. Other people have different kinds of problems. For example, many students work at jobs, have numerous family commitments, and are facing a course schedule full of difficult exams, assignments, papers, and speeches. How can they find enough time to devote to their studies and still fulfill their other obligations? Speaking of students and their problems: Show that a ball thrown vertically upward with initial velocity v0 takes twice as much time to return as to reach the highest point (from Spiegel, 1981).

These are three very different situations, but we have called them all problems. What makes them all the same, despite the differences? A psychologist might define a  problem   as a situation with an initial state, a goal state, and a set of possible intermediate states. Somewhat more meaningfully, we might consider a problem a situation in which you are in here one state (e.g., daughter is always late), you want to be there in another state (e.g., daughter is not always late), and with no obvious way to get from here to there. Defined this way, each of the three situations we outlined can now be seen as an example of the same general concept, a problem. At this point, you might begin to wonder what is not a problem, given such a general definition. It seems that nearly every non-routine task we engage in could qualify as a problem. As long as you realize that problems are not necessarily bad (it can be quite fun and satisfying to rise to the challenge and solve a problem), this may be a useful way to think about it.

Can we identify a set of problem-solving skills that would apply to these very different kinds of situations? That task, in a nutshell, is a major goal of this section. Let us try to begin to make sense of the wide variety of ways that problems can be solved with an important observation: the process of solving problems can be divided into two key parts. First, people have to notice, comprehend, and represent the problem properly in their minds (called  problem representation ). Second, they have to apply some kind of solution strategy to the problem. Psychologists have studied both of these key parts of the process in detail.

When you first think about the problem-solving process, you might guess that most of our difficulties would occur because we are failing in the second step, the application of strategies. Although this can be a significant difficulty much of the time, the more important source of difficulty is probably problem representation. In short, we often fail to solve a problem because we are looking at it, or thinking about it, the wrong way.

problem :  a situation in which we are in an initial state, have a desired goal state, and there is a number of possible intermediate states (i.e., there is no obvious way to get from the initial to the goal state)

problem representation :  noticing, comprehending and forming a mental conception of a problem

Defining and Mentally Representing Problems in Order to Solve Them

So, the main obstacle to solving a problem is that we do not clearly understand exactly what the problem is. Recall the problem with Mary’s daughter always being late. One way to represent, or to think about, this problem is that she is being defiant. She refuses to get ready in time. This type of representation or definition suggests a particular type of solution. Another way to think about the problem, however, is to consider the possibility that she is simply being sidetracked by interesting diversions. This different conception of what the problem is (i.e., different representation) suggests a very different solution strategy. For example, if Mary defines the problem as defiance, she may be tempted to solve the problem using some kind of coercive tactics, that is, to assert her authority as her mother and force her to listen. On the other hand, if Mary defines the problem as distraction, she may try to solve it by simply removing the distracting objects.

As you might guess, when a problem is represented one way, the solution may seem very difficult, or even impossible. Seen another way, the solution might be very easy. For example, consider the following problem (from Nasar, 1998):

Two bicyclists start 20 miles apart and head toward each other, each going at a steady rate of 10 miles per hour. At the same time, a fly that travels at a steady 15 miles per hour starts from the front wheel of the southbound bicycle and flies to the front wheel of the northbound one, then turns around and flies to the front wheel of the southbound one again, and continues in this manner until he is crushed between the two front wheels. Question: what total distance did the fly cover?

Please take a few minutes to try to solve this problem.

Most people represent this problem as a question about a fly because, well, that is how the question is asked. The solution, using this representation, is to figure out how far the fly travels on the first leg of its journey, then add this total to how far it travels on the second leg of its journey (when it turns around and returns to the first bicycle), then continue to add the smaller distance from each leg of the journey until you converge on the correct answer. You would have to be quite skilled at math to solve this problem, and you would probably need some time and pencil and paper to do it.

If you consider a different representation, however, you can solve this problem in your head. Instead of thinking about it as a question about a fly, think about it as a question about the bicycles. They are 20 miles apart, and each is traveling 10 miles per hour. How long will it take for the bicycles to reach each other? Right, one hour. The fly is traveling 15 miles per hour; therefore, it will travel a total of 15 miles back and forth in the hour before the bicycles meet. Represented one way (as a problem about a fly), the problem is quite difficult. Represented another way (as a problem about two bicycles), it is easy. Changing your representation of a problem is sometimes the best—sometimes the only—way to solve it.

Unfortunately, however, changing a problem’s representation is not the easiest thing in the world to do. Often, problem solvers get stuck looking at a problem one way. This is called  fixation . Most people who represent the preceding problem as a problem about a fly probably do not pause to reconsider, and consequently change, their representation. A parent who thinks her daughter is being defiant is unlikely to consider the possibility that her behavior is far less purposeful.

Problem-solving fixation was examined by a group of German psychologists called Gestalt psychologists during the 1930’s and 1940’s. Karl Dunker, for example, discovered an important type of failure to take a different perspective called  functional fixedness . Imagine being a participant in one of his experiments. You are asked to figure out how to mount two candles on a door and are given an assortment of odds and ends, including a small empty cardboard box and some thumbtacks. Perhaps you have already figured out a solution: tack the box to the door so it forms a platform, then put the candles on top of the box. Most people are able to arrive at this solution. Imagine a slight variation of the procedure, however. What if, instead of being empty, the box had matches in it? Most people given this version of the problem do not arrive at the solution given above. Why? Because it seems to people that when the box contains matches, it already has a function; it is a matchbox. People are unlikely to consider a new function for an object that already has a function. This is functional fixedness.

Mental set is a type of fixation in which the problem solver gets stuck using the same solution strategy that has been successful in the past, even though the solution may no longer be useful. It is commonly seen when students do math problems for homework. Often, several problems in a row require the reapplication of the same solution strategy. Then, without warning, the next problem in the set requires a new strategy. Many students attempt to apply the formerly successful strategy on the new problem and therefore cannot come up with a correct answer.

The thing to remember is that you cannot solve a problem unless you correctly identify what it is to begin with (initial state) and what you want the end result to be (goal state). That may mean looking at the problem from a different angle and representing it in a new way. The correct representation does not guarantee a successful solution, but it certainly puts you on the right track.

A bit more optimistically, the Gestalt psychologists discovered what may be considered the opposite of fixation, namely  insight . Sometimes the solution to a problem just seems to pop into your head. Wolfgang Kohler examined insight by posing many different problems to chimpanzees, principally problems pertaining to their acquisition of out-of-reach food. In one version, a banana was placed outside of a chimpanzee’s cage and a short stick inside the cage. The stick was too short to retrieve the banana, but was long enough to retrieve a longer stick also located outside of the cage. This second stick was long enough to retrieve the banana. After trying, and failing, to reach the banana with the shorter stick, the chimpanzee would try a couple of random-seeming attempts, react with some apparent frustration or anger, then suddenly rush to the longer stick, the correct solution fully realized at this point. This sudden appearance of the solution, observed many times with many different problems, was termed insight by Kohler.

Lest you think it pertains to chimpanzees only, Karl Dunker demonstrated that children also solve problems through insight in the 1930s. More importantly, you have probably experienced insight yourself. Think back to a time when you were trying to solve a difficult problem. After struggling for a while, you gave up. Hours later, the solution just popped into your head, perhaps when you were taking a walk, eating dinner, or lying in bed.

fixation :  when a problem solver gets stuck looking at a problem a particular way and cannot change his or her representation of it (or his or her intended solution strategy)

functional fixedness :  a specific type of fixation in which a problem solver cannot think of a new use for an object that already has a function

mental set :  a specific type of fixation in which a problem solver gets stuck using the same solution strategy that has been successful in the past

insight :  a sudden realization of a solution to a problem

Solving Problems by Trial and Error

Correctly identifying the problem and your goal for a solution is a good start, but recall the psychologist’s definition of a problem: it includes a set of possible intermediate states. Viewed this way, a problem can be solved satisfactorily only if one can find a path through some of these intermediate states to the goal. Imagine a fairly routine problem, finding a new route to school when your ordinary route is blocked (by road construction, for example). At each intersection, you may turn left, turn right, or go straight. A satisfactory solution to the problem (of getting to school) is a sequence of selections at each intersection that allows you to wind up at school.

If you had all the time in the world to get to school, you might try choosing intermediate states randomly. At one corner you turn left, the next you go straight, then you go left again, then right, then right, then straight. Unfortunately, trial and error will not necessarily get you where you want to go, and even if it does, it is not the fastest way to get there. For example, when a friend of ours was in college, he got lost on the way to a concert and attempted to find the venue by choosing streets to turn onto randomly (this was long before the use of GPS). Amazingly enough, the strategy worked, although he did end up missing two out of the three bands who played that night.

Trial and error is not all bad, however. B.F. Skinner, a prominent behaviorist psychologist, suggested that people often behave randomly in order to see what effect the behavior has on the environment and what subsequent effect this environmental change has on them. This seems particularly true for the very young person. Picture a child filling a household’s fish tank with toilet paper, for example. To a child trying to develop a repertoire of creative problem-solving strategies, an odd and random behavior might be just the ticket. Eventually, the exasperated parent hopes, the child will discover that many of these random behaviors do not successfully solve problems; in fact, in many cases they create problems. Thus, one would expect a decrease in this random behavior as a child matures. You should realize, however, that the opposite extreme is equally counterproductive. If the children become too rigid, never trying something unexpected and new, their problem solving skills can become too limited.

Effective problem solving seems to call for a happy medium that strikes a balance between using well-founded old strategies and trying new ground and territory. The individual who recognizes a situation in which an old problem-solving strategy would work best, and who can also recognize a situation in which a new untested strategy is necessary is halfway to success.

Solving Problems with Algorithms and Heuristics

For many problems there is a possible strategy available that will guarantee a correct solution. For example, think about math problems. Math lessons often consist of step-by-step procedures that can be used to solve the problems. If you apply the strategy without error, you are guaranteed to arrive at the correct solution to the problem. This approach is called using an  algorithm , a term that denotes the step-by-step procedure that guarantees a correct solution. Because algorithms are sometimes available and come with a guarantee, you might think that most people use them frequently. Unfortunately, however, they do not. As the experience of many students who have struggled through math classes can attest, algorithms can be extremely difficult to use, even when the problem solver knows which algorithm is supposed to work in solving the problem. In problems outside of math class, we often do not even know if an algorithm is available. It is probably fair to say, then, that algorithms are rarely used when people try to solve problems.

Because algorithms are so difficult to use, people often pass up the opportunity to guarantee a correct solution in favor of a strategy that is much easier to use and yields a reasonable chance of coming up with a correct solution. These strategies are called  problem solving heuristics . Similar to what you saw in section 6.2 with reasoning heuristics, a problem solving heuristic is a shortcut strategy that people use when trying to solve problems. It usually works pretty well, but does not guarantee a correct solution to the problem. For example, one problem solving heuristic might be “always move toward the goal” (so when trying to get to school when your regular route is blocked, you would always turn in the direction you think the school is). A heuristic that people might use when doing math homework is “use the same solution strategy that you just used for the previous problem.”

By the way, we hope these last two paragraphs feel familiar to you. They seem to parallel a distinction that you recently learned. Indeed, algorithms and problem-solving heuristics are another example of the distinction between Type 1 thinking and Type 2 thinking.

Although it is probably not worth describing a large number of specific heuristics, two observations about heuristics are worth mentioning. First, heuristics can be very general or they can be very specific, pertaining to a particular type of problem only. For example, “always move toward the goal” is a general strategy that you can apply to countless problem situations. On the other hand, “when you are lost without a functioning gps, pick the most expensive car you can see and follow it” is specific to the problem of being lost. Second, all heuristics are not equally useful. One heuristic that many students know is “when in doubt, choose c for a question on a multiple-choice exam.” This is a dreadful strategy because many instructors intentionally randomize the order of answer choices. Another test-taking heuristic, somewhat more useful, is “look for the answer to one question somewhere else on the exam.”

You really should pay attention to the application of heuristics to test taking. Imagine that while reviewing your answers for a multiple-choice exam before turning it in, you come across a question for which you originally thought the answer was c. Upon reflection, you now think that the answer might be b. Should you change the answer to b, or should you stick with your first impression? Most people will apply the heuristic strategy to “stick with your first impression.” What they do not realize, of course, is that this is a very poor strategy (Lilienfeld et al, 2009). Most of the errors on exams come on questions that were answered wrong originally and were not changed (so they remain wrong). There are many fewer errors where we change a correct answer to an incorrect answer. And, of course, sometimes we change an incorrect answer to a correct answer. In fact, research has shown that it is more common to change a wrong answer to a right answer than vice versa (Bruno, 2001).

The belief in this poor test-taking strategy (stick with your first impression) is based on the  confirmation bias   (Nickerson, 1998; Wason, 1960). You first saw the confirmation bias in Module 1, but because it is so important, we will repeat the information here. People have a bias, or tendency, to notice information that confirms what they already believe. Somebody at one time told you to stick with your first impression, so when you look at the results of an exam you have taken, you will tend to notice the cases that are consistent with that belief. That is, you will notice the cases in which you originally had an answer correct and changed it to the wrong answer. You tend not to notice the other two important (and more common) cases, changing an answer from wrong to right, and leaving a wrong answer unchanged.

Because heuristics by definition do not guarantee a correct solution to a problem, mistakes are bound to occur when we employ them. A poor choice of a specific heuristic will lead to an even higher likelihood of making an error.

algorithm :  a step-by-step procedure that guarantees a correct solution to a problem

problem solving heuristic :  a shortcut strategy that we use to solve problems. Although they are easy to use, they do not guarantee correct judgments and solutions

confirmation bias :  people’s tendency to notice information that confirms what they already believe

An Effective Problem-Solving Sequence

You may be left with a big question: If algorithms are hard to use and heuristics often don’t work, how am I supposed to solve problems? Robert Sternberg (1996), as part of his theory of what makes people successfully intelligent (Module 8) described a problem-solving sequence that has been shown to work rather well:

  • Identify the existence of a problem.  In school, problem identification is often easy; problems that you encounter in math classes, for example, are conveniently labeled as problems for you. Outside of school, however, realizing that you have a problem is a key difficulty that you must get past in order to begin solving it. You must be very sensitive to the symptoms that indicate a problem.
  • Define the problem.  Suppose you realize that you have been having many headaches recently. Very likely, you would identify this as a problem. If you define the problem as “headaches,” the solution would probably be to take aspirin or ibuprofen or some other anti-inflammatory medication. If the headaches keep returning, however, you have not really solved the problem—likely because you have mistaken a symptom for the problem itself. Instead, you must find the root cause of the headaches. Stress might be the real problem. For you to successfully solve many problems it may be necessary for you to overcome your fixations and represent the problems differently. One specific strategy that you might find useful is to try to define the problem from someone else’s perspective. How would your parents, spouse, significant other, doctor, etc. define the problem? Somewhere in these different perspectives may lurk the key definition that will allow you to find an easier and permanent solution.
  • Formulate strategy.  Now it is time to begin planning exactly how the problem will be solved. Is there an algorithm or heuristic available for you to use? Remember, heuristics by their very nature guarantee that occasionally you will not be able to solve the problem. One point to keep in mind is that you should look for long-range solutions, which are more likely to address the root cause of a problem than short-range solutions.
  • Represent and organize information.  Similar to the way that the problem itself can be defined, or represented in multiple ways, information within the problem is open to different interpretations. Suppose you are studying for a big exam. You have chapters from a textbook and from a supplemental reader, along with lecture notes that all need to be studied. How should you (represent and) organize these materials? Should you separate them by type of material (text versus reader versus lecture notes), or should you separate them by topic? To solve problems effectively, you must learn to find the most useful representation and organization of information.
  • Allocate resources.  This is perhaps the simplest principle of the problem solving sequence, but it is extremely difficult for many people. First, you must decide whether time, money, skills, effort, goodwill, or some other resource would help to solve the problem Then, you must make the hard choice of deciding which resources to use, realizing that you cannot devote maximum resources to every problem. Very often, the solution to problem is simply to change how resources are allocated (for example, spending more time studying in order to improve grades).
  • Monitor and evaluate solutions.  Pay attention to the solution strategy while you are applying it. If it is not working, you may be able to select another strategy. Another fact you should realize about problem solving is that it never does end. Solving one problem frequently brings up new ones. Good monitoring and evaluation of your problem solutions can help you to anticipate and get a jump on solving the inevitable new problems that will arise.

Please note that this as  an  effective problem-solving sequence, not  the  effective problem solving sequence. Just as you can become fixated and end up representing the problem incorrectly or trying an inefficient solution, you can become stuck applying the problem-solving sequence in an inflexible way. Clearly there are problem situations that can be solved without using these skills in this order.

Additionally, many real-world problems may require that you go back and redefine a problem several times as the situation changes (Sternberg et al. 2000). For example, consider the problem with Mary’s daughter one last time. At first, Mary did represent the problem as one of defiance. When her early strategy of pleading and threatening punishment was unsuccessful, Mary began to observe her daughter more carefully. She noticed that, indeed, her daughter’s attention would be drawn by an irresistible distraction or book. Fresh with a re-representation of the problem, she began a new solution strategy. She began to remind her daughter every few minutes to stay on task and remind her that if she is ready before it is time to leave, she may return to the book or other distracting object at that time. Fortunately, this strategy was successful, so Mary did not have to go back and redefine the problem again.

Pick one or two of the problems that you listed when you first started studying this section and try to work out the steps of Sternberg’s problem solving sequence for each one.

a mental representation of a category of things in the world

an assumption about the truth of something that is not stated. Inferences come from our prior knowledge and experience, and from logical reasoning

knowledge about one’s own cognitive processes; thinking about your thinking

individuals who are less competent tend to overestimate their abilities more than individuals who are more competent do

Thinking like a scientist in your everyday life for the purpose of drawing correct conclusions. It entails skepticism; an ability to identify biases, distortions, omissions, and assumptions; and excellent deductive and inductive reasoning, and problem solving skills.

a way of thinking in which you refrain from drawing a conclusion or changing your mind until good evidence has been provided

an inclination, tendency, leaning, or prejudice

a type of reasoning in which the conclusion is guaranteed to be true any time the statements leading up to it are true

a set of statements in which the beginning statements lead to a conclusion

an argument for which true beginning statements guarantee that the conclusion is true

a type of reasoning in which we make judgments about likelihood from sets of evidence

an inductive argument in which the beginning statements lead to a conclusion that is probably true

fast, automatic, and emotional thinking

slow, effortful, and logical thinking

a shortcut strategy that we use to make judgments and solve problems. Although they are easy to use, they do not guarantee correct judgments and solutions

udging the frequency or likelihood of some event type according to how easily examples of the event can be called to mind (i.e., how available they are to memory)

judging the likelihood that something is a member of a category on the basis of how much it resembles a typical category member (i.e., how representative it is of the category)

a situation in which we are in an initial state, have a desired goal state, and there is a number of possible intermediate states (i.e., there is no obvious way to get from the initial to the goal state)

noticing, comprehending and forming a mental conception of a problem

when a problem solver gets stuck looking at a problem a particular way and cannot change his or her representation of it (or his or her intended solution strategy)

a specific type of fixation in which a problem solver cannot think of a new use for an object that already has a function

a specific type of fixation in which a problem solver gets stuck using the same solution strategy that has been successful in the past

a sudden realization of a solution to a problem

a step-by-step procedure that guarantees a correct solution to a problem

The tendency to notice and pay attention to information that confirms your prior beliefs and to ignore information that disconfirms them.

a shortcut strategy that we use to solve problems. Although they are easy to use, they do not guarantee correct judgments and solutions

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3 Simple Strategies to Improve Students’ Problem-Solving Skills

These strategies are designed to make sure students have a good understanding of problems before attempting to solve them.

Two students in math class

Research provides a striking revelation about problem solvers. The best problem solvers approach problems much differently than novices. For instance, one meta-study showed that when experts evaluate graphs , they tend to spend less time on tasks and answer choices and more time on evaluating the axes’ labels and the relationships of variables within the graphs. In other words, they spend more time up front making sense of the data before moving to addressing the task.

While slower in solving problems, experts use this additional up-front time to more efficiently and effectively solve the problem. In one study, researchers found that experts were much better at “information extraction” or pulling the information they needed to solve the problem later in the problem than novices. This was due to the fact that they started a problem-solving process by evaluating specific assumptions within problems, asking predictive questions, and then comparing and contrasting their predictions with results. For example, expert problem solvers look at the problem context and ask a number of questions:

  • What do we know about the context of the problem?
  • What assumptions are underlying the problem? What’s the story here?
  • What qualitative and quantitative information is pertinent?
  • What might the problem context be telling us? What questions arise from the information we are reading or reviewing?
  • What are important trends and patterns?

As such, expert problem solvers don’t jump to the presented problem or rush to solutions. They invest the time necessary to make sense of the problem.

Now, think about your own students: Do they immediately jump to the question, or do they take time to understand the problem context? Do they identify the relevant variables, look for patterns, and then focus on the specific tasks?

If your students are struggling to develop the habit of sense-making in a problem- solving context, this is a perfect time to incorporate a few short and sharp strategies to support them.

3 Ways to Improve Student Problem-Solving

1. Slow reveal graphs: The brilliant strategy crafted by K–8 math specialist Jenna Laib and her colleagues provides teachers with an opportunity to gradually display complex graphical information and build students’ questioning, sense-making, and evaluating predictions.

For instance, in one third-grade class, students are given a bar graph without any labels or identifying information except for bars emerging from a horizontal line on the bottom of the slide. Over time, students learn about the categories on the x -axis (types of animals) and the quantities specified on the y -axis (number of baby teeth).

The graphs and the topics range in complexity from studying the standard deviation of temperatures in Antarctica to the use of scatterplots to compare working hours across OECD (Organization for Economic Cooperation and Development) countries. The website offers a number of graphs on Google Slides and suggests questions that teachers may ask students. Furthermore, this site allows teachers to search by type of graph (e.g., scatterplot) or topic (e.g., social justice).

2. Three reads: The three-reads strategy tasks students with evaluating a word problem in three different ways . First, students encounter a problem without having access to the question—for instance, “There are 20 kangaroos on the grassland. Three hop away.” Students are expected to discuss the context of the problem without emphasizing the quantities. For instance, a student may say, “We know that there are a total amount of kangaroos, and the total shrinks because some kangaroos hop away.”

Next, students discuss the important quantities and what questions may be generated. Finally, students receive and address the actual problem. Here they can both evaluate how close their predicted questions were from the actual questions and solve the actual problem.

To get started, consider using the numberless word problems on educator Brian Bushart’s site . For those teaching high school, consider using your own textbook word problems for this activity. Simply create three slides to present to students that include context (e.g., on the first slide state, “A salesman sold twice as much pears in the afternoon as in the morning”). The second slide would include quantities (e.g., “He sold 360 kilograms of pears”), and the third slide would include the actual question (e.g., “How many kilograms did he sell in the morning and how many in the afternoon?”). One additional suggestion for teams to consider is to have students solve the questions they generated before revealing the actual question.

3. Three-Act Tasks: Originally created by Dan Meyer, three-act tasks follow the three acts of a story . The first act is typically called the “setup,” followed by the “confrontation” and then the “resolution.”

This storyline process can be used in mathematics in which students encounter a contextual problem (e.g., a pool is being filled with soda). Here students work to identify the important aspects of the problem. During the second act, students build knowledge and skill to solve the problem (e.g., they learn how to calculate the volume of particular spaces). Finally, students solve the problem and evaluate their answers (e.g., how close were their calculations to the actual specifications of the pool and the amount of liquid that filled it).

Often, teachers add a fourth act (i.e., “the sequel”), in which students encounter a similar problem but in a different context (e.g., they have to estimate the volume of a lava lamp). There are also a number of elementary examples that have been developed by math teachers including GFletchy , which offers pre-kindergarten to middle school activities including counting squares , peas in a pod , and shark bait .

Students need to learn how to slow down and think through a problem context. The aforementioned strategies are quick ways teachers can begin to support students in developing the habits needed to effectively and efficiently tackle complex problem-solving.

The Impact of the Zone of Proximal Development Concept (Scaffolding) on the Students Problem Solving Skills and Learning Outcomes

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Schools regularly use the zone of proximal development (ZPD), also known as scaffolding, to help students learn new skills. Students who do not receive enough scaffolding may not be able to acquire the skills at all, while students who receive too much scaffolding may suffer when it is taken away. Additionally, this will have an impact on their capacity for problem-solving and learning outcomes. This systematic literature review's goal is to examine how ZPD and scaffolding effect students’ learning outcomes and the growth of their problem-solving abilities.

Through a selection of pertinent publications that have undergone extensive analysis, the study addresses three main research topics.

The study's findings revealed that in order to achieve a high level of learning independence for the students and the ability to adapt to new situations leading to more advanced skills, a re-definition of certain concepts along with modifications and amendments on how to apply these new redefined ones, using more advanced teaching methodologies with incorporating technology to help students in exploring new ideas using critical thinking techniques and providing constructive feedback, are needed.

  • zone of proximal development
  • learning outcomes
  • problem solving skills
  • forms of scaffolding
  • re-conceptualize
  • sociocultural theory

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1 Introduction

The zone of proximal development (ZPD), also known as scaffolding, is a concept that is frequently utilized in schools to assist children learn skills. As the student gains proficiency, the expert gradually withdraws assistance until the student can complete the task on his or her own. ZPD as defined by Vygotsky, was designed with the development of children in mind. It depicts how children's cognitive development progresses. Vygotsky stated that rather than utilizing a static measure such as an IQ score to determine a student’s educational aptitude, a developmental measure was required.

Many research find that scaffolding is a good way to assist children learn new abilities and solve issues on their own, through providing a short-term help that will be eliminated after the students have mastered the new skills.

However, there are competing motives to give more or less assistance to students when determining the appropriate quantity of assistance to provide. Children who receive more scaffolding may struggle when it is removed, while students who do not receive enough scaffolding may not be able to gain the abilities at all.

And this in turn, will affect their learning outcomes and their problem-solving abilities.

The purpose of this systematic literature review is to study the impact of ZPD and scaffolding on the learning outcomes of students and how they affect the development of their problem-solving skills.

My scholarly study tackles three primary research concerns through a collection of relevant articles that are thoroughly reviewed:

1. How does the assigning content based on the zone of proximal development of a student affect his/her mastering of the material?

2. How efficient is scaffolding by adults as a technique when it comes to boosting problem-solving outcomes?

3. Do we need to re-conceptualize the concepts of ZPD and scaffolding and to achieve better learning outcomes for students and promote their skills of problem-solving?

The paper elaborates on the findings displaying the different arguments of many studies on the implications of the ZPD and scaffolding in teaching and learning, as well as on the efficiency of scaffolding by adults in boosting problem-solving outcomes.

Furthermore, it discusses if there is a need to reconsider the associations of these concepts in the teaching process.

2 Conceptual Framework

The zone of proximal development (ZPD or Zoped) is described as the difference between a child's “actual developmental level as determined by independent problem solving” and the child's “potential development as determined through problem solving under adult guidance or in collaboration with more capable peers” (Vygotsky, 1978 ).

The ZPD refers to a learner's capacity to do tasks successfully with the assistance of more skilled others, and it's often used in conjunction with aided or “scaffolded” learning. The creation of ZPDs necessitates assistance with cognitive task structuring as well as sensitivity to the learner's current skills.

Scaffolded learning, often known as ZPD, is a two-fold concept. To begin with, it represents a new approach to intelligence testing: analyzing children's intellectual potential in optimal conditions, that is, circumstances that are tailored to the child's specific learning needs and build on his or her current talents. Second, the ZPD is a model for determining how social engagement with more experienced partners affects children's intellectual development. As a result, it establishes connections between the mind of the particular child and the minds of others. According to Obikwelu et al. ( 2013 ), scaffolding is a method of instruction which can help a youngster bridge the gap between what he or she currently knows and what they are expected to learn.

The controversy over the implications of the ZPD and scaffolding concepts in teaching relates to their positive and negative impacts on learners’ learning outcomes and their problem-solving abilities. Some educators find the concept of ZPD and scaffolded learning is ambiguous and lacks a detailed picture of a child's preferred learning method, current level of competence, or intrinsic motivation. According to Lee ( 2011 ), actual learning does not occur when adults just give detailed instructions and demonstrate the work to youngsters.

3 Literature Review

The literature review is organized according to the questions’ topical order:

Q1- How Does the Assigning Content Based on the Zone of Proximal Development of a Student Affect His/her Mastering of the Material?

In China, Learnta TAD which stands for “Teacher + Artificial Intelligence + Data,” A learning platform for K-12 kids is a system that gives teachers information on their learners’ progress in school and uses AI algorithms to recommend the best learning path, allowing teachers to choose the topic students should focus on.

In 2019, Learnta TAD data was obtained from 7913 students in middle and elementary school who completed 250,783 task cards with different skills assigned with each task.

Zou et al. ( 2019 ), who were the researchers of the study, used computerized student achievement assessments via a curriculum based on a knowledge graph to compare “Ready-to-Learn” (RtL) information within the ZPD against “Unready-to-Learn” (UtL) content by the students. During the class, students under the supervision of their teacher perform the required tasks. According to the homework contract, students should finish independently their assignments at home.

According to the research, students’ participation rates vary based on their overall academic accomplishment. In-class assignments were completed at a rate of 75.7% and 74.7% for Math and English respectively, while activities to be done at home were completed at a rate of 65.3% for Math and 70.3% for English. This revealed the more likely completion of activities during the class than at home.

In the light of their study, results indicated that students would grasp more skills if they were given activities within their ZPD (Ready-to-Learn content) rather than (Unready-to-Learn content), which means not aligned with their ZPD. In addition, according to their findings, learners were more likely to understand mathematics in their classes than at home.

Q2- How Efficient is Scaffolding by Adults as a Technique When It Comes to Boosting Problem-Solving Outcomes?

Scaffolding research, which started in the 70s, typically focused on the relationship between scaffolding provided by the parents their children's problem-solving abilities.

In 2003, Conner and Cross conducted a study to look at the impact of maternal scaffolding on kids’ abilities to solve problems. A total of 45 mother-child dyads were included in the study (children aged 16, 26, 44 and 54 months). Every mother was asked to help her child in constructing a tower in the correct order by utilizing all the essential blocks. From no parent interaction through parent demonstration, there were seven levels of maternal scaffolding. According to the research, mothers with contextual scaffolding had a positive impact on the immediate and subsequent results of their children during problem-solving interactions.

These findings back up a study by Bates ( 2005 ) in which scaffolding was assessed using six types of response (corrective feedback, give answer, accept child's response, reinforces, allows child to continue, and asks child to demonstrate knowledge) and six types of feedback (questioning, directing, guiding, pointing, specific pointing and nonverbal pointing) provided by mothers to their kids during play sessions, depending on the children's needs. In a game setting, Bates looked at the role of maternal scaffolding on kids’ attempts to solve comparison problems in quantities. This study included 36 mothers, each with a child aged between three to five years old).

According to Wittwer and Renkl ( 2008 ), before giving scaffolding, the adult must determine the children's current comprehension levels. The above studies have made a substantial contribution to the understanding of children's problem-solving abilities by offering scaffolding focusing on the demands of children with their capability. However, more research into various types of scaffolding is needed to establish if there are any relationships between scaffolding and problem-solving abilities of children.

Q3- Do We Need to Re-conceptualize the Concepts of ZPD and Scaffolding and to Achieve Better Learning Outcomes for Students and Promote Their Skills of Problem-Solving?

Although the concepts of scaffolding and the Zone of Proximal Development are used frequently in teaching and learning, educators nowadays start to consider the re-conceptualization of these concepts to achieve better problem-solving and learning outcomes.

When Vygotsky mentioned peer collaboration, it's worth noting that he only referred to “more able peers,” meaning that there must be an intellectual asymmetry between participants in any collaborative endeavor.

Several researchers have noted (Cowie and van der Aalsvort, 2000 ) that learning can also happen via interaction among students having similar levels of cognitive ability, and as that is, ‘symmetrical’ interactions may also result in learning and development. Analyzing the participants’ communication in this specific setting can allow us to have a deeper grasp of the learning process.in general.

A new notion can be useful, according to Mercer ( 2000a ) and Mercer ( 2000b ), for understanding how interpersonal communication might contribute to the education and conceptual growth. This he called the Intermental Development Zone (IDZ). This idea reflects how the interactive process of teaching and learning is founded on communication and cooperative activity, of a dynamic specific context for shared knowledge. In contrast to the original ZPD, the IDZ is not an individual aptitude, but a dialogic process generated and sustained by people. This coherent textual framework promotes a shared focus of participants and is adapted to the level of changing knowledge as the activity progresses in a professor's and student's successful interaction.

For the re-conception of both ZPD and ‘scaffolding,’ in order to take into account collaborative learning, they discovered that a concept based on the conscious intentions of a teacher outside of dialogue should be shifted into concepts based on dynamic process characterization, which reciprocally and responsively employ language in dialogue between learners. Furthermore, some educators find that scaffolding must go beyond the providing of leading questions in the instillation of systematic and creative thinking. They think that actual learning happens when assisting students in thinking systemically and creatively by learning from examples and generating their own thoughts, without substituting the examples they have acquired mechanically; guiding them to develop their ideas meaningfully; and leading them to consider other alternatives while maintaining associations between these alternatives (parts) to the goal (whole).

4 Methodology

In the planning stage of my literature review, I started to formulate my study questions of the topic that I chose, which later has directed my search and selection of studies to be included in the review.

My proposed research question was: (How does the concepts of ZPD and scaffolding affect the students’ learning outcomes and their problem-solving skills?). After doing an initial search on the topic, I did a quick mapping to identify the types of research linked to the research question.

Only English articles and studies from the last 2 decades (the year of 2000 till 2020/2021) were included in the SLR. The studies focused the results of implementing the ZPD on learning outcomes and the role of scaffolding in developing children problem-solving abilities. Articles in the domains of education and social psychology were incorporated in the literature search. On the other hand, studies in the areas of public health, economy, and politics were omitted in the search process. In addition, articles and research conducted before the year of 2000 were not included.

The keywords used in the search were: ‘zone of proximal development’, ‘learning outcomes’, ‘problem solving skills’, ‘forms of scaffolding’, ‘re-conceptualize’ and ‘sociocultural theory’. Most of the articles and the research were collected from ResearchGate, an online scholarly professional network for shared scholar articles and research papers. Moreover, some articles were obtained from the British University in Dubai online library, EBSCO, Web of Science; few were accessed from Google scholar search engine.

The relevance of each journal article was determined using SCIMAGOJR, an online tool that reviews and evaluates journals and scientific topics. In addition, articles labeled as peer-reviewed were considered. Then, articles and research collected and accessed were evaluated based on their relevance to the SLR title. Abstracts and parts of the introductions were examined to evaluate their value to the SLR topic. Each study's data was compiled and organized into a table for the systematic literature review, to facilitate being assessed for its relevance to the research questions.

5 Discussion

Teaching and learning have evolved dramatically in recent years because of the introduction of educational concepts based on information technology (IT) (Whitaker, New, & Ireland, 2016). Given the outcome-oriented application in teaching with an emphasis on higher-order learning, technology-enhanced scaffolding for individual problem solving in an innovative learning environment is critical. (Raes et al., 2012 ). On highlighting the necessity of tying students’ problem-solving work to content, skills, and tactics, it's crucial to raise difficulties with them, from non-reflective work and compelling them to engage fundamental disciplinary ideas in their tasks. The engagement of users in work is shaped by the tools they utilize. As a result, technologies can be built to impact users’ perspectives, learner-to-learner and learner-to-teacher discourse, and the ways they express themselves in work products.

To conclude, deep cognitive learning cannot take place if a student's level of comprehension is too low (i.e., the support is not within the child’s ZPD since too little help is supplied). In other words, the child is unable to connect his or her prior knowledge and the cognitive effort associated with processing the data is excessive (Wittwer et al., 2010 ). If the learner's level of control matches his or her comprehension, the learner has enough mental skills to actively process the information and make connections between it and previously learned material in long-term memory. However, there are many other elements that affect the impact of the use of scaffolding within the ZPD on the learning outcomes and problem-solving skills, as well as help to determine the amount of support to be provided and methods of providing it, such as the use of technology, the nature of the task, if it is a group work task or individual task, the ability to communicate, teachers’ quality reflected on their teaching strategies and the usage of the platform's learning support which requires different pedagogies than in typical classrooms.

6 Limitations, Recommendations and Implications for Future Research

Most of the limitations in the study came from the fact that there is few experimental research on the impacts scaffolding provided by teachers during classes. Only tutoring studies on one student interacting with a highly skilled peer to perform organized and/or hands-on activities, use an experimental design for face-to-face, non-parental scaffolding.

However, in contrast to instructor scaffolding, most of the studies focused on parental scaffolding. Parental scaffolding differs from teacher scaffolding in that the parent knows his or her child better than a teacher knows his or her students, making the support more customizable. Furthermore, the parental scaffolding studies noted above were conducted in one-on-one scenarios, which are not analogous to classroom scenarios where one teacher is responsible for approximately 30 students at a time.

It is suggested that in future systematic literature studies, different types of scaffolding learning to be chosen to compare the benefits and drawbacks of each style on students learning outcomes and problem-solving abilities. Future research should focus on the circumstances in which these styles are implemented, like whether it is an online classroom, or a regular class. It's also a good idea to reduce the search area, especially the sample, by selecting certain material or subject categories like effect of scaffolding on problem solving abilities in mathematics, or the impact of the ZPD on teaching Science or Chemistry.

For a greater significance of the findings, it would be beneficial to limit the sample by focusing on a certain group age of students, such as in students in foundation stage or in senior grades.

7 Conclusion

Undoubtedly, incorporating the concepts of scaffolding and the ZPD in classrooms, in the same way introduced by Vygotsky has shown a great effect on the development of students’ skills, especially in the aspects of solving problems and untangle challenges.

However, a re-defining of these concepts along with modifications and amendments on how to apply these new redefined ones, using more advanced teaching methodology with incorporating technology to help students in exploring new ideas using critical thinking techniques and providing constructive feedback, are needed in order to achieve a high level of independency of learning for the students and the ability to adapt with new situations resulting in more advanced skills in problem-solving and better learning outcomes.

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Raslan, G. (2024). The Impact of the Zone of Proximal Development Concept (Scaffolding) on the Students Problem Solving Skills and Learning Outcomes. In: Al Marri, K., Mir, F.A., David, S.A., Al-Emran, M. (eds) BUiD Doctoral Research Conference 2023. Lecture Notes in Civil Engineering, vol 473. Springer, Cham. https://doi.org/10.1007/978-3-031-56121-4_6

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    Explaining concepts. Self-directed learning. ... Problem solving across disciplines. Considerations for Using Problem-Based Learning. Rather than teaching relevant material and subsequently having students apply the knowledge to solve problems, the problem is presented first. PBL assignments can be short, or they can be more involved and take a ...

  3. Problem-Based Learning (PBL)

    Problem-Based Learning (PBL) is a teaching method in which complex real-world problems are used as the vehicle to promote student learning of concepts and principles as opposed to direct presentation of facts and concepts. In addition to course content, PBL can promote the development of critical thinking skills, problem-solving abilities, and ...

  4. The Stuff of Problem Solving: Discovering Concepts and Applying

    The Stuff of Problem Solving: Discovering Concepts and Applying Principles. Few would disagree that building critical thinking and creative problem solving skills is imperative for today's students. However, subject matter knowledge is equally important. The 21st Century Skills framework includes a Core Subjects section in addition to skills ...

  5. Educational Strategies Problem-Solving Concepts and Theories

    Problem-solving knowledge is, conceptually, of two kinds. Declarative knowledge is knowing that something is the case. It is knowledge of facts, theories, events, and objects. Proce-dural knowledge is knowing how to do something. It includes motor skills, cognitive skills, and cognitive strategies. Both declarative and procedural knowledge are ...

  6. What is Problem-Based Learning (PBL)

    An Overview of Problem-Based Learning. Problem-based learning (PBL) is a teaching style that pushes students to become the drivers of their learning education. Problem-based learning uses complex, real-world issues as the classroom's subject matter, encouraging students to develop problem-solving skills and learn concepts instead of just ...

  7. Motivation to learn and problem solving

    Learning motivation is usually considered to be conducive to problem solving as it influences the initiation, direction, and intensity of cognitive processing (Baars et al., 2017 ). The motivation to deal with problem-solving tasks can come from the learners themselves or be triggered by task design.

  8. Teaching Problem Solving

    Problem solving is a necessary skill in all disciplines and one that the Sheridan Center is focusing on as part of the Brown Learning Collaborative, which provides students the opportunity to achieve new levels of excellence in six key skills traditionally honed in a liberal arts education ­- critical reading, writing, research, data ...

  9. Teaching Problem Solving

    Make students articulate their problem solving process . In a one-on-one tutoring session, ask the student to work his/her problem out loud. This slows down the thinking process, making it more accurate and allowing you to access understanding. When working with larger groups you can ask students to provide a written "two-column solution.".

  10. Learning strategies: a synthesis and conceptual model

    Walker et al. 89 also noted that novice problem-based learning students tended to engage in far more backward-driven reasoning, which results in more errors during problem solving and may persist ...

  11. Effective Learning Behavior in Problem-Based Learning: a Scoping Review

    Problem-based learning (PBL) emphasizes learning behavior that leads to critical thinking, problem-solving, communication, and collaborative skills in preparing students for a professional medical career. However, learning behavior that develops these skills has not been systematically described. This review aimed to unearth the elements of ...

  12. STEM Problem Solving: Inquiry, Concepts, and Reasoning

    Balancing disciplinary knowledge and practical reasoning in problem solving is needed for meaningful learning. In STEM problem solving, science subject matter with associated practices often appears distant to learners due to its abstract nature. Consequently, learners experience difficulties making meaningful connections between science and their daily experiences. Applying Dewey's idea of ...

  13. Module 13: Complementary Cognitive Processes

    Though the module is entitled Learning Concepts, we will discuss several cognitive processes related to the learning of concepts (and other elements of cognitions) and what we do with them to include problem-solving and reasoning and end with a discussion of intelligence. ... memory, language, reasoning, decision making, problem-solving, and ...

  14. The Problem-Solving Process

    Problem-solving is a mental process that involves discovering, analyzing, and solving problems. The ultimate goal of problem-solving is to overcome obstacles and find a solution that best resolves the issue. The best strategy for solving a problem depends largely on the unique situation. In some cases, people are better off learning everything ...

  15. Introduction to Problem Solving Skills

    Today's employers look for the following skills in new employees: to analyze a problem logically, formulate a solution, and effectively communicate with others. In this video, industry professionals share their own problem solving processes, the problem solving expectations of their employees, and an example of how a problem was solved.

  16. Problem-Based Learning (PBL)

    PBL is a student-centered approach to learning that involves groups of students working to solve a real-world problem, quite different from the direct teaching method of a teacher presenting facts and concepts about a specific subject to a classroom of students. Through PBL, students not only strengthen their teamwork, communication, and ...

  17. Introduction to Thinking and Problem-Solving

    This is only one facet of the complex processes involved in cognition. Simply put, cognition is thinking, and it encompasses the processes associated with perception, knowledge, problem solving, judgment, language, and memory. Scientists who study cognition are searching for ways to understand how we integrate, organize, and utilize our ...

  18. Thinking, Language, and Problem Solving

    For example, before learning the concept of "area of a square" (and the formula to find it), you must understand what a square is. Once the concept of "area of a square" is understood, an understanding of area for other geometric shapes can be built upon the original understanding of area. ... Problem-solving abilities can improve with ...

  19. Problem-Based Learning

    Problem-based learning (PBL) challenges students to identify and examine real problems, then work together to address and solve those problems through advocacy and by mobilizing resources. Importantly, every aspect of the problem solving process involves students in real work—work that is a reflection of the range of expertise required to ...

  20. PDF Transfer of Learning: Connecting Concepts During Problem Solving

    Transfer of Learning: Connecting Concepts During Problem Solving. A concern of many educators and managers is students' ability to transfer concepts and procedures learned in school to the work environment. According to the Committee on Science (2007) the high school experience does not provide enough authentic problem-solving and project ...

  21. Concept Learning versus Problem Solving: A Cognitive Difference

    An initial sample of 94 students enrolled in a first-term general chemistry course was tested with paired algorithmic-conceptual questions, which included questions first used by Nurrenbern and Pickering. The topics of these questions were density, stoichiometry, gas laws, and molarity. Scientific reasoning skill was measured with the Classroom Test of Scientific Reasoning. The skills ...

  22. Fluency, Reasoning & Problem Solving: What They REALLY Are

    Fluency, reasoning and problem solving are central strands of mathematical competency, as recognized by the National Council of Teachers of Mathematics (NCTM) and the National Research Council's report 'Adding It Up'. They are key components to the Standards of Mathematical Practice, standards that are interwoven into every mathematics ...

  23. 7 Module 7: Thinking, Reasoning, and Problem-Solving

    Module 7: Thinking, Reasoning, and Problem-Solving. This module is about how a solid working knowledge of psychological principles can help you to think more effectively, so you can succeed in school and life. You might be inclined to believe that—because you have been thinking for as long as you can remember, because you are able to figure ...

  24. 3 Ways to Improve Student Problem-Solving

    3. Three-Act Tasks: Originally created by Dan Meyer, three-act tasks follow the three acts of a story. The first act is typically called the "setup," followed by the "confrontation" and then the "resolution.". This storyline process can be used in mathematics in which students encounter a contextual problem (e.g., a pool is being ...

  25. The Impact of the Zone of Proximal Development Concept ...

    The zone of proximal development (ZPD or Zoped) is described as the difference between a child's "actual developmental level as determined by independent problem solving" and the child's "potential development as determined through problem solving under adult guidance or in collaboration with more capable peers" (Vygotsky, 1978). The ZPD refers to a learner's capacity to do tasks ...

  26. Research: How Different Fields Are Using GenAI to Redefine Roles

    The interactive, conversational, analytical, and generative features of GenAI offer support for creativity, problem-solving, and processing and digestion of large bodies of information. Therefore ...

  27. Game-Based Learning

    Game-based learning integrates educational content into interactive games, engaging learners in immersive experiences that promote active participation and problem-solving skills. By combining entertainment with learning objectives, it fosters intrinsic motivation and deep engagement, making concepts more memorable for learners of all ages.

  28. Ask AT&T: Revolutionizing Efficiency and Creativity with AI

    The TDP's AI Learning & Problem-Solving Challenge was an inclusive event, involving around 700 employees from the corporate systems organization. The competition comprised 16 teams and over 70 participants, from new hires to veterans. The most innovative teams proposed diverse learning and training tools.

  29. On Size and Hardness Generalization in Unsupervised Learning for the

    View PDF HTML (experimental) Abstract: We study the generalization capability of Unsupervised Learning in solving the Travelling Salesman Problem (TSP). We use a Graph Neural Network (GNN) trained with a surrogate loss function to generate an embedding for each node. We use these embeddings to construct a heat map that indicates the likelihood of each edge being part of the optimal route.

  30. Hospitality students creatively solving problems with Lego Learning

    Penn State students are building physical representations of business strategies and practicing creative problem-solving as part of the Lego Learning Initiative for Hospitality Management Education.