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what is a complex problem solver

The 7 Timeless Steps to Guide You Through Complex Problem Solving

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As we go through life, we inevitably encounter problems that require extensive forethought, critical thinking , and creativity . Solving complex problems is a crucial skill for success, whether it’s a business challenge, a personal dilemma, or a societal issue.

This guide will explore the fundamentals of complex problem-solving and provide practical tips and strategies for mastering this critical skill.

This article is part of a series on complex problem-solving. The list below will guide you through the different subtopics.

Complex Problem-Solving Guide in 7 Steps

The Nature of Complex Problems

What Does the Nature of the Problem Tell Us About Its Solution

Gaussian Distributions vs Power Laws

Your Ultimate Guide to Making Sense of Natural and Social Phenomena

Complex Problem-Solving in Groups

An Exploratory Overview of ProbleSolving Processes in Groups

The Power of Critical Thinking

An Essential Guide for Personal and Professional Development

Group-Decision Making

6 Modes That Tell Us How Teams Decide

1. What Is a Complex Problem?

1.1 generic definition of complex problems.

Four properties allow us to distinguish complex problems from simple ones.

  • Complex problems accept alternative solutions
  • Choices can weighed in multiple ways
  • Data supports multiple hypotheses
  • Breakdown of causal chains.

In crude terms, a complex problem presents no trivial or obvious solution. In other words, it shows the following characteristics:

Now that we have defined the general notion of a complex problem, let’s look at some specific cases related to software development , business management , and complexity theory.

1.2 Complex Problems in Software Development

A complex software development problem involves intricate interactions between numerous system components and requires a sophisticated understanding of the business problem, computing , algorithms and data structures.

Source: “Domain-Driven Design: Tackling Complexity in the Heart of Software” by Eric Evans

1.3 Complex Problems in Business Management

In business management , a complex problem is characterized by interconnected elements, uncertainty, and dynamic interactions, making it challenging to predict outcomes and devise straightforward solutions. This is most obviously seen in formulating effective organisational strategies or leading successful enterprise transformations.

Source: “ Strategic Management and Organisational Dynamics: The Challenge of Complexity ” by Ralph D. Stacey

1.4 Complex Problems in Complexity Theory

From a complexity theory standpoint, a complex problem involves many interacting agents or components, often exhibiting emergent properties that cannot be easily deduced from the properties of individual agents.

Source: “ The Quark and the Jaguar: Adventures in the Simple and the Complex ” by Murray Gell-Mann

Complex problems are contrasted with complicated problems. Complicated problems have clear causes and effects, can be broken down into smaller parts, and have predictable solutions. Complex problems, however, are dynamic, have interconnected parts, and exhibit emergent properties (unpredictable outcomes from the interaction of parts).

Source:  “Cynefin Framework” (2007) by Dave Snowden

1.5 What are Complex Problem Solving Skills?

Complex problem-solving skills involve identifying , analysing , and solving non-routine problems requiring high cognitive effort.

These problems typically involve a large number of variables and require the application of creative and critical thinking skills to identify potential solutions. Individuals with complex problem-solving skills can work through ambiguity and uncertainty and use logical reasoning to develop effective solutions.

2. Solving Complex Problems: A Generic Approach

While developing a universal solution that works in any context would be very challenging, we will describe a generic approach consisting of seven steps that will assist you in creating a bespoke method suitable to the specific context you are working in.

At the heart of this approach is logical decomposition , or breaking down a complex problem into smaller, more manageable ones and then developing and implementing effective solutions for each. It is a key skill essential for success in many areas of life, including business, education , and personal relationships.

Logical decomposition is at the heart of scientific thought, as described in Edsger W. Dijkstra’s paper “ On the Role of Scientific Thought “.

The seven steps to solving complex problems are listed below. We will go through them in great detail in the following sections.

what is a complex problem solver

The 7 steps to creative solutions

Complexity in Natural and Human Systems — Why and When We Should Care

3. Complex Problem-Solving Skills

3.1 why are complex problem solving skills essential.

In today’s rapidly changing world, individuals and organizations must possess complex problem-solving skills to succeed. These skills are essential for several reasons:

Dealing with Uncertainty

In many situations, there is no clear-cut solution to a problem. Complex problem-solving skills enable individuals to work through ambiguity and uncertainty and develop effective solutions.

Identifying Root Causes

Complex problems often have multiple causes that are difficult to identify. Individuals with complex problem-solving skills can identify and address the root causes of problems rather than just treating the symptoms.

Developing Creative Solutions

Complex problems require creative solutions that go beyond traditional approaches. Individuals who possess complex problem-solving skills can think outside the box and develop innovative solutions.

Achieving Business Success

Organizations with complex problem-solving skills are better equipped to overcome challenges, identify opportunities, and succeed in today’s competitive business environment.

3.2 How to Develop Complex Problem-Solving Skills

While some individuals possess a natural aptitude for complex problem-solving, these skills can be developed and improved over time. Here are some tips to help you develop complex problem-solving skills:

3.2.1 Build Your Knowledge Base

Developing complex problem-solving skills requires a strong foundation of knowledge in your area of expertise. Stay updated on your field’s latest trends, research, and developments to enhance your problem-solving abilities.

3.2.2 Practice Critical Thinking

Developing critical thinking skills is essential for complex problem-solving. Practice questioning assumptions, analyzing information , and evaluating arguments to develop critical thinking skills.

3.2.3 Embrace Creativity

Complex problems require creative solutions. Embrace your creativity by exploring new ideas, brainstorming solutions, and seeking diverse perspectives.

3.2.4 Collaborate with Others

Collaborating with others can help you develop your complex problem-solving skills. Working in a team environment can expose you to new ideas and approaches, help you identify blind spots, and provide opportunities for feedback and support.

3.2.5 Seek Out Challenging Problems

Developing complex problem-solving skills requires practice. Seek out challenging problems and apply your problem-solving skills to real-world situations.

4. Step 1: Understanding the Nature of Complex vs Complicated

4.1 the cynefin framework.

Complex and complicated problems are two distinct types of challenges that require different approaches to solve. Dave Snowden, a management consultant and researcher, developed the Cynefin framework, a conceptual model used to understand complex systems and situations. The framework identifies five domains: simple, complicated, complex, chaotic, and disordered, and guides how to approach challenges in each domain.

4.2 Complicated Problems

what is a complex problem solver

Complicated Problems:

  • are characterized by having many interrelated parts and require specialized knowledge and expertise to solve.
  • have a clear cause-and-effect relationship , and the solution can be discovered by systematically analysing the components.
  • are best addressed through a top-down, expert-driven approach , where the experts can identify the best solution through analysis and evaluation.

4.3 Complex Problems

Complex problems are characterized by uncertainty, ambiguity, and the involvement of multiple interconnected factors. There is no clear cause-and-effect relationship, and the solution cannot be found by simply analysing the components. Complex problems require a bottom-up, participatory approach, where multiple perspectives and ideas are considered to develop a solution. The solution may not be clear initially but involves experimentation, adaptation, and feedback.

The Cynefin framework proposes that complex problems belong to the complex domain, where emergent solutions cannot be predicted or prescribed. The complex domain should explore the problem, generate hypotheses, and test them through experimentation. The emphasis is on learning from the process , adapting to changing circumstances, and using feedback to guide the solution.

4.4 Practical Tips on Identifying an Appropriate Framework

Objective — Classify the problem as complex, complicated, or disordered. This classification will determine the approach to be used.

How it’s done — You can do that by asking the following questions.

  • Do we have multiple, internally consistent, competing hypotheses explaining the issue?
  • Does the available data support both theories?

In this case, the problem lies in the complex domain, and the preferred approach is to identify good solutions and conduct safe-to-fail experiments. If it’s a complicated (but not complex) problem, the following questions can be answered in the affirmative:

  • Do we have a single view that explains the problem?
  • Do we know the engineering part of the solution?
  • Is the problem sufficiently familiar to be solved by an expert?

5. Step 2: Identifying and Defining the Problem

5.1 problem identification.

The first step in problem-solving is identifying the problem. This step involves recognizing that a problem exists and understanding its nature. Some tips for identifying the problem include:

Once you have identified the problem, the next step is to define it. This step involves breaking down the problem into smaller parts and better understanding its nature. Some tips for defining the problem include:

  • Writing it down: Write down the problem statement clearly and concisely. This will help you to focus on the specific issue and avoid confusion.
  • Breaking it down: Break the problem into smaller parts to better understand its nature. This can help you to identify the underlying causes and potential solutions. The logical decomposition of the issues is vital, and we have dedicated the next section.
  • Identifying the scope: Identify the scope of the problem and determine its impact. This can help you to prioritize the problem and allocate resources accordingly.

Reliable data and statistical analysis skills are crucial in problem-solving. Data provides information and insights necessary for understanding the root cause of the problem. Statistical analysis allows us to make sense of the data and extract meaningful information. This article will discuss the importance of reliable data and statistical analysis skills in problem identification.

5.2 Practical Tips on Identifying the Problem

Objective — Paint a full picture of the problem by laying out the details, preferably on a piece of paper, classifying it, and deciding on an approach to solving it.

How it’s done — Write down a complete description of the problem, including its scope and impact on the various stakeholders or aspects of the business. Use data as evidence to support initial hypotheses. Find out if the problem is localised and can be resolved locally or whether it might need escalation and support from higher levels of management.

6. Step 3: Gathering and Analyzing Data

6.1 gathering reliable data.

In today’s fast-paced business environment, reliable data is more critical than ever. It is vital to have accurate and objective information to identify problems and determine their root cause.

Reliable data is the basis of any evidence-based decision-making, without which what we have is opinions and assumptions.

Without reliable data, it is difficult to make informed decisions that can lead to effective problem-solving. Here are some of the benefits of using reliable data in problem identification:

  • Objective information: Reliable data provides an objective perspective of the situation.
  • Evidence-based decision-making: Using reliable data ensures that decisions are based on evidence rather than assumptions or opinions.
  • Improved accuracy: Reliable data improves the accuracy of problem identification, leading to better solutions.
  • Better understanding: Reliable data provides a better understanding of the situation, leading to a more comprehensive and holistic approach to problem-solving.
  • Improved Risk Management : Reliable helps put problems into perspective by allowing analysts to calculate their occurrence probabilities and impacts. Based on impact and probability , risk can then be categorised and prioritized.

6.2 Statistical Analysis Skills

Statistical analysis skills are necessary for making sense of the data and extracting meaningful information. These skills allow us to identify patterns and trends, understand the relationships between different variables, and (sometimes) predict future outcomes.

How statistical analysis can help with complex problem solving.

Some benefits of using statistical analysis skills in problem identification include the following:

  • Identifying patterns: Statistical analysis skills enable us to identify patterns and trends in the data, which can help identify the problem accurately.
  • Understanding relationships: Statistical analysis skills help us understand the relationships between different variables, which can help identify the problem’s root cause.
  • Predictive capabilities: Statistical analysis skills allow us to predict future outcomes based on the data, which can help develop effective solutions.
  • Objective analysis: Statistical analysis provides objective data analysis, which can help make evidence-based decisions.

Interpreting data, however, requires technical skills to avoid misinterpretations. The following is a common list of statistical analysis mistakes non-professionals can make.

6.3 How Software Team Leads Can Gather Reliable Data

Software team leads need reliable data on their performance to make informed decisions and identify areas for improvement. Here are some sources where software team leads can gather reliable data on their team’s performance:

  • Project management tools: Most project management tools have built-in reporting features, allowing team leads to track performance metrics such as task completion rates, sprint velocity, and burn-down charts. This data can be used to identify areas for improvement and make data-driven decisions.
  • Team feedback: Gathering feedback from team members through one-on-one meetings or anonymous feedback forms can provide valuable insights into team performance . This data can help team leads identify areas where team members may struggle or additional training or resources may be needed. Crucially, it also provides insights into the organisational culture .
  • Code analysis tools like SonarQube or Code Climate can provide insights into code quality , maintainability, and security. This data can help team leads identify needed code improvements and prioritize technical debt reduction.
  • Customer feedback: Customer feedback, such as ratings, reviews, and support tickets, can provide insights into the usability and functionality of deployed applications. This data can help team leads identify areas for improvement and prioritize feature development.

The software team should gather data from multiple sources, use that data to inform decisions and identify areas for improvement. By using reliable data sources and monitoring team performance metrics regularly, software team leads can drive continuous improvement and ensure project success.

6.4 Practical Tips on Gathering Data to Support the Proposed Hypotheses

Objective — The availability of data can help place the problem into perspective. For example, a dollar figure of the losses due to process inefficiencies can help identify the potential solutions that management will deem feasible.

How it’s done — All modern project management and tracking tools have sophisticated built-in data capture tools that can be exported, cleaned, and analysed for insights.

For example, when evaluating a team’s productivity , you can export data from JIRA, Jenkins, or BitBucket and measure performance metrics such as team velocity, overruns, and time-to-market.

When evidence is insufficient, you can gather more data, abandon the hypothesis, or temporarily shelve it.

7 Step 4: Logical Decomposition in Problem Solving

7.1 logical decomposition.

Logical decomposition is a problem-solving technique that breaks down complex problems into smaller, more manageable pieces. It is a structured approach that enables individuals to examine a problem from multiple angles, identify key issues and sub-problems, and develop a solution that addresses each piece of the problem.

The process of logical decomposition involves breaking down the main problem into smaller sub-problems, which are then broken down into smaller pieces. Each piece is analyzed in detail to determine its underlying cause-and-effect relationships and potential solutions. By breaking down the problem into smaller pieces, the individual can better understand the overall problem, identify potential solutions more easily, and prioritize which sub-problems to address first.

Logical decomposition is particularly useful for dealing with complex issues, as it allows individuals to break down a large, overwhelming problem into smaller, more manageable pieces. This not only makes the problem easier to understand and solve but also makes it less daunting and more approachable. Additionally, by breaking down the problem into smaller pieces, individuals can identify and focus on the underlying root causes of the problem rather than just treating the symptoms.

Logical decomposition is a vital stage of architecting large systems and solutions.

7.2 Practical Tips on Logical Decomposition

Objective — Most problems worth tackling are also overwhelming in size and complexity (or complicatedness). Luckily, a logical decomposition into specialized areas or modules will help focus the team’s efforts on a small enough subproblem or bring in the right expertise.

How it’s done — This author prefers mindmaps. A mindmap is a tree that starts with a single node and branches off into different areas, views, or perspectives of the problem. Mindmaps help analysts stay focused on a key area and ensure that all aspects of a problem are covered.

Once a mindmap has been created, potential solutions can be explored.

From Abstract Concepts to Tangible Value: Solution Architecture in Modern IT Systems

8. Step 5: Generating and Evaluating (Several) Potential Solutions

Generating multiple solutions to solve a problem is an effective way to increase creativity and innovation in problem-solving. By exploring different options, individuals can identify the strengths and weaknesses of each solution and determine the most effective approach to solving the problem. This section will discuss the advantages and techniques of generating multiple solutions to solve problems more effectively.

8.1 Advantages of Generating Multiple Solutions

The advantages of generating multiple solutions during problem-solving are:

8.2 Techniques for Generating Multiple Solutions

Techniques for generating multiple solutions:

8.3 Practical Tips on Solution Generation and Selection

Objective — The key principle of solution generation is comprehensively exploring the solution space. This exploration allows teams to avoid local minima or overcommitting to a suboptimal solution.

How it’s done — The most effective approach is to bring in several people from different areas of expertise or seniority and to offer every suggestion the opportunity to be heard and thoroughly explored.

Also, different stakeholders might favour solutions that maximise their (potentially) narrow gains. If not consulted, they might actively block the implementation of the selected solution if it adversely impacts their interests.

The technical aspect of problem-solving is relatively easy to generate and implement without budgetary or scheduling constraints . It’s only when you consider the cost and impact of a solution that complexity arises.

5 Key Concepts You Need to Know From Herbert Simon’s Paper on the Architecture of Complexity

9. Step 6: Implementing and Assessing Solutions

Implementing solutions to complex problems requires a structured approach that considers the unique challenges and variables involved. Effective problem-solving involves implementing practical, feasible, and sustainable solutions.

This section will first discuss two approaches to implementing solutions to complex problems: small, safe-to-fail solutions and solving easy problems with large benefits.

9.1 Implementing Many Safe-to-Fail Solutions

One effective approach to implementing solutions to complex problems is small, safe-to-fail solutions. This technique involves implementing a small-scale solution that can be tested quickly and easily to gather feedback.

Exploring multiple paths allows analysts to avoid over-commitment to suboptimal solutions.

Starting with small-scale solutions allows individuals to gather feedback and adjust before investing significant resources in a larger solution. This approach can save time and resources while ensuring that the final solution meets the needs of stakeholders.

Small safe-to-fail experiments effectively deal with complexity where an engineering solution is unknown priori.

9.2 Prioritizing High-Yield Solutions

Another effective approach to implementing solutions to complex problems is to first solve easy problems with large benefits. This technique involves identifying and solving simple, straightforward problems that significantly impact the overall problem.

By prioritising easy problems, individuals can progress quickly and gain momentum towards solving the larger problem. This approach can also help build trust and credibility with stakeholders, as progress is visible and measurable.

9.3 A Systematic Approach to Implementing Solutions

It is important to note that both approaches should be used with a broader problem-solving methodology . Effective problem-solving requires a systematic approach that involves identifying the problem, gathering information, analyzing data, developing and evaluating potential solutions, and implementing the best solution. By implementing small, safe-to-fail solutions and solving easy problems with large benefits, individuals can enhance their problem-solving approach and increase the likelihood of success.

In conclusion, implementing solutions to complex problems requires a structured approach that considers the unique challenges and variables involved. Implementing small, safe-to-fail solutions and solving easy problems with large benefits are two effective techniques for enhancing problem-solving. These techniques should be used with a broader problem-solving methodology to ensure the final solution is practical, feasible, and sustainable.

9.4 Implementing the Solution

Objective — This stage aims to efficiently and effectively implement the (optimal) selected solution(s).

How it’s done — Three principal techniques are required for the implementation of the solution to succeed. The first is conducting safe-to-fail experiments. The second is allocating resources to conduct each experiment. The third is setting up the criteria for success or failure.

10. Step 7: Evaluating the Solution

Objective — Solutions might work well under laboratory conditions but fail spectacularly in the field. Evaluating solutions after a trial is vital to avoid continuing investment in failed solutions.

How it’s done — The best way to evaluate a solution is to monitor the Key Performance Indicators (KPIs) originally used in the problem diagnosis. When solutions are successful, noticeable and measurable improvements should be observed.

Measuring second-order effects or observing undesirable team or business dynamics changes is key to continuing or aborting initiatives.

Complex problem-solving refers to the ability to solve complex, ambiguous problems that often require creative and innovative solutions. It involves identifying the root cause of a problem, analyzing different variables and factors, developing and evaluating possible solutions, and selecting the best course of action.

Complex problem-solving is essential because it allows individuals and organizations to overcome challenges and obstacles hindering their progress and success. It enables them to identify opportunities, improve processes, and innovate to stay ahead of the competition.

To develop your complex problem-solving skills, you can practice consistently, develop a systematic approach, and leverage the right tools and resources. You can also seek feedback from others, learn from your mistakes, and adopt a growth mindset that values continuous learning and improvement.

Some common obstacles to effective problem-solving include cognitive biases , lack of information, unclear objectives, and groupthink. These obstacles can hinder individuals and teams from developing effective solutions to complex problems.

Various tools and techniques for complex problem-solving include root cause analysis, fishbone diagrams, SWOT analysis, Pareto analysis, decision trees, and scenario planning. These tools can help individuals and teams to analyze complex problems, identify underlying causes, and develop effective solutions.

To improve your decision-making skills, you can develop a structured approach, gather and analyze relevant data, evaluate different options, and consider each alternative’s potential risks and benefits. You can also seek feedback from others and reflect on your past decisions to learn from your mistakes.

Complex problem-solving skills can be applied in various aspects of your personal life, such as improving your relationships, managing your finances, and achieving your goals. You can overcome obstacles and succeed personally by systematically analyzing different variables and factors and developing creative and innovative solutions.

To overcome cognitive biases in problem-solving, you can challenge your assumptions, seek diverse perspectives, and use data and evidence to inform your decisions. You can also use brainstorming and mind-mapping techniques to generate new ideas and avoid tunnel vision.

12. Final Words

In conclusion, complex problem-solving is a crucial skill that can significantly impact your professional and personal life. It allows you to navigate complex challenges, identify the root cause of a problem, and develop effective solutions.

By mastering the art of complex problem-solving, you can enhance your critical thinking, analytical skills, and decision-making abilities, which are essential for success in today’s fast-paced and dynamic business environment.

The key to mastering complex problem-solving is to practice consistently, develop a systematic approach, and leverage the right tools and resources. With patience, persistence, and a growth mindset, anyone can become a skilled problem solver and tackle even the most challenging problems.

Decision Making In a Professional Environment: Techniques and Pitfalls

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CONCEPTUAL ANALYSIS article

Complex problem solving: what it is and what it is not.

\r\nDietrich Drner

  • 1 Department of Psychology, University of Bamberg, Bamberg, Germany
  • 2 Department of Psychology, Heidelberg University, Heidelberg, Germany

Computer-simulated scenarios have been part of psychological research on problem solving for more than 40 years. The shift in emphasis from simple toy problems to complex, more real-life oriented problems has been accompanied by discussions about the best ways to assess the process of solving complex problems. Psychometric issues such as reliable assessments and addressing correlations with other instruments have been in the foreground of these discussions and have left the content validity of complex problem solving in the background. In this paper, we return the focus to content issues and address the important features that define complex problems.

Succeeding in the 21st century requires many competencies, including creativity, life-long learning, and collaboration skills (e.g., National Research Council, 2011 ; Griffin and Care, 2015 ), to name only a few. One competence that seems to be of central importance is the ability to solve complex problems ( Mainzer, 2009 ). Mainzer quotes the Nobel prize winner Simon (1957) who wrote as early as 1957:

The capacity of the human mind for formulating and solving complex problems is very small compared with the size of the problem whose solution is required for objectively rational behavior in the real world or even for a reasonable approximation to such objective rationality. (p. 198)

The shift from well-defined to ill-defined problems came about as a result of a disillusion with the “general problem solver” ( Newell et al., 1959 ): The general problem solver was a computer software intended to solve all kind of problems that can be expressed through well-formed formulas. However, it soon became clear that this procedure was in fact a “special problem solver” that could only solve well-defined problems in a closed space. But real-world problems feature open boundaries and have no well-determined solution. In fact, the world is full of wicked problems and clumsy solutions ( Verweij and Thompson, 2006 ). As a result, solving well-defined problems and solving ill-defined problems requires different cognitive processes ( Schraw et al., 1995 ; but see Funke, 2010 ).

Well-defined problems have a clear set of means for reaching a precisely described goal state. For example: in a match-stick arithmetic problem, a person receives a false arithmetic expression constructed out of matchsticks (e.g., IV = III + III). According to the instructions, moving one of the matchsticks will make the equations true. Here, both the problem (find the appropriate stick to move) and the goal state (true arithmetic expression; solution is: VI = III + III) are defined clearly.

Ill-defined problems have no clear problem definition, their goal state is not defined clearly, and the means of moving towards the (diffusely described) goal state are not clear. For example: The goal state for solving the political conflict in the near-east conflict between Israel and Palestine is not clearly defined (living in peaceful harmony with each other?) and even if the conflict parties would agree on a two-state solution, this goal again leaves many issues unresolved. This type of problem is called a “complex problem” and is of central importance to this paper. All psychological processes that occur within individual persons and deal with the handling of such ill-defined complex problems will be subsumed under the umbrella term “complex problem solving” (CPS).

Systematic research on CPS started in the 1970s with observations of the behavior of participants who were confronted with computer simulated microworlds. For example, in one of those microworlds participants assumed the role of executives who were tasked to manage a company over a certain period of time (see Brehmer and Dörner, 1993 , for a discussion of this methodology). Today, CPS is an established concept and has even influenced large-scale assessments such as PISA (“Programme for International Student Assessment”), organized by the Organization for Economic Cooperation and Development ( OECD, 2014 ). According to the World Economic Forum, CPS is one of the most important competencies required in the future ( World Economic Forum, 2015 ). Numerous articles on the subject have been published in recent years, documenting the increasing research activity relating to this field. In the following collection of papers we list only those published in 2010 and later: theoretical papers ( Blech and Funke, 2010 ; Funke, 2010 ; Knauff and Wolf, 2010 ; Leutner et al., 2012 ; Selten et al., 2012 ; Wüstenberg et al., 2012 ; Greiff et al., 2013b ; Fischer and Neubert, 2015 ; Schoppek and Fischer, 2015 ), papers about measurement issues ( Danner et al., 2011a ; Greiff et al., 2012 , 2015a ; Alison et al., 2013 ; Gobert et al., 2015 ; Greiff and Fischer, 2013 ; Herde et al., 2016 ; Stadler et al., 2016 ), papers about applications ( Fischer and Neubert, 2015 ; Ederer et al., 2016 ; Tremblay et al., 2017 ), papers about differential effects ( Barth and Funke, 2010 ; Danner et al., 2011b ; Beckmann and Goode, 2014 ; Greiff and Neubert, 2014 ; Scherer et al., 2015 ; Meißner et al., 2016 ; Wüstenberg et al., 2016 ), one paper about developmental effects ( Frischkorn et al., 2014 ), one paper with a neuroscience background ( Osman, 2012 ) 1 , papers about cultural differences ( Güss and Dörner, 2011 ; Sonnleitner et al., 2014 ; Güss et al., 2015 ), papers about validity issues ( Goode and Beckmann, 2010 ; Greiff et al., 2013c ; Schweizer et al., 2013 ; Mainert et al., 2015 ; Funke et al., 2017 ; Greiff et al., 2017 , 2015b ; Kretzschmar et al., 2016 ; Kretzschmar, 2017 ), review papers and meta-analyses ( Osman, 2010 ; Stadler et al., 2015 ), and finally books ( Qudrat-Ullah, 2015 ; Csapó and Funke, 2017b ) and book chapters ( Funke, 2012 ; Hotaling et al., 2015 ; Funke and Greiff, 2017 ; Greiff and Funke, 2017 ; Csapó and Funke, 2017a ; Fischer et al., 2017 ; Molnàr et al., 2017 ; Tobinski and Fritz, 2017 ; Viehrig et al., 2017 ). In addition, a new “Journal of Dynamic Decision Making” (JDDM) has been launched ( Fischer et al., 2015 , 2016 ) to give the field an open-access outlet for research and discussion.

This paper aims to clarify aspects of validity: what should be meant by the term CPS and what not? This clarification seems necessary because misunderstandings in recent publications provide – from our point of view – a potentially misleading picture of the construct. We start this article with a historical review before attempting to systematize different positions. We conclude with a working definition.

Historical Review

The concept behind CPS goes back to the German phrase “komplexes Problemlösen” (CPS; the term “komplexes Problemlösen” was used as a book title by Funke, 1986 ). The concept was introduced in Germany by Dörner and colleagues in the mid-1970s (see Dörner et al., 1975 ; Dörner, 1975 ) for the first time. The German phrase was later translated to CPS in the titles of two edited volumes by Sternberg and Frensch (1991) and Frensch and Funke (1995a) that collected papers from different research traditions. Even though it looks as though the term was coined in the 1970s, Edwards (1962) used the term “dynamic decision making” to describe decisions that come in a sequence. He compared static with dynamic decision making, writing:

In dynamic situations, a new complication not found in the static situations arises. The environment in which the decision is set may be changing, either as a function of the sequence of decisions, or independently of them, or both. It is this possibility of an environment which changes while you collect information about it which makes the task of dynamic decision theory so difficult and so much fun. (p. 60)

The ability to solve complex problems is typically measured via dynamic systems that contain several interrelated variables that participants need to alter. Early work (see, e.g., Dörner, 1980 ) used a simulation scenario called “Lohhausen” that contained more than 2000 variables that represented the activities of a small town: Participants had to take over the role of a mayor for a simulated period of 10 years. The simulation condensed these ten years to ten hours in real time. Later, researchers used smaller dynamic systems as scenarios either based on linear equations (see, e.g., Funke, 1993 ) or on finite state automata (see, e.g., Buchner and Funke, 1993 ). In these contexts, CPS consisted of the identification and control of dynamic task environments that were previously unknown to the participants. Different task environments came along with different degrees of fidelity ( Gray, 2002 ).

According to Funke (2012) , the typical attributes of complex systems are (a) complexity of the problem situation which is usually represented by the sheer number of involved variables; (b) connectivity and mutual dependencies between involved variables; (c) dynamics of the situation, which reflects the role of time and developments within a system; (d) intransparency (in part or full) about the involved variables and their current values; and (e) polytely (greek term for “many goals”), representing goal conflicts on different levels of analysis. This mixture of features is similar to what is called VUCA (volatility, uncertainty, complexity, ambiguity) in modern approaches to management (e.g., Mack et al., 2016 ).

In his evaluation of the CPS movement, Sternberg (1995) compared (young) European approaches to CPS with (older) American research on expertise. His analysis of the differences between the European and American traditions shows advantages but also potential drawbacks for each side. He states (p. 301): “I believe that although there are problems with the European approach, it deals with some fundamental questions that American research scarcely addresses.” So, even though the echo of the European approach did not enjoy strong resonance in the US at that time, it was valued by scholars like Sternberg and others. Before attending to validity issues, we will first present a short review of different streams.

Different Approaches to CPS

In the short history of CPS research, different approaches can be identified ( Buchner, 1995 ; Fischer et al., 2017 ). To systematize, we differentiate between the following five lines of research:

(a) The search for individual differences comprises studies identifying interindividual differences that affect the ability to solve complex problems. This line of research is reflected, for example, in the early work by Dörner et al. (1983) and their “Lohhausen” study. Here, naïve student participants took over the role of the mayor of a small simulated town named Lohhausen for a simulation period of ten years. According to the results of the authors, it is not intelligence (as measured by conventional IQ tests) that predicts performance, but it is the ability to stay calm in the face of a challenging situation and the ability to switch easily between an analytic mode of processing and a more holistic one.

(b) The search for cognitive processes deals with the processes behind understanding complex dynamic systems. Representative of this line of research is, for example, Berry and Broadbent’s (1984) work on implicit and explicit learning processes when people interact with a dynamic system called “Sugar Production”. They found that those who perform best in controlling a dynamic system can do so implicitly, without explicit knowledge of details regarding the systems’ relations.

(c) The search for system factors seeks to identify the aspects of dynamic systems that determine the difficulty of complex problems and make some problems harder than others. Representative of this line of research is, for example, work by Funke (1985) , who systematically varied the number of causal effects within a dynamic system or the presence/absence of eigendynamics. He found, for example, that solution quality decreases as the number of systems relations increases.

(d) The psychometric approach develops measurement instruments that can be used as an alternative to classical IQ tests, as something that goes “beyond IQ”. The MicroDYN approach ( Wüstenberg et al., 2012 ) is representative for this line of research that presents an alternative to reasoning tests (like Raven matrices). These authors demonstrated that a small improvement in predicting school grade point average beyond reasoning is possible with MicroDYN tests.

(e) The experimental approach explores CPS under different experimental conditions. This approach uses CPS assessment instruments to test hypotheses derived from psychological theories and is sometimes used in research about cognitive processes (see above). Exemplary for this line of research is the work by Rohe et al. (2016) , who test the usefulness of “motto goals” in the context of complex problems compared to more traditional learning and performance goals. Motto goals differ from pure performance goals by activating positive affect and should lead to better goal attainment especially in complex situations (the mentioned study found no effect).

To be clear: these five approaches are not mutually exclusive and do overlap. But the differentiation helps to identify different research communities and different traditions. These communities had different opinions about scaling complexity.

The Race for Complexity: Use of More and More Complex Systems

In the early years of CPS research, microworlds started with systems containing about 20 variables (“Tailorshop”), soon reached 60 variables (“Moro”), and culminated in systems with about 2000 variables (“Lohhausen”). This race for complexity ended with the introduction of the concept of “minimal complex systems” (MCS; Greiff and Funke, 2009 ; Funke and Greiff, 2017 ), which ushered in a search for the lower bound of complexity instead of the higher bound, which could not be defined as easily. The idea behind this concept was that whereas the upper limits of complexity are unbound, the lower limits might be identifiable. Imagine starting with a simple system containing two variables with a simple linear connection between them; then, step by step, increase the number of variables and/or the type of connections. One soon reaches a point where the system can no longer be considered simple and has become a “complex system”. This point represents a minimal complex system. Despite some research having been conducted in this direction, the point of transition from simple to complex has not been identified clearly as of yet.

Some years later, the original “minimal complex systems” approach ( Greiff and Funke, 2009 ) shifted to the “multiple complex systems” approach ( Greiff et al., 2013a ). This shift is more than a slight change in wording: it is important because it taps into the issue of validity directly. Minimal complex systems have been introduced in the context of challenges from large-scale assessments like PISA 2012 that measure new aspects of problem solving, namely interactive problems besides static problem solving ( Greiff and Funke, 2017 ). PISA 2012 required test developers to remain within testing time constraints (given by the school class schedule). Also, test developers needed a large item pool for the construction of a broad class of problem solving items. It was clear from the beginning that MCS deal with simple dynamic situations that require controlled interaction: the exploration and control of simple ticket machines, simple mobile phones, or simple MP3 players (all of these example domains were developed within PISA 2012) – rather than really complex situations like managerial or political decision making.

As a consequence of this subtle but important shift in interpreting the letters MCS, the definition of CPS became a subject of debate recently ( Funke, 2014a ; Greiff and Martin, 2014 ; Funke et al., 2017 ). In the words of Funke (2014b , p. 495):

It is funny that problems that nowadays come under the term ‘CPS’, are less complex (in terms of the previously described attributes of complex situations) than at the beginning of this new research tradition. The emphasis on psychometric qualities has led to a loss of variety. Systems thinking requires more than analyzing models with two or three linear equations – nonlinearity, cyclicity, rebound effects, etc. are inherent features of complex problems and should show up at least in some of the problems used for research and assessment purposes. Minimal complex systems run the danger of becoming minimal valid systems.

Searching for minimal complex systems is not the same as gaining insight into the way how humans deal with complexity and uncertainty. For psychometric purposes, it is appropriate to reduce complexity to a minimum; for understanding problem solving under conditions of overload, intransparency, and dynamics, it is necessary to realize those attributes with reasonable strength. This aspect is illustrated in the next section.

Importance of the Validity Issue

The most important reason for discussing the question of what complex problem solving is and what it is not stems from its phenomenology: if we lose sight of our phenomena, we are no longer doing good psychology. The relevant phenomena in the context of complex problems encompass many important aspects. In this section, we discuss four phenomena that are specific to complex problems. We consider these phenomena as critical for theory development and for the construction of assessment instruments (i.e., microworlds). These phenomena require theories for explaining them and they require assessment instruments eliciting them in a reliable way.

The first phenomenon is the emergency reaction of the intellectual system ( Dörner, 1980 ): When dealing with complex systems, actors tend to (a) reduce their intellectual level by decreasing self-reflections, by decreasing their intentions, by stereotyping, and by reducing their realization of intentions, (b) they show a tendency for fast action with increased readiness for risk, with increased violations of rules, and with increased tendency to escape the situation, and (c) they degenerate their hypotheses formation by construction of more global hypotheses and reduced tests of hypotheses, by increasing entrenchment, and by decontextualizing their goals. This phenomenon illustrates the strong connection between cognition, emotion, and motivation that has been emphasized by Dörner (see, e.g., Dörner and Güss, 2013 ) from the beginning of his research tradition; the emergency reaction reveals a shift in the mode of information processing under the pressure of complexity.

The second phenomenon comprises cross-cultural differences with respect to strategy use ( Strohschneider and Güss, 1999 ; Güss and Wiley, 2007 ; Güss et al., 2015 ). Results from complex task environments illustrate the strong influence of context and background knowledge to an extent that cannot be found for knowledge-poor problems. For example, in a comparison between Brazilian and German participants, it turned out that Brazilians accept the given problem descriptions and are more optimistic about the results of their efforts, whereas Germans tend to inquire more about the background of the problems and take a more active approach but are less optimistic (according to Strohschneider and Güss, 1998 , p. 695).

The third phenomenon relates to failures that occur during the planning and acting stages ( Jansson, 1994 ; Ramnarayan et al., 1997 ), illustrating that rational procedures seem to be unlikely to be used in complex situations. The potential for failures ( Dörner, 1996 ) rises with the complexity of the problem. Jansson (1994) presents seven major areas for failures with complex situations: acting directly on current feedback; insufficient systematization; insufficient control of hypotheses and strategies; lack of self-reflection; selective information gathering; selective decision making; and thematic vagabonding.

The fourth phenomenon describes (a lack of) training and transfer effects ( Kretzschmar and Süß, 2015 ), which again illustrates the context dependency of strategies and knowledge (i.e., there is no strategy that is so universal that it can be used in many different problem situations). In their own experiment, the authors could show training effects only for knowledge acquisition, not for knowledge application. Only with specific feedback, performance in complex environments can be increased ( Engelhart et al., 2017 ).

These four phenomena illustrate why the type of complexity (or degree of simplicity) used in research really matters. Furthermore, they demonstrate effects that are specific for complex problems, but not for toy problems. These phenomena direct the attention to the important question: does the stimulus material used (i.e., the computer-simulated microworld) tap and elicit the manifold of phenomena described above?

Dealing with partly unknown complex systems requires courage, wisdom, knowledge, grit, and creativity. In creativity research, “little c” and “BIG C” are used to differentiate between everyday creativity and eminent creativity ( Beghetto and Kaufman, 2007 ; Kaufman and Beghetto, 2009 ). Everyday creativity is important for solving everyday problems (e.g., finding a clever fix for a broken spoke on my bicycle), eminent creativity changes the world (e.g., inventing solar cells for energy production). Maybe problem solving research should use a similar differentiation between “little p” and “BIG P” to mark toy problems on the one side and big societal challenges on the other. The question then remains: what can we learn about BIG P by studying little p? What phenomena are present in both types, and what phenomena are unique to each of the two extremes?

Discussing research on CPS requires reflecting on the field’s research methods. Even if the experimental approach has been successful for testing hypotheses (for an overview of older work, see Funke, 1995 ), other methods might provide additional and novel insights. Complex phenomena require complex approaches to understand them. The complex nature of complex systems imposes limitations on psychological experiments: The more complex the environments, the more difficult is it to keep conditions under experimental control. And if experiments have to be run in labs one should bring enough complexity into the lab to establish the phenomena mentioned, at least in part.

There are interesting options to be explored (again): think-aloud protocols , which have been discredited for many years ( Nisbett and Wilson, 1977 ) and yet are a valuable source for theory testing ( Ericsson and Simon, 1983 ); introspection ( Jäkel and Schreiber, 2013 ), which seems to be banned from psychological methods but nevertheless offers insights into thought processes; the use of life-streaming ( Wendt, 2017 ), a medium in which streamers generate a video stream of think-aloud data in computer-gaming; political decision-making ( Dhami et al., 2015 ) that demonstrates error-proneness in groups; historical case studies ( Dörner and Güss, 2011 ) that give insights into the thinking styles of political leaders; the use of the critical incident technique ( Reuschenbach, 2008 ) to construct complex scenarios; and simulations with different degrees of fidelity ( Gray, 2002 ).

The methods tool box is full of instruments that have to be explored more carefully before any individual instrument receives a ban or research narrows its focus to only one paradigm for data collection. Brehmer and Dörner (1993) discussed the tensions between “research in the laboratory and research in the field”, optimistically concluding “that the new methodology of computer-simulated microworlds will provide us with the means to bridge the gap between the laboratory and the field” (p. 183). The idea behind this optimism was that computer-simulated scenarios would bring more complexity from the outside world into the controlled lab environment. But this is not true for all simulated scenarios. In his paper on simulated environments, Gray (2002) differentiated computer-simulated environments with respect to three dimensions: (1) tractability (“the more training subjects require before they can use a simulated task environment, the less tractable it is”, p. 211), correspondence (“High correspondence simulated task environments simulate many aspects of one task environment. Low correspondence simulated task environments simulate one aspect of many task environments”, p. 214), and engagement (“A simulated task environment is engaging to the degree to which it involves and occupies the participants; that is, the degree to which they agree to take it seriously”, p. 217). But the mere fact that a task is called a “computer-simulated task environment” does not mean anything specific in terms of these three dimensions. This is one of several reasons why we should differentiate between those studies that do not address the core features of CPS and those that do.

What is not CPS?

Even though a growing number of references claiming to deal with complex problems exist (e.g., Greiff and Wüstenberg, 2015 ; Greiff et al., 2016 ), it would be better to label the requirements within these tasks “dynamic problem solving,” as it has been done adequately in earlier work ( Greiff et al., 2012 ). The dynamics behind on-off-switches ( Thimbleby, 2007 ) are remarkable but not really complex. Small nonlinear systems that exhibit stunningly complex and unstable behavior do exist – but they are not used in psychometric assessments of so-called CPS. There are other small systems (like MicroDYN scenarios: Greiff and Wüstenberg, 2014 ) that exhibit simple forms of system behavior that are completely predictable and stable. This type of simple systems is used frequently. It is even offered commercially as a complex problem-solving test called COMPRO ( Greiff and Wüstenberg, 2015 ) for business applications. But a closer look reveals that the label is not used correctly; within COMPRO, the used linear equations are far from being complex and the system can be handled properly by using only one strategy (see for more details Funke et al., 2017 ).

Why do simple linear systems not fall within CPS? At the surface, nonlinear and linear systems might appear similar because both only include 3–5 variables. But the difference is in terms of systems behavior as well as strategies and learning. If the behavior is simple (as in linear systems where more input is related to more output and vice versa), the system can be easily understood (participants in the MicroDYN world have 3 minutes to explore a complex system). If the behavior is complex (as in systems that contain strange attractors or negative feedback loops), things become more complicated and much more observation is needed to identify the hidden structure of the unknown system ( Berry and Broadbent, 1984 ; Hundertmark et al., 2015 ).

Another issue is learning. If tasks can be solved using a single (and not so complicated) strategy, steep learning curves are to be expected. The shift from problem solving to learned routine behavior occurs rapidly, as was demonstrated by Luchins (1942) . In his water jar experiments, participants quickly acquired a specific strategy (a mental set) for solving certain measurement problems that they later continued applying to problems that would have allowed for easier approaches. In the case of complex systems, learning can occur only on very general, abstract levels because it is difficult for human observers to make specific predictions. Routines dealing with complex systems are quite different from routines relating to linear systems.

What should not be studied under the label of CPS are pure learning effects, multiple-cue probability learning, or tasks that can be solved using a single strategy. This last issue is a problem for MicroDYN tasks that rely strongly on the VOTAT strategy (“vary one thing at a time”; see Tschirgi, 1980 ). In real-life, it is hard to imagine a business manager trying to solve her or his problems by means of VOTAT.

What is CPS?

In the early days of CPS research, planet Earth’s dynamics and complexities gained attention through such books as “The limits to growth” ( Meadows et al., 1972 ) and “Beyond the limits” ( Meadows et al., 1992 ). In the current decade, for example, the World Economic Forum (2016) attempts to identify the complexities and risks of our modern world. In order to understand the meaning of complexity and uncertainty, taking a look at the worlds’ most pressing issues is helpful. Searching for strategies to cope with these problems is a difficult task: surely there is no place for the simple principle of “vary-one-thing-at-a-time” (VOTAT) when it comes to global problems. The VOTAT strategy is helpful in the context of simple problems ( Wüstenberg et al., 2014 ); therefore, whether or not VOTAT is helpful in a given problem situation helps us distinguish simple from complex problems.

Because there exist no clear-cut strategies for complex problems, typical failures occur when dealing with uncertainty ( Dörner, 1996 ; Güss et al., 2015 ). Ramnarayan et al. (1997) put together a list of generic errors (e.g., not developing adequate action plans; lack of background control; learning from experience blocked by stereotype knowledge; reactive instead of proactive action) that are typical of knowledge-rich complex systems but cannot be found in simple problems.

Complex problem solving is not a one-dimensional, low-level construct. On the contrary, CPS is a multi-dimensional bundle of competencies existing at a high level of abstraction, similar to intelligence (but going beyond IQ). As Funke et al. (2018) state: “Assessment of transversal (in educational contexts: cross-curricular) competencies cannot be done with one or two types of assessment. The plurality of skills and competencies requires a plurality of assessment instruments.”

There are at least three different aspects of complex systems that are part of our understanding of a complex system: (1) a complex system can be described at different levels of abstraction; (2) a complex system develops over time, has a history, a current state, and a (potentially unpredictable) future; (3) a complex system is knowledge-rich and activates a large semantic network, together with a broad list of potential strategies (domain-specific as well as domain-general).

Complex problem solving is not only a cognitive process but is also an emotional one ( Spering et al., 2005 ; Barth and Funke, 2010 ) and strongly dependent on motivation (low-stakes versus high-stakes testing; see Hermes and Stelling, 2016 ).

Furthermore, CPS is a dynamic process unfolding over time, with different phases and with more differentiation than simply knowledge acquisition and knowledge application. Ideally, the process should entail identifying problems (see Dillon, 1982 ; Lee and Cho, 2007 ), even if in experimental settings, problems are provided to participants a priori . The more complex and open a given situation, the more options can be generated (T. S. Schweizer et al., 2016 ). In closed problems, these processes do not occur in the same way.

In analogy to the difference between formative (process-oriented) and summative (result-oriented) assessment ( Wiliam and Black, 1996 ; Bennett, 2011 ), CPS should not be reduced to the mere outcome of a solution process. The process leading up to the solution, including detours and errors made along the way, might provide a more differentiated impression of a person’s problem-solving abilities and competencies than the final result of such a process. This is one of the reasons why CPS environments are not, in fact, complex intelligence tests: research on CPS is not only about the outcome of the decision process, but it is also about the problem-solving process itself.

Complex problem solving is part of our daily life: finding the right person to share one’s life with, choosing a career that not only makes money, but that also makes us happy. Of course, CPS is not restricted to personal problems – life on Earth gives us many hard nuts to crack: climate change, population growth, the threat of war, the use and distribution of natural resources. In sum, many societal challenges can be seen as complex problems. To reduce that complexity to a one-hour lab activity on a random Friday afternoon puts it out of context and does not address CPS issues.

Theories about CPS should specify which populations they apply to. Across populations, one thing to consider is prior knowledge. CPS research with experts (e.g., Dew et al., 2009 ) is quite different from problem solving research using tasks that intentionally do not require any specific prior knowledge (see, e.g., Beckmann and Goode, 2014 ).

More than 20 years ago, Frensch and Funke (1995b) defined CPS as follows:

CPS occurs to overcome barriers between a given state and a desired goal state by means of behavioral and/or cognitive, multi-step activities. The given state, goal state, and barriers between given state and goal state are complex, change dynamically during problem solving, and are intransparent. The exact properties of the given state, goal state, and barriers are unknown to the solver at the outset. CPS implies the efficient interaction between a solver and the situational requirements of the task, and involves a solver’s cognitive, emotional, personal, and social abilities and knowledge. (p. 18)

The above definition is rather formal and does not account for content or relations between the simulation and the real world. In a sense, we need a new definition of CPS that addresses these issues. Based on our previous arguments, we propose the following working definition:

Complex problem solving is a collection of self-regulated psychological processes and activities necessary in dynamic environments to achieve ill-defined goals that cannot be reached by routine actions. Creative combinations of knowledge and a broad set of strategies are needed. Solutions are often more bricolage than perfect or optimal. The problem-solving process combines cognitive, emotional, and motivational aspects, particularly in high-stakes situations. Complex problems usually involve knowledge-rich requirements and collaboration among different persons.

The main differences to the older definition lie in the emphasis on (a) the self-regulation of processes, (b) creativity (as opposed to routine behavior), (c) the bricolage type of solution, and (d) the role of high-stakes challenges. Our new definition incorporates some aspects that have been discussed in this review but were not reflected in the 1995 definition, which focused on attributes of complex problems like dynamics or intransparency.

This leads us to the final reflection about the role of CPS for dealing with uncertainty and complexity in real life. We will distinguish thinking from reasoning and introduce the sense of possibility as an important aspect of validity.

CPS as Combining Reasoning and Thinking in an Uncertain Reality

Leading up to the Battle of Borodino in Leo Tolstoy’s novel “War and Peace”, Prince Andrei Bolkonsky explains the concept of war to his friend Pierre. Pierre expects war to resemble a game of chess: You position the troops and attempt to defeat your opponent by moving them in different directions.

“Far from it!”, Andrei responds. “In chess, you know the knight and his moves, you know the pawn and his combat strength. While in war, a battalion is sometimes stronger than a division and sometimes weaker than a company; it all depends on circumstances that can never be known. In war, you do not know the position of your enemy; some things you might be able to observe, some things you have to divine (but that depends on your ability to do so!) and many things cannot even be guessed at. In chess, you can see all of your opponent’s possible moves. In war, that is impossible. If you decide to attack, you cannot know whether the necessary conditions are met for you to succeed. Many a time, you cannot even know whether your troops will follow your orders…”

In essence, war is characterized by a high degree of uncertainty. A good commander (or politician) can add to that what he or she sees, tentatively fill in the blanks – and not just by means of logical deduction but also by intelligently bridging missing links. A bad commander extrapolates from what he sees and thus arrives at improper conclusions.

Many languages differentiate between two modes of mentalizing; for instance, the English language distinguishes between ‘thinking’ and ‘reasoning’. Reasoning denotes acute and exact mentalizing involving logical deductions. Such deductions are usually based on evidence and counterevidence. Thinking, however, is what is required to write novels. It is the construction of an initially unknown reality. But it is not a pipe dream, an unfounded process of fabrication. Rather, thinking asks us to imagine reality (“Wirklichkeitsfantasie”). In other words, a novelist has to possess a “sense of possibility” (“Möglichkeitssinn”, Robert Musil; in German, sense of possibility is often used synonymously with imagination even though imagination is not the same as sense of possibility, for imagination also encapsulates the impossible). This sense of possibility entails knowing the whole (or several wholes) or being able to construe an unknown whole that could accommodate a known part. The whole has to align with sociological and geographical givens, with the mentality of certain peoples or groups, and with the laws of physics and chemistry. Otherwise, the entire venture is ill-founded. A sense of possibility does not aim for the moon but imagines something that might be possible but has not been considered possible or even potentially possible so far.

Thinking is a means to eliminate uncertainty. This process requires both of the modes of thinking we have discussed thus far. Economic, political, or ecological decisions require us to first consider the situation at hand. Though certain situational aspects can be known, but many cannot. In fact, von Clausewitz (1832) posits that only about 25% of the necessary information is available when a military decision needs to be made. Even then, there is no way to guarantee that whatever information is available is also correct: Even if a piece of information was completely accurate yesterday, it might no longer apply today.

Once our sense of possibility has helped grasping a situation, problem solvers need to call on their reasoning skills. Not every situation requires the same action, and we may want to act this way or another to reach this or that goal. This appears logical, but it is a logic based on constantly shifting grounds: We cannot know whether necessary conditions are met, sometimes the assumptions we have made later turn out to be incorrect, and sometimes we have to revise our assumptions or make completely new ones. It is necessary to constantly switch between our sense of possibility and our sense of reality, that is, to switch between thinking and reasoning. It is an arduous process, and some people handle it well, while others do not.

If we are to believe Tuchman’s (1984) book, “The March of Folly”, most politicians and commanders are fools. According to Tuchman, not much has changed in the 3300 years that have elapsed since the misguided Trojans decided to welcome the left-behind wooden horse into their city that would end up dismantling Troy’s defensive walls. The Trojans, too, had been warned, but decided not to heed the warning. Although Laocoön had revealed the horse’s true nature to them by attacking it with a spear, making the weapons inside the horse ring, the Trojans refused to see the forest for the trees. They did not want to listen, they wanted the war to be over, and this desire ended up shaping their perception.

The objective of psychology is to predict and explain human actions and behavior as accurately as possible. However, thinking cannot be investigated by limiting its study to neatly confined fractions of reality such as the realms of propositional logic, chess, Go tasks, the Tower of Hanoi, and so forth. Within these systems, there is little need for a sense of possibility. But a sense of possibility – the ability to divine and construe an unknown reality – is at least as important as logical reasoning skills. Not researching the sense of possibility limits the validity of psychological research. All economic and political decision making draws upon this sense of possibility. By not exploring it, psychological research dedicated to the study of thinking cannot further the understanding of politicians’ competence and the reasons that underlie political mistakes. Christopher Clark identifies European diplomats’, politicians’, and commanders’ inability to form an accurate representation of reality as a reason for the outbreak of World War I. According to Clark’s (2012) book, “The Sleepwalkers”, the politicians of the time lived in their own make-believe world, wrongfully assuming that it was the same world everyone else inhabited. If CPS research wants to make significant contributions to the world, it has to acknowledge complexity and uncertainty as important aspects of it.

For more than 40 years, CPS has been a new subject of psychological research. During this time period, the initial emphasis on analyzing how humans deal with complex, dynamic, and uncertain situations has been lost. What is subsumed under the heading of CPS in modern research has lost the original complexities of real-life problems. From our point of view, the challenges of the 21st century require a return to the origins of this research tradition. We would encourage researchers in the field of problem solving to come back to the original ideas. There is enough complexity and uncertainty in the world to be studied. Improving our understanding of how humans deal with these global and pressing problems would be a worthwhile enterprise.

Author Contributions

JF drafted a first version of the manuscript, DD added further text and commented on the draft. JF finalized the manuscript.

Authors Note

After more than 40 years of controversial discussions between both authors, this is the first joint paper. We are happy to have done this now! We have found common ground!

Conflict of Interest Statement

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Acknowledgments

The authors thank the Deutsche Forschungsgemeinschaft (DFG) for the continuous support of their research over many years. Thanks to Daniel Holt for his comments on validity issues, thanks to Julia Nolte who helped us by translating German text excerpts into readable English and helped us, together with Keri Hartman, to improve our style and grammar – thanks for that! We also thank the two reviewers for their helpful critical comments on earlier versions of this manuscript. Finally, we acknowledge financial support by Deutsche Forschungsgemeinschaft and Ruprecht-Karls-Universität Heidelberg within their funding programme Open Access Publishing .

  • ^ The fMRI-paper from Anderson (2012) uses the term “complex problem solving” for tasks that do not fall in our understanding of CPS and is therefore excluded from this list.

Alison, L., van den Heuvel, C., Waring, S., Power, N., Long, A., O’Hara, T., et al. (2013). Immersive simulated learning environments for researching critical incidents: a knowledge synthesis of the literature and experiences of studying high-risk strategic decision making. J. Cogn. Eng. Deci. Mak. 7, 255–272. doi: 10.1177/1555343412468113

CrossRef Full Text | Google Scholar

Anderson, J. R. (2012). Tracking problem solving by multivariate pattern analysis and hidden markov model algorithms. Neuropsychologia 50, 487–498. doi: 10.1016/j.neuropsychologia.2011.07.025

PubMed Abstract | CrossRef Full Text | Google Scholar

Barth, C. M., and Funke, J. (2010). Negative affective environments improve complex solving performance. Cogn. Emot. 24, 1259–1268. doi: 10.1080/02699930903223766

Beckmann, J. F., and Goode, N. (2014). The benefit of being naïve and knowing it: the unfavourable impact of perceived context familiarity on learning in complex problem solving tasks. Instruct. Sci. 42, 271–290. doi: 10.1007/s11251-013-9280-7

Beghetto, R. A., and Kaufman, J. C. (2007). Toward a broader conception of creativity: a case for “mini-c” creativity. Psychol. Aesthetics Creat. Arts 1, 73–79. doi: 10.1037/1931-3896.1.2.73

Bennett, R. E. (2011). Formative assessment: a critical review. Assess. Educ. Princ. Policy Pract. 18, 5–25. doi: 10.1080/0969594X.2010.513678

Berry, D. C., and Broadbent, D. E. (1984). On the relationship between task performance and associated verbalizable knowledge. Q. J. Exp. Psychol. 36, 209–231. doi: 10.1080/14640748408402156

Blech, C., and Funke, J. (2010). You cannot have your cake and eat it, too: how induced goal conflicts affect complex problem solving. Open Psychol. J. 3, 42–53. doi: 10.2174/1874350101003010042

Brehmer, B., and Dörner, D. (1993). Experiments with computer-simulated microworlds: escaping both the narrow straits of the laboratory and the deep blue sea of the field study. Comput. Hum. Behav. 9, 171–184. doi: 10.1016/0747-5632(93)90005-D

Buchner, A. (1995). “Basic topics and approaches to the study of complex problem solving,” in Complex Problem Solving: The European Perspective , eds P. A. Frensch and J. Funke (Hillsdale, NJ: Erlbaum), 27–63.

Google Scholar

Buchner, A., and Funke, J. (1993). Finite state automata: dynamic task environments in problem solving research. Q. J. Exp. Psychol. 46A, 83–118. doi: 10.1080/14640749308401068

Clark, C. (2012). The Sleepwalkers: How Europe Went to War in 1914 . London: Allen Lane.

Csapó, B., and Funke, J. (2017a). “The development and assessment of problem solving in 21st-century schools,” in The Nature of Problem Solving: Using Research to Inspire 21st Century Learning , eds B. Csapó and J. Funke (Paris: OECD Publishing), 19–31.

Csapó, B., and Funke, J. (eds) (2017b). The Nature of Problem Solving. Using Research to Inspire 21st Century Learning. Paris: OECD Publishing.

Danner, D., Hagemann, D., Holt, D. V., Hager, M., Schankin, A., Wüstenberg, S., et al. (2011a). Measuring performance in dynamic decision making. Reliability and validity of the Tailorshop simulation. J. Ind. Differ. 32, 225–233. doi: 10.1027/1614-0001/a000055

CrossRef Full Text

Danner, D., Hagemann, D., Schankin, A., Hager, M., and Funke, J. (2011b). Beyond IQ: a latent state-trait analysis of general intelligence, dynamic decision making, and implicit learning. Intelligence 39, 323–334. doi: 10.1016/j.intell.2011.06.004

Dew, N., Read, S., Sarasvathy, S. D., and Wiltbank, R. (2009). Effectual versus predictive logics in entrepreneurial decision-making: differences between experts and novices. J. Bus. Ventur. 24, 287–309. doi: 10.1016/j.jbusvent.2008.02.002

Dhami, M. K., Mandel, D. R., Mellers, B. A., and Tetlock, P. E. (2015). Improving intelligence analysis with decision science. Perspect. Psychol. Sci. 10, 753–757. doi: 10.1177/1745691615598511

Dillon, J. T. (1982). Problem finding and solving. J. Creat. Behav. 16, 97–111. doi: 10.1002/j.2162-6057.1982.tb00326.x

Dörner, D. (1975). Wie Menschen eine Welt verbessern wollten [How people wanted to improve a world]. Bild Der Wissenschaft 12, 48–53.

Dörner, D. (1980). On the difficulties people have in dealing with complexity. Simulat. Gam. 11, 87–106. doi: 10.1177/104687818001100108

Dörner, D. (1996). The Logic of Failure: Recognizing and Avoiding Error in Complex Situations. New York, NY: Basic Books.

Dörner, D., Drewes, U., and Reither, F. (1975). “Über das Problemlösen in sehr komplexen Realitätsbereichen,” in Bericht über den 29. Kongreß der DGfPs in Salzburg 1974, Band 1 , ed. W. H. Tack (Göttingen: Hogrefe), 339–340.

Dörner, D., and Güss, C. D. (2011). A psychological analysis of Adolf Hitler’s decision making as commander in chief: summa confidentia et nimius metus. Rev. Gen. Psychol. 15, 37–49. doi: 10.1037/a0022375

Dörner, D., and Güss, C. D. (2013). PSI: a computational architecture of cognition, motivation, and emotion. Rev. Gen. Psychol. 17, 297–317. doi: 10.1037/a0032947

Dörner, D., Kreuzig, H. W., Reither, F., and Stäudel, T. (1983). Lohhausen. Vom Umgang mit Unbestimmtheit und Komplexität. Bern: Huber.

Ederer, P., Patt, A., and Greiff, S. (2016). Complex problem-solving skills and innovativeness – evidence from occupational testing and regional data. Eur. J. Educ. 51, 244–256. doi: 10.1111/ejed.12176

Edwards, W. (1962). Dynamic decision theory and probabiIistic information processing. Hum. Factors 4, 59–73. doi: 10.1177/001872086200400201

Engelhart, M., Funke, J., and Sager, S. (2017). A web-based feedback study on optimization-based training and analysis of human decision making. J. Dynamic Dec. Mak. 3, 1–23.

Ericsson, K. A., and Simon, H. A. (1983). Protocol Analysis: Verbal Reports As Data. Cambridge, MA: Bradford.

Fischer, A., Greiff, S., and Funke, J. (2017). “The history of complex problem solving,” in The Nature of Problem Solving: Using Research to Inspire 21st Century Learning , eds B. Csapó and J. Funke (Paris: OECD Publishing), 107–121.

Fischer, A., Holt, D. V., and Funke, J. (2015). Promoting the growing field of dynamic decision making. J. Dynamic Decis. Mak. 1, 1–3. doi: 10.11588/jddm.2015.1.23807

Fischer, A., Holt, D. V., and Funke, J. (2016). The first year of the “journal of dynamic decision making.” J. Dynamic Decis. Mak. 2, 1–2. doi: 10.11588/jddm.2016.1.28995

Fischer, A., and Neubert, J. C. (2015). The multiple faces of complex problems: a model of problem solving competency and its implications for training and assessment. J. Dynamic Decis. Mak. 1, 1–14. doi: 10.11588/jddm.2015.1.23945

Frensch, P. A., and Funke, J. (eds) (1995a). Complex Problem Solving: The European Perspective. Hillsdale, NJ: Erlbaum.

Frensch, P. A., and Funke, J. (1995b). “Definitions, traditions, and a general framework for understanding complex problem solving,” in Complex Problem Solving: The European Perspective , eds P. A. Frensch and J. Funke (Hillsdale, NJ: Lawrence Erlbaum), 3–25.

Frischkorn, G. T., Greiff, S., and Wüstenberg, S. (2014). The development of complex problem solving in adolescence: a latent growth curve analysis. J. Educ. Psychol. 106, 1004–1020. doi: 10.1037/a0037114

Funke, J. (1985). Steuerung dynamischer Systeme durch Aufbau und Anwendung subjektiver Kausalmodelle. Z. Psychol. 193, 435–457.

Funke, J. (1986). Komplexes Problemlösen - Bestandsaufnahme und Perspektiven [Complex Problem Solving: Survey and Perspectives]. Heidelberg: Springer.

Funke, J. (1993). “Microworlds based on linear equation systems: a new approach to complex problem solving and experimental results,” in The Cognitive Psychology of Knowledge , eds G. Strube and K.-F. Wender (Amsterdam: Elsevier Science Publishers), 313–330.

Funke, J. (1995). “Experimental research on complex problem solving,” in Complex Problem Solving: The European Perspective , eds P. A. Frensch and J. Funke (Hillsdale, NJ: Erlbaum), 243–268.

Funke, J. (2010). Complex problem solving: a case for complex cognition? Cogn. Process. 11, 133–142. doi: 10.1007/s10339-009-0345-0

Funke, J. (2012). “Complex problem solving,” in Encyclopedia of the Sciences of Learning , Vol. 38, ed. N. M. Seel (Heidelberg: Springer), 682–685.

Funke, J. (2014a). Analysis of minimal complex systems and complex problem solving require different forms of causal cognition. Front. Psychol. 5:739. doi: 10.3389/fpsyg.2014.00739

Funke, J. (2014b). “Problem solving: what are the important questions?,” in Proceedings of the 36th Annual Conference of the Cognitive Science Society , eds P. Bello, M. Guarini, M. McShane, and B. Scassellati (Austin, TX: Cognitive Science Society), 493–498.

Funke, J., Fischer, A., and Holt, D. V. (2017). When less is less: solving multiple simple problems is not complex problem solving—A comment on Greiff et al. (2015). J. Intell. 5:5. doi: 10.3390/jintelligence5010005

Funke, J., Fischer, A., and Holt, D. V. (2018). “Competencies for complexity: problem solving in the 21st century,” in Assessment and Teaching of 21st Century Skills , eds E. Care, P. Griffin, and M. Wilson (Dordrecht: Springer), 3.

Funke, J., and Greiff, S. (2017). “Dynamic problem solving: multiple-item testing based on minimally complex systems,” in Competence Assessment in Education. Research, Models and Instruments , eds D. Leutner, J. Fleischer, J. Grünkorn, and E. Klieme (Heidelberg: Springer), 427–443.

Gobert, J. D., Kim, Y. J., Pedro, M. A. S., Kennedy, M., and Betts, C. G. (2015). Using educational data mining to assess students’ skills at designing and conducting experiments within a complex systems microworld. Think. Skills Creat. 18, 81–90. doi: 10.1016/j.tsc.2015.04.008

Goode, N., and Beckmann, J. F. (2010). You need to know: there is a causal relationship between structural knowledge and control performance in complex problem solving tasks. Intelligence 38, 345–352. doi: 10.1016/j.intell.2010.01.001

Gray, W. D. (2002). Simulated task environments: the role of high-fidelity simulations, scaled worlds, synthetic environments, and laboratory tasks in basic and applied cognitive research. Cogn. Sci. Q. 2, 205–227.

Greiff, S., and Fischer, A. (2013). Measuring complex problem solving: an educational application of psychological theories. J. Educ. Res. 5, 38–58.

Greiff, S., Fischer, A., Stadler, M., and Wüstenberg, S. (2015a). Assessing complex problem-solving skills with multiple complex systems. Think. Reason. 21, 356–382. doi: 10.1080/13546783.2014.989263

Greiff, S., Stadler, M., Sonnleitner, P., Wolff, C., and Martin, R. (2015b). Sometimes less is more: comparing the validity of complex problem solving measures. Intelligence 50, 100–113. doi: 10.1016/j.intell.2015.02.007

Greiff, S., Fischer, A., Wüstenberg, S., Sonnleitner, P., Brunner, M., and Martin, R. (2013a). A multitrait–multimethod study of assessment instruments for complex problem solving. Intelligence 41, 579–596. doi: 10.1016/j.intell.2013.07.012

Greiff, S., Holt, D. V., and Funke, J. (2013b). Perspectives on problem solving in educational assessment: analytical, interactive, and collaborative problem solving. J. Problem Solv. 5, 71–91. doi: 10.7771/1932-6246.1153

Greiff, S., Wüstenberg, S., Molnár, G., Fischer, A., Funke, J., and Csapó, B. (2013c). Complex problem solving in educational contexts—something beyond g: concept, assessment, measurement invariance, and construct validity. J. Educ. Psychol. 105, 364–379. doi: 10.1037/a0031856

Greiff, S., and Funke, J. (2009). “Measuring complex problem solving: the MicroDYN approach,” in The Transition to Computer-Based Assessment. New Approaches to Skills Assessment and Implications for Large-Scale Testing , eds F. Scheuermann and J. Björnsson (Luxembourg: Office for Official Publications of the European Communities), 157–163.

Greiff, S., and Funke, J. (2017). “Interactive problem solving: exploring the potential of minimal complex systems,” in The Nature of Problem Solving: Using Research to Inspire 21st Century Learning , eds B. Csapó and J. Funke (Paris: OECD Publishing), 93–105.

Greiff, S., and Martin, R. (2014). What you see is what you (don’t) get: a comment on Funke’s (2014) opinion paper. Front. Psychol. 5:1120. doi: 10.3389/fpsyg.2014.01120

Greiff, S., and Neubert, J. C. (2014). On the relation of complex problem solving, personality, fluid intelligence, and academic achievement. Learn. Ind. Diff. 36, 37–48. doi: 10.1016/j.lindif.2014.08.003

Greiff, S., Niepel, C., Scherer, R., and Martin, R. (2016). Understanding students’ performance in a computer-based assessment of complex problem solving: an analysis of behavioral data from computer-generated log files. Comput. Hum. Behav. 61, 36–46. doi: 10.1016/j.chb.2016.02.095

Greiff, S., Stadler, M., Sonnleitner, P., Wolff, C., and Martin, R. (2017). Sometimes more is too much: a rejoinder to the commentaries on Greiff et al. (2015). J. Intell. 5:6. doi: 10.3390/jintelligence5010006

Greiff, S., and Wüstenberg, S. (2014). Assessment with microworlds using MicroDYN: measurement invariance and latent mean comparisons. Eur. J. Psychol. Assess. 1, 1–11. doi: 10.1027/1015-5759/a000194

Greiff, S., and Wüstenberg, S. (2015). Komplexer Problemlösetest COMPRO [Complex Problem-Solving Test COMPRO]. Mödling: Schuhfried.

Greiff, S., Wüstenberg, S., and Funke, J. (2012). Dynamic problem solving: a new assessment perspective. Appl. Psychol. Measure. 36, 189–213. doi: 10.1177/0146621612439620

Griffin, P., and Care, E. (2015). “The ATC21S method,” in Assessment and Taching of 21st Century Skills , eds P. Griffin and E. Care (Dordrecht, NL: Springer), 3–33.

Güss, C. D., and Dörner, D. (2011). Cultural differences in dynamic decision-making strategies in a non-linear, time-delayed task. Cogn. Syst. Res. 12, 365–376. doi: 10.1016/j.cogsys.2010.12.003

Güss, C. D., Tuason, M. T., and Orduña, L. V. (2015). Strategies, tactics, and errors in dynamic decision making in an Asian sample. J. Dynamic Deci. Mak. 1, 1–14. doi: 10.11588/jddm.2015.1.13131

Güss, C. D., and Wiley, B. (2007). Metacognition of problem-solving strategies in Brazil, India, and the United States. J. Cogn. Cult. 7, 1–25. doi: 10.1163/156853707X171793

Herde, C. N., Wüstenberg, S., and Greiff, S. (2016). Assessment of complex problem solving: what we know and what we don’t know. Appl. Meas. Educ. 29, 265–277. doi: 10.1080/08957347.2016.1209208

Hermes, M., and Stelling, D. (2016). Context matters, but how much? Latent state – trait analysis of cognitive ability assessments. Int. J. Sel. Assess. 24, 285–295. doi: 10.1111/ijsa.12147

Hotaling, J. M., Fakhari, P., and Busemeyer, J. R. (2015). “Dynamic decision making,” in International Encyclopedia of the Social & Behavioral Sciences , 2nd Edn, eds N. J. Smelser and P. B. Batles (New York, NY: Elsevier), 709–714.

Hundertmark, J., Holt, D. V., Fischer, A., Said, N., and Fischer, H. (2015). System structure and cognitive ability as predictors of performance in dynamic system control tasks. J. Dynamic Deci. Mak. 1, 1–10. doi: 10.11588/jddm.2015.1.26416

Jäkel, F., and Schreiber, C. (2013). Introspection in problem solving. J. Problem Solv. 6, 20–33. doi: 10.7771/1932-6246.1131

Jansson, A. (1994). Pathologies in dynamic decision making: consequences or precursors of failure? Sprache Kogn. 13, 160–173.

Kaufman, J. C., and Beghetto, R. A. (2009). Beyond big and little: the four c model of creativity. Rev. Gen. Psychol. 13, 1–12. doi: 10.1037/a0013688

Knauff, M., and Wolf, A. G. (2010). Complex cognition: the science of human reasoning, problem-solving, and decision-making. Cogn. Process. 11, 99–102. doi: 10.1007/s10339-010-0362-z

Kretzschmar, A. (2017). Sometimes less is not enough: a commentary on Greiff et al. (2015). J. Intell. 5:4. doi: 10.3390/jintelligence5010004

Kretzschmar, A., Neubert, J. C., Wüstenberg, S., and Greiff, S. (2016). Construct validity of complex problem solving: a comprehensive view on different facets of intelligence and school grades. Intelligence 54, 55–69. doi: 10.1016/j.intell.2015.11.004

Kretzschmar, A., and Süß, H.-M. (2015). A study on the training of complex problem solving competence. J. Dynamic Deci. Mak. 1, 1–14. doi: 10.11588/jddm.2015.1.15455

Lee, H., and Cho, Y. (2007). Factors affecting problem finding depending on degree of structure of problem situation. J. Educ. Res. 101, 113–123. doi: 10.3200/JOER.101.2.113-125

Leutner, D., Fleischer, J., Wirth, J., Greiff, S., and Funke, J. (2012). Analytische und dynamische Problemlösekompetenz im Lichte internationaler Schulleistungsvergleichsstudien: Untersuchungen zur Dimensionalität. Psychol. Rundschau 63, 34–42. doi: 10.1026/0033-3042/a000108

Luchins, A. S. (1942). Mechanization in problem solving: the effect of einstellung. Psychol. Monogr. 54, 1–95. doi: 10.1037/h0093502

Mack, O., Khare, A., Krämer, A., and Burgartz, T. (eds) (2016). Managing in a VUCA world. Heidelberg: Springer.

Mainert, J., Kretzschmar, A., Neubert, J. C., and Greiff, S. (2015). Linking complex problem solving and general mental ability to career advancement: does a transversal skill reveal incremental predictive validity? Int. J. Lifelong Educ. 34, 393–411. doi: 10.1080/02601370.2015.1060024

Mainzer, K. (2009). Challenges of complexity in the 21st century. An interdisciplinary introduction. Eur. Rev. 17, 219–236. doi: 10.1017/S1062798709000714

Meadows, D. H., Meadows, D. L., and Randers, J. (1992). Beyond the Limits. Vermont, VA: Chelsea Green Publishing.

Meadows, D. H., Meadows, D. L., Randers, J., and Behrens, W. W. (1972). The Limits to Growth. New York, NY: Universe Books.

Meißner, A., Greiff, S., Frischkorn, G. T., and Steinmayr, R. (2016). Predicting complex problem solving and school grades with working memory and ability self-concept. Learn. Ind. Differ. 49, 323–331. doi: 10.1016/j.lindif.2016.04.006

Molnàr, G., Greiff, S., Wüstenberg, S., and Fischer, A. (2017). “Empirical study of computer-based assessment of domain-general complex problem-solving skills,” in The Nature of Problem Solving: Using research to Inspire 21st Century Learning , eds B. Csapó and J. Funke (Paris: OECD Publishing), 125–141.

National Research Council (2011). Assessing 21st Century Skills: Summary of a Workshop. Washington, DC: The National Academies Press.

Newell, A., Shaw, J. C., and Simon, H. A. (1959). A general problem-solving program for a computer. Comput. Automat. 8, 10–16.

Nisbett, R. E., and Wilson, T. D. (1977). Telling more than we can know: verbal reports on mental processes. Psychol. Rev. 84, 231–259. doi: 10.1037/0033-295X.84.3.231

OECD (2014). “PISA 2012 results,” in Creative Problem Solving: Students’ Skills in Tackling Real-Life problems , Vol. 5 (Paris: OECD Publishing).

Osman, M. (2010). Controlling uncertainty: a review of human behavior in complex dynamic environments. Psychol. Bull. 136, 65–86. doi: 10.1037/a0017815

Osman, M. (2012). The role of reward in dynamic decision making. Front. Neurosci. 6:35. doi: 10.3389/fnins.2012.00035

Qudrat-Ullah, H. (2015). Better Decision Making in Complex, Dynamic Tasks. Training with Human-Facilitated Interactive Learning Environments. Heidelberg: Springer.

Ramnarayan, S., Strohschneider, S., and Schaub, H. (1997). Trappings of expertise and the pursuit of failure. Simulat. Gam. 28, 28–43. doi: 10.1177/1046878197281004

Reuschenbach, B. (2008). Planen und Problemlösen im Komplexen Handlungsfeld Pflege. Berlin: Logos.

Rohe, M., Funke, J., Storch, M., and Weber, J. (2016). Can motto goals outperform learning and performance goals? Influence of goal setting on performance, intrinsic motivation, processing style, and affect in a complex problem solving task. J. Dynamic Deci. Mak. 2, 1–15. doi: 10.11588/jddm.2016.1.28510

Scherer, R., Greiff, S., and Hautamäki, J. (2015). Exploring the relation between time on task and ability in complex problem solving. Intelligence 48, 37–50. doi: 10.1016/j.intell.2014.10.003

Schoppek, W., and Fischer, A. (2015). Complex problem solving – single ability or complex phenomenon? Front. Psychol. 6:1669. doi: 10.3389/fpsyg.2015.01669

Schraw, G., Dunkle, M., and Bendixen, L. D. (1995). Cognitive processes in well-defined and ill-defined problem solving. Appl. Cogn. Psychol. 9, 523–538. doi: 10.1002/acp.2350090605

Schweizer, F., Wüstenberg, S., and Greiff, S. (2013). Validity of the MicroDYN approach: complex problem solving predicts school grades beyond working memory capacity. Learn. Ind. Differ. 24, 42–52. doi: 10.1016/j.lindif.2012.12.011

Schweizer, T. S., Schmalenberger, K. M., Eisenlohr-Moul, T. A., Mojzisch, A., Kaiser, S., and Funke, J. (2016). Cognitive and affective aspects of creative option generation in everyday life situations. Front. Psychol. 7:1132. doi: 10.3389/fpsyg.2016.01132

Selten, R., Pittnauer, S., and Hohnisch, M. (2012). Dealing with dynamic decision problems when knowledge of the environment is limited: an approach based on goal systems. J. Behav. Deci. Mak. 25, 443–457. doi: 10.1002/bdm.738

Simon, H. A. (1957). Administrative Behavior: A Study of Decision-Making Processes in Administrative Organizations , 2nd Edn. New York, NY: Macmillan.

Sonnleitner, P., Brunner, M., Keller, U., and Martin, R. (2014). Differential relations between facets of complex problem solving and students’ immigration background. J. Educ. Psychol. 106, 681–695. doi: 10.1037/a0035506

Spering, M., Wagener, D., and Funke, J. (2005). The role of emotions in complex problem solving. Cogn. Emot. 19, 1252–1261. doi: 10.1080/02699930500304886

Stadler, M., Becker, N., Gödker, M., Leutner, D., and Greiff, S. (2015). Complex problem solving and intelligence: a meta-analysis. Intelligence 53, 92–101. doi: 10.1016/j.intell.2015.09.005

Stadler, M., Niepel, C., and Greiff, S. (2016). Easily too difficult: estimating item difficulty in computer simulated microworlds. Comput. Hum. Behav. 65, 100–106. doi: 10.1016/j.chb.2016.08.025

Sternberg, R. J. (1995). “Expertise in complex problem solving: a comparison of alternative conceptions,” in Complex Problem Solving: The European Perspective , eds P. A. Frensch and J. Funke (Hillsdale, NJ: Erlbaum), 295–321.

Sternberg, R. J., and Frensch, P. A. (1991). Complex Problem Solving: Principles and Mechanisms. (eds) R. J. Sternberg and P. A. Frensch. Hillsdale, NJ: Erlbaum.

Strohschneider, S., and Güss, C. D. (1998). Planning and problem solving: differences between brazilian and german students. J. Cross-Cult. Psychol. 29, 695–716. doi: 10.1177/0022022198296002

Strohschneider, S., and Güss, C. D. (1999). The fate of the Moros: a cross-cultural exploration of strategies in complex and dynamic decision making. Int. J. Psychol. 34, 235–252. doi: 10.1080/002075999399873

Thimbleby, H. (2007). Press On. Principles of Interaction. Cambridge, MA: MIT Press.

Tobinski, D. A., and Fritz, A. (2017). “EcoSphere: a new paradigm for problem solving in complex systems,” in The Nature of Problem Solving: Using Research to Inspire 21st Century Learning , eds B. Csapó and J. Funke (Paris: OECD Publishing), 211–222.

Tremblay, S., Gagnon, J.-F., Lafond, D., Hodgetts, H. M., Doiron, M., and Jeuniaux, P. P. J. M. H. (2017). A cognitive prosthesis for complex decision-making. Appl. Ergon. 58, 349–360. doi: 10.1016/j.apergo.2016.07.009

Tschirgi, J. E. (1980). Sensible reasoning: a hypothesis about hypotheses. Child Dev. 51, 1–10. doi: 10.2307/1129583

Tuchman, B. W. (1984). The March of Folly. From Troy to Vietnam. New York, NY: Ballantine Books.

Verweij, M., and Thompson, M. (eds) (2006). Clumsy Solutions for A Complex World. Governance, Politics and Plural Perceptions. New York, NY: Palgrave Macmillan. doi: 10.1057/9780230624887

Viehrig, K., Siegmund, A., Funke, J., Wüstenberg, S., and Greiff, S. (2017). “The heidelberg inventory of geographic system competency model,” in Competence Assessment in Education. Research, Models and Instruments , eds D. Leutner, J. Fleischer, J. Grünkorn, and E. Klieme (Heidelberg: Springer), 31–53.

von Clausewitz, C. (1832). Vom Kriege [On war]. Berlin: Dämmler.

Wendt, A. N. (2017). The empirical potential of live streaming beyond cognitive psychology. J. Dynamic Deci. Mak. 3, 1–9. doi: 10.11588/jddm.2017.1.33724

Wiliam, D., and Black, P. (1996). Meanings and consequences: a basis for distinguishing formative and summative functions of assessment? Br. Educ. Res. J. 22, 537–548. doi: 10.1080/0141192960220502

World Economic Forum (2015). New Vsion for Education Unlocking the Potential of Technology. Geneva: World Economic Forum.

World Economic Forum (2016). Global Risks 2016: Insight Report , 11th Edn. Geneva: World Economic Forum.

Wüstenberg, S., Greiff, S., and Funke, J. (2012). Complex problem solving — more than reasoning? Intelligence 40, 1–14. doi: 10.1016/j.intell.2011.11.003

Wüstenberg, S., Greiff, S., Vainikainen, M.-P., and Murphy, K. (2016). Individual differences in students’ complex problem solving skills: how they evolve and what they imply. J. Educ. Psychol. 108, 1028–1044. doi: 10.1037/edu0000101

Wüstenberg, S., Stadler, M., Hautamäki, J., and Greiff, S. (2014). The role of strategy knowledge for the application of strategies in complex problem solving tasks. Technol. Knowl. Learn. 19, 127–146. doi: 10.1007/s10758-014-9222-8

Keywords : complex problem solving, validity, assessment, definition, MicroDYN

Citation: Dörner D and Funke J (2017) Complex Problem Solving: What It Is and What It Is Not. Front. Psychol. 8:1153. doi: 10.3389/fpsyg.2017.01153

Received: 14 March 2017; Accepted: 23 June 2017; Published: 11 July 2017.

Reviewed by:

Copyright © 2017 Dörner and Funke. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Joachim Funke, [email protected]

Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.

Bryan Lindsley

How To Solve Complex Problems

In today’s increasingly complex world, we are constantly faced with ill-defined problems that don’t have a clear solution. From poverty and climate change to crime and addiction, complex situations surround us. Unlike simple problems with a pre-defined or “right” answer, complex problems share several basic characteristics that make them hard to solve. While these problems can be frustrating and overwhelming, they also offer an opportunity for growth and creativity. Complex problem-solving skills are the key to addressing these tough issues.

In this article, I will discuss simple versus complex problems, define complex problem solving, and describe why it is so important in complex dynamic environments. I will also explain how to develop problem-solving skills and share some tips for effectively solving complex problems.

How is simple problem-solving different from complex problem-solving?

Solving problems is about getting from a currently undesirable state to an intended goal state. In other words, about bridging the gap between “what is” and “what ought to be”. However, the challenge of reaching a solution varies based on the kind of problem that is being solved. There are generally three different kinds of problems you should consider.

Simple problems have one problem solution. The goal is to find that answer as quickly and efficiently as possible. Puzzles are classic examples of simple problem solving. The objective is to find the one correct solution out of many possibilities.

Puzzles complex problem-solving

Problems are different from puzzles in that they don’t have a known problem solution. As such, many people may agree that there is an issue to be solved, but they may not agree on the intended goal state or how to get there. In this type of problem, people spend a lot of time debating the best solution and the optimal way to achieve it.

Messes are collections of interrelated problems where many stakeholders may not even agree on what the issue is. Unlike problems where there is agreement about what the problem is, in messes, there isn’t agreement amongst stakeholders. In other words, even “what is” can’t be taken for granted. Most complex social problems are messes, made up of interrelated social issues with ill-defined boundaries and goals.

Problems and messes can be complicated or complex

Puzzles are simple, but problems and messes exist on a continuum between complicated and complex. Complicated problems are technical in nature. There may be many involved variables, but the relationships are linear. As a result, complicated problems have step-by-step, systematic solutions. Repairing an engine or building a rocket may be difficult because of the many parts involved, but it is a technical problem we call complicated.

On the other hand, solving a complex problem is entirely different. Unlike complicated problems that may have many variables with linear relationships, a complex problem is characterized by connectivity patterns that are harder to understand and predict.

Characteristics of complex problems and messes

So what else makes a problem complex? Here are seven additional characteristics (from Funke and Hester and Adams ).

  • Lack of information. There is often a lack of data or information about the problem itself. In some cases, variables are unknown or cannot be measured.
  • Many goals. A complex problem has a mix of conflicting objectives. In some sense, every stakeholder involved with the problem may have their own goals. However, with limited resources, not all goals can be simultaneously satisfied.
  • Unpredictable feedback loops. In part due to many variables connected by a range of different relationships, a change in one variable is likely to have effects on other variables in the system. However, because we do not know all of the variables it will affect, small changes can have disproportionate system-wide effects. These unexpected events that have big, unpredictable effects are sometimes called Black Swans.
  • Dynamic. A complex problem changes over time and there is a significant impact based on when you act. In other words, because the problem and its parts and relationships are constantly changing, an action taken today won’t have the same effects as the same action taken tomorrow.
  • Time-delayed. It takes a while for cause and effect to be realized. Thus it is very hard to know if any given intervention is working.
  • Unknown unknowns. Building off the previous point about a lack of information, in a complex problem you may not even know what you don’t know. In other words, there may be very important variables that you are not even aware of.
  • Affected by (error-prone) humans. Simply put, human behavior tends to be illogical and unpredictable. When humans are involved in a problem, avoiding error may be impossible.

What is complex problem-solving?

“Complex problem solving” is the term for how to address a complex problem or messes that have the characteristics listed above.

Since a complex problem is a different phenomenon than a simple or complicated problem, solving them requires a different approach. Methods designed for simple problems, like systematic organization, deductive logic, and linear thinking don’t work well on their own for a complex problem.

And yet, despite its importance, there isn’t complete agreement about what exactly it is.

How is complex problem solving defined by experts?

Let’s look at what scientists, researchers, and system thinkers have come up with in terms of a definition for solving a complex problem. 

As a series of observations and informed decisions

For many employers, the focus is on making smart decisions. These must weigh the future effects to the company of any given solution. According to Indeed.com , it is defined as “a series of observations and informed decisions used to find and implement a solution to a problem. Beyond finding and implementing a solution, complex problem solving also involves considering future changes to circumstance, resources, and capabilities that may affect the trajectory of the process and success of the solution. Complex problem solving also involves considering the impact of the solution on the surrounding environment and individuals.”

As using information to review options and develop solutions

For others, it is more of a systematic way to consider a range of options. According to O*NET ,  the definition focuses on “identifying complex problems and reviewing related information to develop and evaluate options and implement solutions.”

As a self-regulated psychological process

Others emphasize the broad range of skills and emotions needed for change. In addition, they endorse an inspired kind of pragmatism. For example, Dietrich Dorner and Joachim Funke define it as “a collection of self-regulated psychological processes and activities necessary in dynamic environments to achieve ill-defined goals that cannot be reached by routine actions. Creative combinations of knowledge and a broad set of strategies are needed. Solutions are often more bricolage than perfect or optimal. The problem-solving process combines cognitive, emotional, and motivational aspects, particularly in high-stakes situations. Complex problems usually involve knowledge-rich requirements and collaboration among different persons.”

As a novel way of thinking and reasoning

Finally, some emphasize the multidisciplinary nature of knowledge and processes needed to tackle a complex problem. Patrick Hester and Kevin MacG. Adams have stated that “no single discipline can solve truly complex problems. Problems of real interest, those vexing ones that keep you up at night, require a discipline-agnostic approach…Simply they require us to think systemically about our problem…a novel way of thinking and reasoning about complex problems that encourages increased understanding and deliberate intervention.”

A synthesis definition

By pulling the main themes of these definitions together, we can get a sense of what complex problem-solvers must do:

Gain a better understanding of the phenomena of a complex problem or mess. Use a discipline-agnostic approach in order to develop deliberate interventions. Take into consideration future impacts on the surrounding environment.

Why is complex problem solving important?

Many efforts aimed at complex social problems like reducing homelessness and improving public health – despite good intentions giving more effort than ever before – are destined to fail because their approach is based on simple problem-solving. And some efforts might even unwittingly be contributing to the problems they’re trying to solve. 

Einstein said that “We can’t solve problems by using the same kind of thinking we used when we created them.” I think he could have easily been alluding to the need for more complex problem solvers who think differently. So what skills are required to do this?

What are complex problem-solving skills?

The skills required to solve a complex problem aren’t from one domain, nor are they an easily-packaged bundle. Rather, I like to think of them as a balancing act between a series of seemingly opposite approaches but synthesized. This brings a sort of cognitive dissonance into the process, which is itself informative.

It brings F. Scott Fitzgerald’s maxim to mind: 

“The test of a first-rate intelligence is the ability to hold two opposing ideas in mind at the same time and still retain the ability to function. One should, for example, be able to see that things are hopeless yet be determined to make them otherwise.” 

To see the problem situation clearly, for example, but also with a sense of optimism and possibility.

Here are the top three dialectics to keep in mind:

Thinking and reasoning

Reasoning is the ability to make logical deductions based on evidence and counterevidence. On the other hand, thinking is more about imagining an unknown reality based on thoughts about the whole picture and how the parts could fit together. By thinking clearly, one can have a sense of possibility that prepares the mind to deduce the right action in the unique moment at hand.

As Dorner and Funke explain: “Not every situation requires the same action,  and we may want to act this way or another to reach this or that goal. This appears logical, but it is a logic based on constantly shifting grounds: We cannot know whether necessary conditions are met, sometimes the assumptions we have made later turn out to be incorrect, and sometimes we have to revise our assumptions or make completely new ones. It is necessary to constantly switch between our sense of possibility and our sense of reality, that is, to switch between thinking and reasoning. It is an arduous process, and some people handle it well, while others do not.”

Analysis and reductionism combined with synthesis and holism

It’s important to be able to use scientific processes to break down a complex problem into its parts and analyze them. But at the same time, a complex problem is more than the sum of its parts. In most cases, the relationships between the parts are more important than the parts themselves. Therefore, decomposing problems with rigor isn’t enough. What’s needed, once problems are reduced and understood, is a way of understanding the relationships between various components as well as putting the pieces back together. However, synthesis and holism on their own without deductive analysis can often miss details and relationships that matter.  

What makes this balancing act more difficult is that certain professions tend to be trained in and prefer one domain over the other. Scientists prefer analysis and reductionism whereas most social scientists and practitioners default to synthesis and holism. Unfortunately, this divide of preferences results in people working in their silos at the expense of multi-disciplinary approaches that together can better “see” complexity.

seeing complex problem solving

Situational awareness and self-awareness 

Dual awareness is the ability to pay attention to two experiences simultaneously. In the case of complex problems, context really matters. In other words, problem-solving exists in an ecosystem of environmental factors that are not incidental. Personal and cultural preferences play a part as do current events unfolding over time. But as a problem solver, knowing the environment is only part of the equation. 

The other crucial part is the internal psychological process unique to every individual who also interacts with the problem and the environment. Problem solvers inevitably come into contact with others who may disagree with them, or be advancing seemingly counterproductive solutions, and these interactions result in emotions and motivations. Without self-awareness, we can become attached to our own subjective opinions, fall in love with “our” solutions, and generally be driven by the desire to be seen as problem solvers at the expense of actually solving the problem.

By balancing these three dialectics, practitioners can better deal with uncertainty as well as stay motivated despite setbacks. Self-regulation among these seemingly opposite approaches also reminds one to stay open-minded.

How do you develop complex problem-solving skills?

There is no one answer to this question, as the best way to develop them will vary depending on your strengths and weaknesses. However, there are a few general things that you can do to improve your ability to solve problems.

Ground yourself in theory and knowledge

First, it is important to learn about systems thinking and complexity theories. These frameworks will help you understand how complex systems work, and how different parts of a system interact with each other. This conceptual understanding will allow you to identify potential solutions to problems more quickly and effectively.

Practice switching between approaches

Second, practice switching between the dialectics mentioned above. For example, in your next meeting try to spend roughly half your time thinking and half your time reasoning. The important part is trying to get habituated to regularly switching lenses. It may seem disjointed at first, but after a while, it becomes second nature to simultaneously see how the parts interact and the big picture.

Focus on the specific problem phenomena

Third, it may sound obvious, but people often don’t spend very much time studying the problem itself and how it functions. In some sense, becoming a good problem-solver involves becoming a problem scientist. Your time should be spent regularly investigating the phenomena of “what is” rather than “what ought to be”. A holistic understanding of the problem is the required prerequisite to coming up with good solutions.

Stay curious

Finally, after we have worked on a problem for a while, we tend to think we know everything about it, including how to solve it. Even if we’re working on a problem, which may change dynamically from day to day, we start treating it more like a puzzle with a definite solution. When that happens, we can lose our motivation to continue learning about the problem. This is very risky because it closes the door to learning from others, regardless of whether we completely agree with them or not.

As Neils Bohr said, “Two different perspectives or models about a system will reveal truths regarding the system that are neither entirely independent nor entirely compatible.”

By staying curious, we can retain our ability to learn on a daily basis.

Tips for how to solve complex problems

Focus on processes over results.

It’s easy to get lost in utopian thinking. Many people spend so much time on “what ought to be” that they forget that problem solving is about the gap between “what is” and “what ought to be”. It is said that “life is a journey, not a destination.” The same is true for complex problem-solving. To do it well, a problem solver must focus on enjoying the process of gaining a holistic understanding of the problem. 

Adaptive and iterative methods and tools

A variety of adaptive and iterative methods have been developed to address complexity. They share a laser focus on gaining holistic understanding with tools that best match the phenomena of complexity. They are also non-ideological, trans-disciplinary, and flexible. In most cases, your journey through a set of steps won’t be linear. Rather, as you think and reason, analyze and synthesize, you’ll jump around to get a holistic picture.

adapting complex problem-solving

In my online course , we generally follow a seven-step method:

  • Get clear sight with a complex problem-solving frame
  • Establish a secure base of operation
  • Gain a deep understanding of the problem
  • Create an interactive model of the problem
  • Develop an impact strategy
  • Create an action plan and implement
  • Embed systemic solutions

Of course, each of these steps involves testing to see what works and consistently evaluating our process and progress.

Resolution is about systematically managing a problem over time

One last thing to keep in mind. Most social problems are not just solved one day, never to return. In reality,  most complex problems are managed, not solved. For all practical purposes, what this means is that “the solution” is a way of systematically dealing with the problem over time. Some find this disappointing, but it’s actually a pragmatic pointer to think about resolution – a way move problems in the right direction – rather than final solutions.

Problem solvers regularly train and practice

If you need help developing your complex problem-solving skills, I have an online class where you can learn everything you need to know. 

Sign up today and learn how to be successful at making a difference in the world!

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what is a complex problem solver

November 8, 2022

An introduction to complex problem solving, by jordan nottrodt.

Human beings love a quick fix. If there’s an issue, let’s get a team on it to be solved right away. The thing is, many of the problems we face are not so easy to solve. And sometimes, the solutions we find actually create a slew of other problems that cascade all around us so that the proper solution seems impossible to find. How do you solve the problem while ensuring everyone is reasonably satisfied with the result? Enter complex problem solving. 

Solving complex problems isn’t easy. It’s right there in the name. In this article, we’ll provide an introduction to complex problem solving, including some introductory strategies that your team can put into practice today. 

What is a Complex Problem

We are faced with many different kinds of problems every day. If we’re lucky, most of those problems are simple. If you notice it’s starting to become dark in the room where you’re working, you can switch on a light or light a candle. If you’re cold, you can put on a sweater or wrap yourself in a blanket. Generally speaking, these are simple problems with simple solutions.

A complex problem is, well, complex. It involves a number of different layers and impacts a wide range of people, and the more you learn about the problem, the more people it seems to affect. A solution is hard to find because the people involved have competing interests, and what works for some won’t work for others. How do you find a solution that will please everyone and ensure every person is treated equally? Where do you even begin?

One of the most complex problems facing the world today is climate change, which affects literally every person, creature, plant, and microbe on the planet. How do you hold every country and company to the same standard? Should India be held to the same standard as the United States? What will happen to the Albertan workers in the oil and gas sector who will lose the only profession they know? What about the children being born post-2021; what future can they expect if drastic actions aren’t taken to reduce carbon emissions and save a planet on fire? The gravity and convoluted intricacies of the issue and all of the people it affects are what make the problem so complex.

Intro to Complex Problem Solving  

Solving a complex problem requires a deeper understanding of the actual problem and all of the people it affects. Complex problem solving involves gathering observations and asking questions to make informed decisions, considering how future developments could affect a potential solution’s continued success, and understanding how the solution will affect both the people involved and the surrounding environment. 

As you can tell, it’s called complex problem solving for a reason. While finding solutions to complicated problems is challenging, there are strategies you can employ to solve complex problems effectively. 

1. Clearly Define the Problem

“A problem well-defined is a problem half-solved.” — attributed to or repeated by at least John Dewey and Charles Kettering.

If you don’t know what the problem is, how can you hope to solve it? 

To solve a complex problem, you must clearly and objectively define what the problem is—what is the root cause of the problem, and what are each of its contributing factors? Who does the problem affect, and how does it affect them—physically, emotionally, financially, or spiritually? Does the problem affect their safety? This involves a collaborative and systematic analysis of any and all relevant data. 

By seeking to understand exactly how the problem negatively impacts the people and the surrounding environment, you can begin to prioritize potential solutions that will relieve those impacts. But keep in mind that defining the problem is only the beginning. 

2. Push the Limits of Your Assumptions

How to catch a big fish: 1. Catch a lot of fish. 2. Throw back all the little ones. Linda Carson

Cast a wide net when you’re coming up with new ideas. It’s important to bring as many different perspectives to the table as possible to limit any potential biases. Collaborate with a team of different minds from different backgrounds and with different skill sets to gather as many ideas as you can. 

Focus on quantity because you need the not-so-good ideas to find the good ones. Don’t focus on what’s possible at this stage—you’re ideating, so encourage your team to be creative and open to any possibility.

Don’t limit yourself to your assumptions or what you believe to be possible. What if you did the opposite? What if you deeply explored an idea you previously thought wouldn’t work out? Complex problems require you to be open to all possibilities.

Once you’ve gathered potential solutions together, it’s time to test them, break them down, and seek feedback. 

3. Test Assumptions and Gather Feedback

We like to think of complex problem solving as an excavation site. Defining the problem is you putting the stakes in the ground and determining where to start digging. Meaning, defining the problem is only the beginning. Once the problem is defined and you’ve ideated on it, it’s time to do your research, gather feedback, and test your assumptions around the problem space. In terms of an excavation site, it’s time to begin the dig. 

A well-designed solution is always based on extensive research. Research grounds our solutions in the real world and keeps us thinking about the tangible needs of our stakeholders. Research also prevents us from following misleading assumptions and both over-complicating and over-simplifying a problem. 

To design an effective solution to a complex problem, you need to gather input from everyone the problem and potential solution affects. An effective solution works for everyone, and gathering feedback will inform you about which assumptions should be cast aside and which potential solutions should be explored further. 

Research and gathering feedback is not a one time thing. It’s a process that will take time and many trips out into the community. Each potential solution you arrive at will need to be tested thoroughly and shared with the people it will affect. Just when you think you’ve got the perfect solution, you’ll receive feedback that informs you it won’t work. But don’t lose heart! It’s all part of the process and will yield a better, longer-lasting solution in the end.

4. Seek Continuous Improvement

There’s no single magic strategy for solving complex problems. It’s an ongoing process that takes diligent research, time, and ongoing feedback. Each solution you find will need to be tested and adapted to reveal new insights that you can put into practice next time. 

Complex problem solving is a skill you can continue to improve with each new complex problem. The more you test your assumptions, open your mind, put feedback into practice, and test new ideas, the better you will get at it. It’s not about seeking perfection; it’s about seeking continuous improvement. How can you be better next time? 

And the more you seek continuous improvement, the better you will get at making connections. It’s a skill you can continue learning and refining.

Learning How to Explore Complex Problems

Overlap’s suite of courses share tools and strategies that will help you and your team make better decisions .  

Get started with our introductory level courses, or get your team on board for our Exploring Complex Problems course. We’ll dive deeply into the Define and Research phases of the human-centered design cycle and show why staying in the problem space and iterating between these two phases produces a strong foundation for ideation. Learn how to do the homework around the problem space in a human-centered way to better understand context and develop launch points for solution generation. 

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The Right Way to Solve Complex Business Problems

Corey Phelps, a strategy professor at McGill University, says great problem solvers are hard to find. Even seasoned professionals at the highest levels of organizations regularly...

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Corey Phelps, a strategy professor at McGill University, says great problem solvers are hard to find. Even seasoned professionals at the highest levels of organizations regularly fail to identify the real problem and instead jump to exploring solutions. Phelps identifies the common traps and outlines a research-proven method to solve problems effectively. He’s the coauthor of the book, Cracked it! How to solve big problems and sell solutions like top strategy consultants.

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Welcome to the IdeaCast from Harvard Business Review. I’m Curt Nickisch.

Problem-solving is in demand. It’s considered the top skill for success at management consulting firms. And it’s increasingly desired for everyone, not just new MBA’s.

A report from the World Economic Forum predicts that more than one-third of all jobs across all industries will require complex problem-solving as one of their core skills by 2020.

The problem is, we’re often really bad at problem-solving. Our guest today says even the most educated and experienced of senior leaders go about it the wrong way.

COREY PHELPS: I think this is one of the misnomers about problem-solving. There’s this belief that because we do it so frequently – and especially for senior leaders, they have a lot of experience, they solve problems for a living – and as such we would expect them to be quite good at it. And I think what we find is that they’re not. They don’t solve problems well because they fall prey to basically the foibles of being a human being – they fall prey to the cognitive biases and the pitfalls of problem-solving.

CURT NICKISCH: That’s Corey Phelps. He says fixing these foibles is possible and almost straightforward. You can improve your problem-solving skills by following a disciplined method.

Corey Phelps is a strategy professor at McGill University. He’s also the co-author of the book “Cracked It: How to Solve Big Problems and Sell Solutions like Top Strategy C onsultants.” Corey thanks for coming on the show.

COREY PHELPS: Thank you for the opportunity to talk.

CURT NICKISCH: Another probably many, many biases that prevent people from solving big problems well.

COREY PHELPS: Absolutely.

CURT NICKISCH: What are some of the most common, or your favorite stumbling blocks?

COREY PHELPS: Well, one of my favorites is essentially the problem of jumping to solutions or the challenge of jumping to solutions.

CURT NICKISCH: Oh, come on Corey. That’s so much fun.

COREY PHELPS: It is, and it’s very much a result of how our brains have evolved to process information, but it’s my favorite because we all do it. And especially I would say it happens in organizations because in organizations when you layer on these time pressures and you layer on these concerns about efficiency and productivity, it creates enormous, I would say incentive to say “I don’t have time to carefully define and analyze the problem. I got to get a solution. I got to implement it as quick as possible.” And the fundamental bias I think is, is illustrated beautifully by Danny Kahneman in his book “Thinking, Fast and Slow,” is that our minds are essentially hardwired to think fast.

We are able to pay attention to a tiny little bit of information. We can then weave a very coherent story that makes sense to us. And then we can use that story to jump very quickly to a solution that we just know will work. And if we just were able to move from that approach of what Kahneman and cognitive psychologists called “System 1 thinking” to “System 2 thinking” – that is to slow down, be more deliberative, be more structured – we would be able to better understand the problem that we’re trying to solve and be more effective and exhaustive with the tools that we want to use to understand the problem before we actually go into solution-generation mode.

CURT NICKISCH: Complex problems demand different areas of expertise and often as individuals we’re coming to those problems with one of them. And I wonder if that’s often the problem of problem-solving, which is that a manager is approaching it from their own expertise and because of that, they see the problem through a certain way. Is that one of the cognitive biases that stop people from being effective problem solvers?

COREY PHELPS: Yeah. That’s often referred to as the expertise trap. It basically colors and influences what we pay attention to with respect to a particular problem. And it limits us with respect to the tools that we can bring to bear to solve that problem. In the world of psychology, there’s famous psychologist, Abraham Maslow, who is famous for the hierarchy of needs. He’s also famous for something that was a also known as MaSlow’s axiom, Maslow’s law. It’s also called the law of the instrument, and to paraphrase Maslow, he basically said, “Look, I suppose if the only tool that you have in your toolkit is a hammer, everything looks like a nail.”

His point is that if you’re, for example, a finance expert and your toolkit is the toolkit of let’s say, discounted cash flow analysis for valuation, then you’re going to see problems through that very narrow lens. Now, one of the ways out of this, I think to your point is collaboration becomes fundamentally important. And collaboration starts with the recognition that I don’t have all of the tools, all of the knowledge in me to effectively solve this. So I need to recruit people that can actually help me.

CURT NICKISCH: That’s really interesting. I wonder how much the fact that you have solved a problem before it makes you have a bias for that same solution for future problems?

COREY PHELPS: Yeah, that’s a great question. What you’re alluding to is analogical reasoning, and we know that human beings, one of the things that allows us to operate in novel settings is that we can draw on our past experience. And we do so when it comes to problem solving, often times without being conscious or mentally aware of it. We reach into our memory and we ask ourselves a very simple question: “Have I seen a problem like this before?”

And if it looks familiar to me, the tendency then is to say, “Okay, well what worked in solving that problem that I faced before?” And then to say, “Well, if it worked in that setting, then it should work in this setting.” So that’s reasoning by analogy.

Reasoning by analogy has a great upside. It allows human beings to not become overwhelmed by the tremendous novelty that they face in their daily lives. The downside is that if we don’t truly understand it at sort of a deep level, whether or not the two problems are similar or different, then we can make what cognitive psychologists called surface-level analogies.

And we can then say, “Oh, this looks a lot like the problem I faced before, that solution that worked there is going to easily work here.” And we try that solution and it fails and it fails largely because if we dug a little bit deeper, the two problems actually aren’t much alike at all in terms of their underlying causes.

CURT NICKISCH: The starkest example of this, I think, in your book is Ron Johnson who left Apple to become CEO of JC Penney. Can you talk about that a little bit and what that episode for the company says about this?

COREY PHELPS: So yes, its – Ron Johnson had been hired away from Target in the United States to, by Steve Jobs to help create Apple stores. Apple stores are as many people know the most successful physical retailer on the planet measured by, for example, sales per square foot or per square meter. He’s got the golden touch. He’s created this tremendously successful retail format for Apple.

So the day that it was announced that Ron Johnson was going to step into the CEO role at JC Penney, the stock price of JC Penney went up by almost 18 percent. So clearly he was viewed as the savior. Johnson moves very, very quickly. Within a few months, he announces that he has a strategic plan and it basically comes in three parts.

Part number one is he’s going to eliminate discount pricing. JC Penney had been a very aggressive sales promoter. The second piece of it is he’s going to completely change how they organize merchandise. It’s no longer going to be organized by function – so menswear, housewares, those sorts of things. It’s going to be organized by boutique, so there’s going to be a Levi’s boutique, a Martha Stewart Boutique, a Joe Fresh Boutique and so on.

And it would drop the JC P enney name, they would call it JCP. And he rolls this out over the course of about 12 months across the entire chain of over 1100 stores. What this tells us, he’s so confident in his solution, his strategic transformation, that he doesn’t think it’s worth it to test this out on one or two pilot stores.

CURT NICKISCH: Yeah, he was quoted as saying: “At Apple, we didn’t test anything.”

COREY PHELPS: We didn’t test. Yes. What worked at Apple, he assumed would work at JC Penney. And the critical thing that I think he missed is that JC Penney customers are very different from Apple store customers. In fact, JC Penney customers love the discount. They love the thrill of hunting for a deal.

CURT NICKISCH: Which seems so fundamental to business, right? Understanding your customer. It’s just kind of shocking, I guess, to hear the story.

COREY PHELPS: It is shocking and especially when you consider that Ron Johnson had spent his entire career in retail, so this is someone that had faced, had seen, problems in retailers for decades – for over three decades by the time that he got to JC Penney. So you would expect someone with that degree of experience in that industry wouldn’t make that leap of, well, what worked at Apple stores is going to work at JC Penney stores, but in fact that’s exactly what happened.

CURT NICKISCH: In your book, you essentially suggest four steps that you recommend people use. Tell us about the four steps then.

COREY PHELPS: So in the book we describe what we call the “Four S method,” so four stages, each of which starts with the letter “s”. So the first stage is “state the problem.” Stating the problem is fundamentally about defining what the problem is that you are attempting to solve.

CURT NICKISCH: And you probably would say don’t hurry over that first step or the other three are going to be kind of pointless.

COREY PHELPS: Yeah, that’s exactly the point of of laying out the four s’s. There’s a tremendous amount of desire even amongst senior executives to want to get in and fix the problem. In other words, what’s the trouble? What are the symptoms? What would define success? What are the constraints that we would be operating under? Who owns the problem? And then who are the key stakeholders?

Oftentimes that step is skipped over and we go right into, “I’ve got a hypothesis about what I think the solution is and I’m so obsessed with getting this thing fixed quickly, I’m not going to bother to analyze it particularly well or test the validity of my assumptions. I’m going to go right into implementation mode.”

The second step, what we call “structure the problem” is once you have defined the problem, you need to then start to identify what are the potential causes of that problem. So there are different tools that we talked about in the book that you can structure a problem for analysis. Once you’ve structured the problem for analysis and you’ve conducted the analysis that helps you identify what are the underlying causes that are contributing to it, which will then inform the third stage which is generating solutions for the problem and then testing and evaluating those solutions.

CURT NICKISCH: Is the danger that that third step – generating solutions – is the step that people spend the most time on or have the most fun with?

COREY PHELPS: Yeah. The danger is, is that what that’s naturally what people gravitate towards. So we want to skip over the first two, state and structure.

CURT NICKISCH: As soon as you said it, I was like, “let’s talk about that more.”

COREY PHELPS: Yeah. And we want to jump right into solutioning because people love to talk about their ideas that are going to fix the problem. And that’s actually a useful way to frame a discussion about solutions – we could, or we might do this – because it opens up possibilities for experimentation.

And the problem is that when we often talk about what we could do, we have very little understanding of what the problem is that we’re trying to solve and what are the underlying causes of that problem. Because as you said, solution generation is fun. Look, the classic example is brainstorming. Let’s get a bunch of people in a room and let’s talk about the ideas on how to fix this thing. And again, be deliberate, be disciplined. Do those first stages, the first two stages – state and structure – before you get into the solution generation phase.

CURT NICKISCH: Yeah. The other thing that often happens there is just the lack of awareness of just the cost of the different solutions – how much time, or what they would actually take to do.

COREY PHELPS: Yeah, and again, I’ll go back to that example I used of brainstorming where it’s fun to get a group of people together and talk about our ideas and how to fix the problem. There’s a couple challenges of that. One is what often happens when we do that is we tend to censor the solutions that we come up with. In other words, we ask ourselves, “if I say this idea, people are gonna, think I’m crazy, or people going to say: that’s stupid, that’ll never work, we can’t do that in our organization. It’s going to be too expensive, it’s going to take too much time. We don’t have the resources to do it.”

So brainstorming downside is we we self-sensor, so that’s where you need to have deep insight into your organization in terms of A. what’s going to be feasible, B. what’s going to be desirable on the part of the people that actually have the problem, who you’re trying to solve the problem for and C. from a business standpoint, is it going to be financially attractive for us?

So applying again a set of disciplined criteria that help you choose amongst those ideas for potential solutions. Then the last stage of the process which is selling – because it’s rare in any organization that someone or the group of people that come up with the solution actually have the power and the resources to implement it, so that means they’re going to have to persuade other people to buy into it and want to help.

CURT NICKISCH: Design thinking is another really different method essentially for solving problems or coming up with solutions that just aren’t arrived at through usual problem-solving or usual decision-making processes. I’m just wondering how design thinking comes to play when you’re also outlining these, you know, disciplined methods for stating and solving problems.

COREY PHELPS: For us it’s about choosing the right approach. You know what the potential causes of a problem are. You just don’t know which ones are operating in the particular problem you’re trying to solve. And what that means is that you’ve got a theory – and this is largely the world of strategy consultants – strategy consultants have theories. They have, if you hear them speak, deep understanding of different types of organizational problems, and what they bring is an analytic tool kit that says, “first we’re going to identify all the possible problems, all the possible causes I should say, of this problem. We’re going to figure out which ones are operating and we’re going to use that to come up with a solution.” Then you’ve got problems that you have no idea what the causes are. You’re in a world of unknown unknowns or unk-unks as the operations management people call them.

CURT NICKISCH: That’s terrible.

COREY PHELPS: In other words, you don’t have a theory. So the question is, how do you begin? Well, this is where design thinking can be quite valuable. Design thinking says: first off, let’s find out who are the human beings, the people that are actually experiencing this problem, and let’s go out and let’s talk to them. Let’s observe them. Let’s immerse ourselves in their experience and let’s start to develop an understanding of the causes of the problem from their perspective.

So rather than go into it and say, “I have a theory,” let’s go the design thinking route and let’s actually based upon interactions with users or customers, let’s actually develop a theory. And then we’ll use our new understanding or new insight into the causes of the problem to move into the solution generation phase.

CURT NICKISCH: Problem-solving – we know that that’s something that employers look for when they’re recruiting people. It is one of those phrases that, you know, I’m sure somebody out there has, has the title at a company Chief Problem Solver instead of CEO, right? So, it’s almost one of those phrases that so over used it can lose its meaning.

And if you are being hired or you’re trying to make a case for being on a team that’s tackling a problem, how do you make a compelling case that you are a good problem solver? How can you actually show it?

COREY PHELPS: It’s a great question and then I have two answers to this question. So one is, look at the end of the day, the proof is in the pudding. In other words, can you point to successful solutions that you’ve come up with – solutions that have actually been effective in solving a problem? So that’s one.

The second thing is can you actually articulate how you approach problem-solving? In other words, do you follow a method or are you reinventing the wheel every time you solve a problem? Is it an ad hoc approach? And I think this issue really comes to a head when it comes to the world of strategy consulting firms when they recruit. For example, Mckinsey, you’ve got the Mckinsey problem-solving test, which is again, a test that’s actually trying to elicit the extent to which people are good applicants are good at solving problems

And then you’ve got the case interview. And in the case interview, what they’re looking at is do you have a mastery over certain tools. But what they’re really looking at is, are you actually following a logical process to solve this problem? Because again, what they’re interested in is finding- to your point – people that are going to be good at solving complex organizational problems. So they’re trying to get some evidence that they can demonstrate that they’re good at it and some evidence that they follow a deliberate process.

CURT NICKISCH: So even if you’re not interviewing at a consulting firm, that’s a good approach, to show your thinking, show your process, show the questions you ask?

COREY PHELPS: Yeah, and to your point earlier, at least if we look at what recruiters of MBA students are saying these days, they’re saying, for example, according to the FT’s recent survey, they’re saying that we want people with really good problem solving skills, and by the same token, we find that that’s a skill that’s difficult for us to recruit for. And that reinforces our interest in this area because the fundamental idea for the book is to give people a method. We’re trying to equip not just MBA students but everybody that’s going to face complex problems with a toolkit to solve them better.

CURT NICKISCH: Corey, this has been really great. Thank you.

COREY PHELPS: Thanks for the opportunity. I appreciate it.

CURT NICKISCH: That’s Corey Phelps. He teaches strategy at McGill University, and he co-wrote the book “Cracked It: How to Solve Big Problems and Sell Solutions Like Top Strategy Consultants.”

This episode was produced by Mary Dooe. We got technical help from Rob Eckhardt. Adam Buchholz is our audio product manager.

Thanks for listening to the HBR IdeaCast. I’m Curt Nickisch.

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Complex Problem Solving

Complex Problem Solving

Find solutions to real-world problems

Complex Problem Solving is the skill of applying a method to a problem, often not seen before, to obtain a satisfactory solution. It requires a creative combination of knowledge and strategies to arrive at an answer. Rapid technological change, the increasingly global exchange of ideas, and the proliferation of easy-to-access information – some of which is decidedly unreliable – all contribute greater complexity to the problems that they will need to solve.

Excelling in Complex Problem Solving as a Job Skill means:

  • Engaged in ‘big picture’ thinking
  • Flexible & adaptable to change
  • Highly detail-oriented
  • Someone who sees patterns
  • Someone who works efficiently

Others see you:

  • Demonstrate self-reliance
  • Achieve your dreams and ambitions
  • Capable of higher-order thinking (not just memorizing facts, but demonstrating the ability to deeply understand, apply, analyze, and evaluate information)
  • Achieve increased status & responsibility at school or work
  • Create solutions that balance the facts, but with new insight

“ 4.9 Complex Problem Solving ” from Working in Play: Planning for a Career in the Recreation and Leisure Industry in Canada  by Linda Whitehead, BA, M Ed, MBA is licensed under a  Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

The skill of applying a method to a problem, often not seen before, to obtain a satisfactory solution; it requires a creative combination of knowledge and strategies to arrive at an answer.

Fanshawe SOAR Copyright © 2023 by Kristen Cavanagh is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

35 problem-solving techniques and methods for solving complex problems

Problem solving workshop

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All teams and organizations encounter challenges as they grow. There are problems that might occur for teams when it comes to miscommunication or resolving business-critical issues . You may face challenges around growth , design , user engagement, and even team culture and happiness. In short, problem-solving techniques should be part of every team’s skillset.

Problem-solving methods are primarily designed to help a group or team through a process of first identifying problems and challenges , ideating possible solutions , and then evaluating the most suitable .

Finding effective solutions to complex problems isn’t easy, but by using the right process and techniques, you can help your team be more efficient in the process.

So how do you develop strategies that are engaging, and empower your team to solve problems effectively?

In this blog post, we share a series of problem-solving tools you can use in your next workshop or team meeting. You’ll also find some tips for facilitating the process and how to enable others to solve complex problems.

Let’s get started! 

How do you identify problems?

How do you identify the right solution.

  • Tips for more effective problem-solving

Complete problem-solving methods

  • Problem-solving techniques to identify and analyze problems
  • Problem-solving techniques for developing solutions

Problem-solving warm-up activities

Closing activities for a problem-solving process.

Before you can move towards finding the right solution for a given problem, you first need to identify and define the problem you wish to solve. 

Here, you want to clearly articulate what the problem is and allow your group to do the same. Remember that everyone in a group is likely to have differing perspectives and alignment is necessary in order to help the group move forward. 

Identifying a problem accurately also requires that all members of a group are able to contribute their views in an open and safe manner. It can be scary for people to stand up and contribute, especially if the problems or challenges are emotive or personal in nature. Be sure to try and create a psychologically safe space for these kinds of discussions.

Remember that problem analysis and further discussion are also important. Not taking the time to fully analyze and discuss a challenge can result in the development of solutions that are not fit for purpose or do not address the underlying issue.

Successfully identifying and then analyzing a problem means facilitating a group through activities designed to help them clearly and honestly articulate their thoughts and produce usable insight.

With this data, you might then produce a problem statement that clearly describes the problem you wish to be addressed and also state the goal of any process you undertake to tackle this issue.  

Finding solutions is the end goal of any process. Complex organizational challenges can only be solved with an appropriate solution but discovering them requires using the right problem-solving tool.

After you’ve explored a problem and discussed ideas, you need to help a team discuss and choose the right solution. Consensus tools and methods such as those below help a group explore possible solutions before then voting for the best. They’re a great way to tap into the collective intelligence of the group for great results!

Remember that the process is often iterative. Great problem solvers often roadtest a viable solution in a measured way to see what works too. While you might not get the right solution on your first try, the methods below help teams land on the most likely to succeed solution while also holding space for improvement.

Every effective problem solving process begins with an agenda . A well-structured workshop is one of the best methods for successfully guiding a group from exploring a problem to implementing a solution.

In SessionLab, it’s easy to go from an idea to a complete agenda . Start by dragging and dropping your core problem solving activities into place . Add timings, breaks and necessary materials before sharing your agenda with your colleagues.

The resulting agenda will be your guide to an effective and productive problem solving session that will also help you stay organized on the day!

what is a complex problem solver

Tips for more effective problem solving

Problem-solving activities are only one part of the puzzle. While a great method can help unlock your team’s ability to solve problems, without a thoughtful approach and strong facilitation the solutions may not be fit for purpose.

Let’s take a look at some problem-solving tips you can apply to any process to help it be a success!

Clearly define the problem

Jumping straight to solutions can be tempting, though without first clearly articulating a problem, the solution might not be the right one. Many of the problem-solving activities below include sections where the problem is explored and clearly defined before moving on.

This is a vital part of the problem-solving process and taking the time to fully define an issue can save time and effort later. A clear definition helps identify irrelevant information and it also ensures that your team sets off on the right track.

Don’t jump to conclusions

It’s easy for groups to exhibit cognitive bias or have preconceived ideas about both problems and potential solutions. Be sure to back up any problem statements or potential solutions with facts, research, and adequate forethought.

The best techniques ask participants to be methodical and challenge preconceived notions. Make sure you give the group enough time and space to collect relevant information and consider the problem in a new way. By approaching the process with a clear, rational mindset, you’ll often find that better solutions are more forthcoming.  

Try different approaches  

Problems come in all shapes and sizes and so too should the methods you use to solve them. If you find that one approach isn’t yielding results and your team isn’t finding different solutions, try mixing it up. You’ll be surprised at how using a new creative activity can unblock your team and generate great solutions.

Don’t take it personally 

Depending on the nature of your team or organizational problems, it’s easy for conversations to get heated. While it’s good for participants to be engaged in the discussions, ensure that emotions don’t run too high and that blame isn’t thrown around while finding solutions.

You’re all in it together, and even if your team or area is seeing problems, that isn’t necessarily a disparagement of you personally. Using facilitation skills to manage group dynamics is one effective method of helping conversations be more constructive.

Get the right people in the room

Your problem-solving method is often only as effective as the group using it. Getting the right people on the job and managing the number of people present is important too!

If the group is too small, you may not get enough different perspectives to effectively solve a problem. If the group is too large, you can go round and round during the ideation stages.

Creating the right group makeup is also important in ensuring you have the necessary expertise and skillset to both identify and follow up on potential solutions. Carefully consider who to include at each stage to help ensure your problem-solving method is followed and positioned for success.

Document everything

The best solutions can take refinement, iteration, and reflection to come out. Get into a habit of documenting your process in order to keep all the learnings from the session and to allow ideas to mature and develop. Many of the methods below involve the creation of documents or shared resources. Be sure to keep and share these so everyone can benefit from the work done!

Bring a facilitator 

Facilitation is all about making group processes easier. With a subject as potentially emotive and important as problem-solving, having an impartial third party in the form of a facilitator can make all the difference in finding great solutions and keeping the process moving. Consider bringing a facilitator to your problem-solving session to get better results and generate meaningful solutions!

Develop your problem-solving skills

It takes time and practice to be an effective problem solver. While some roles or participants might more naturally gravitate towards problem-solving, it can take development and planning to help everyone create better solutions.

You might develop a training program, run a problem-solving workshop or simply ask your team to practice using the techniques below. Check out our post on problem-solving skills to see how you and your group can develop the right mental process and be more resilient to issues too!

Design a great agenda

Workshops are a great format for solving problems. With the right approach, you can focus a group and help them find the solutions to their own problems. But designing a process can be time-consuming and finding the right activities can be difficult.

Check out our workshop planning guide to level-up your agenda design and start running more effective workshops. Need inspiration? Check out templates designed by expert facilitators to help you kickstart your process!

In this section, we’ll look at in-depth problem-solving methods that provide a complete end-to-end process for developing effective solutions. These will help guide your team from the discovery and definition of a problem through to delivering the right solution.

If you’re looking for an all-encompassing method or problem-solving model, these processes are a great place to start. They’ll ask your team to challenge preconceived ideas and adopt a mindset for solving problems more effectively.

  • Six Thinking Hats
  • Lightning Decision Jam
  • Problem Definition Process
  • Discovery & Action Dialogue
Design Sprint 2.0
  • Open Space Technology

1. Six Thinking Hats

Individual approaches to solving a problem can be very different based on what team or role an individual holds. It can be easy for existing biases or perspectives to find their way into the mix, or for internal politics to direct a conversation.

Six Thinking Hats is a classic method for identifying the problems that need to be solved and enables your team to consider them from different angles, whether that is by focusing on facts and data, creative solutions, or by considering why a particular solution might not work.

Like all problem-solving frameworks, Six Thinking Hats is effective at helping teams remove roadblocks from a conversation or discussion and come to terms with all the aspects necessary to solve complex problems.

2. Lightning Decision Jam

Featured courtesy of Jonathan Courtney of AJ&Smart Berlin, Lightning Decision Jam is one of those strategies that should be in every facilitation toolbox. Exploring problems and finding solutions is often creative in nature, though as with any creative process, there is the potential to lose focus and get lost.

Unstructured discussions might get you there in the end, but it’s much more effective to use a method that creates a clear process and team focus.

In Lightning Decision Jam, participants are invited to begin by writing challenges, concerns, or mistakes on post-its without discussing them before then being invited by the moderator to present them to the group.

From there, the team vote on which problems to solve and are guided through steps that will allow them to reframe those problems, create solutions and then decide what to execute on. 

By deciding the problems that need to be solved as a team before moving on, this group process is great for ensuring the whole team is aligned and can take ownership over the next stages. 

Lightning Decision Jam (LDJ)   #action   #decision making   #problem solving   #issue analysis   #innovation   #design   #remote-friendly   The problem with anything that requires creative thinking is that it’s easy to get lost—lose focus and fall into the trap of having useless, open-ended, unstructured discussions. Here’s the most effective solution I’ve found: Replace all open, unstructured discussion with a clear process. What to use this exercise for: Anything which requires a group of people to make decisions, solve problems or discuss challenges. It’s always good to frame an LDJ session with a broad topic, here are some examples: The conversion flow of our checkout Our internal design process How we organise events Keeping up with our competition Improving sales flow

3. Problem Definition Process

While problems can be complex, the problem-solving methods you use to identify and solve those problems can often be simple in design. 

By taking the time to truly identify and define a problem before asking the group to reframe the challenge as an opportunity, this method is a great way to enable change.

Begin by identifying a focus question and exploring the ways in which it manifests before splitting into five teams who will each consider the problem using a different method: escape, reversal, exaggeration, distortion or wishful. Teams develop a problem objective and create ideas in line with their method before then feeding them back to the group.

This method is great for enabling in-depth discussions while also creating space for finding creative solutions too!

Problem Definition   #problem solving   #idea generation   #creativity   #online   #remote-friendly   A problem solving technique to define a problem, challenge or opportunity and to generate ideas.

4. The 5 Whys 

Sometimes, a group needs to go further with their strategies and analyze the root cause at the heart of organizational issues. An RCA or root cause analysis is the process of identifying what is at the heart of business problems or recurring challenges. 

The 5 Whys is a simple and effective method of helping a group go find the root cause of any problem or challenge and conduct analysis that will deliver results. 

By beginning with the creation of a problem statement and going through five stages to refine it, The 5 Whys provides everything you need to truly discover the cause of an issue.

The 5 Whys   #hyperisland   #innovation   This simple and powerful method is useful for getting to the core of a problem or challenge. As the title suggests, the group defines a problems, then asks the question “why” five times, often using the resulting explanation as a starting point for creative problem solving.

5. World Cafe

World Cafe is a simple but powerful facilitation technique to help bigger groups to focus their energy and attention on solving complex problems.

World Cafe enables this approach by creating a relaxed atmosphere where participants are able to self-organize and explore topics relevant and important to them which are themed around a central problem-solving purpose. Create the right atmosphere by modeling your space after a cafe and after guiding the group through the method, let them take the lead!

Making problem-solving a part of your organization’s culture in the long term can be a difficult undertaking. More approachable formats like World Cafe can be especially effective in bringing people unfamiliar with workshops into the fold. 

World Cafe   #hyperisland   #innovation   #issue analysis   World Café is a simple yet powerful method, originated by Juanita Brown, for enabling meaningful conversations driven completely by participants and the topics that are relevant and important to them. Facilitators create a cafe-style space and provide simple guidelines. Participants then self-organize and explore a set of relevant topics or questions for conversation.

6. Discovery & Action Dialogue (DAD)

One of the best approaches is to create a safe space for a group to share and discover practices and behaviors that can help them find their own solutions.

With DAD, you can help a group choose which problems they wish to solve and which approaches they will take to do so. It’s great at helping remove resistance to change and can help get buy-in at every level too!

This process of enabling frontline ownership is great in ensuring follow-through and is one of the methods you will want in your toolbox as a facilitator.

Discovery & Action Dialogue (DAD)   #idea generation   #liberating structures   #action   #issue analysis   #remote-friendly   DADs make it easy for a group or community to discover practices and behaviors that enable some individuals (without access to special resources and facing the same constraints) to find better solutions than their peers to common problems. These are called positive deviant (PD) behaviors and practices. DADs make it possible for people in the group, unit, or community to discover by themselves these PD practices. DADs also create favorable conditions for stimulating participants’ creativity in spaces where they can feel safe to invent new and more effective practices. Resistance to change evaporates as participants are unleashed to choose freely which practices they will adopt or try and which problems they will tackle. DADs make it possible to achieve frontline ownership of solutions.

7. Design Sprint 2.0

Want to see how a team can solve big problems and move forward with prototyping and testing solutions in a few days? The Design Sprint 2.0 template from Jake Knapp, author of Sprint, is a complete agenda for a with proven results.

Developing the right agenda can involve difficult but necessary planning. Ensuring all the correct steps are followed can also be stressful or time-consuming depending on your level of experience.

Use this complete 4-day workshop template if you are finding there is no obvious solution to your challenge and want to focus your team around a specific problem that might require a shortcut to launching a minimum viable product or waiting for the organization-wide implementation of a solution.

8. Open space technology

Open space technology- developed by Harrison Owen – creates a space where large groups are invited to take ownership of their problem solving and lead individual sessions. Open space technology is a great format when you have a great deal of expertise and insight in the room and want to allow for different takes and approaches on a particular theme or problem you need to be solved.

Start by bringing your participants together to align around a central theme and focus their efforts. Explain the ground rules to help guide the problem-solving process and then invite members to identify any issue connecting to the central theme that they are interested in and are prepared to take responsibility for.

Once participants have decided on their approach to the core theme, they write their issue on a piece of paper, announce it to the group, pick a session time and place, and post the paper on the wall. As the wall fills up with sessions, the group is then invited to join the sessions that interest them the most and which they can contribute to, then you’re ready to begin!

Everyone joins the problem-solving group they’ve signed up to, record the discussion and if appropriate, findings can then be shared with the rest of the group afterward.

Open Space Technology   #action plan   #idea generation   #problem solving   #issue analysis   #large group   #online   #remote-friendly   Open Space is a methodology for large groups to create their agenda discerning important topics for discussion, suitable for conferences, community gatherings and whole system facilitation

Techniques to identify and analyze problems

Using a problem-solving method to help a team identify and analyze a problem can be a quick and effective addition to any workshop or meeting.

While further actions are always necessary, you can generate momentum and alignment easily, and these activities are a great place to get started.

We’ve put together this list of techniques to help you and your team with problem identification, analysis, and discussion that sets the foundation for developing effective solutions.

Let’s take a look!

  • The Creativity Dice
  • Fishbone Analysis
  • Problem Tree
  • SWOT Analysis
  • Agreement-Certainty Matrix
  • The Journalistic Six
  • LEGO Challenge
  • What, So What, Now What?
  • Journalists

Individual and group perspectives are incredibly important, but what happens if people are set in their minds and need a change of perspective in order to approach a problem more effectively?

Flip It is a method we love because it is both simple to understand and run, and allows groups to understand how their perspectives and biases are formed. 

Participants in Flip It are first invited to consider concerns, issues, or problems from a perspective of fear and write them on a flip chart. Then, the group is asked to consider those same issues from a perspective of hope and flip their understanding.  

No problem and solution is free from existing bias and by changing perspectives with Flip It, you can then develop a problem solving model quickly and effectively.

Flip It!   #gamestorming   #problem solving   #action   Often, a change in a problem or situation comes simply from a change in our perspectives. Flip It! is a quick game designed to show players that perspectives are made, not born.

10. The Creativity Dice

One of the most useful problem solving skills you can teach your team is of approaching challenges with creativity, flexibility, and openness. Games like The Creativity Dice allow teams to overcome the potential hurdle of too much linear thinking and approach the process with a sense of fun and speed. 

In The Creativity Dice, participants are organized around a topic and roll a dice to determine what they will work on for a period of 3 minutes at a time. They might roll a 3 and work on investigating factual information on the chosen topic. They might roll a 1 and work on identifying the specific goals, standards, or criteria for the session.

Encouraging rapid work and iteration while asking participants to be flexible are great skills to cultivate. Having a stage for idea incubation in this game is also important. Moments of pause can help ensure the ideas that are put forward are the most suitable. 

The Creativity Dice   #creativity   #problem solving   #thiagi   #issue analysis   Too much linear thinking is hazardous to creative problem solving. To be creative, you should approach the problem (or the opportunity) from different points of view. You should leave a thought hanging in mid-air and move to another. This skipping around prevents premature closure and lets your brain incubate one line of thought while you consciously pursue another.

11. Fishbone Analysis

Organizational or team challenges are rarely simple, and it’s important to remember that one problem can be an indication of something that goes deeper and may require further consideration to be solved.

Fishbone Analysis helps groups to dig deeper and understand the origins of a problem. It’s a great example of a root cause analysis method that is simple for everyone on a team to get their head around. 

Participants in this activity are asked to annotate a diagram of a fish, first adding the problem or issue to be worked on at the head of a fish before then brainstorming the root causes of the problem and adding them as bones on the fish. 

Using abstractions such as a diagram of a fish can really help a team break out of their regular thinking and develop a creative approach.

Fishbone Analysis   #problem solving   ##root cause analysis   #decision making   #online facilitation   A process to help identify and understand the origins of problems, issues or observations.

12. Problem Tree 

Encouraging visual thinking can be an essential part of many strategies. By simply reframing and clarifying problems, a group can move towards developing a problem solving model that works for them. 

In Problem Tree, groups are asked to first brainstorm a list of problems – these can be design problems, team problems or larger business problems – and then organize them into a hierarchy. The hierarchy could be from most important to least important or abstract to practical, though the key thing with problem solving games that involve this aspect is that your group has some way of managing and sorting all the issues that are raised.

Once you have a list of problems that need to be solved and have organized them accordingly, you’re then well-positioned for the next problem solving steps.

Problem tree   #define intentions   #create   #design   #issue analysis   A problem tree is a tool to clarify the hierarchy of problems addressed by the team within a design project; it represents high level problems or related sublevel problems.

13. SWOT Analysis

Chances are you’ve heard of the SWOT Analysis before. This problem-solving method focuses on identifying strengths, weaknesses, opportunities, and threats is a tried and tested method for both individuals and teams.

Start by creating a desired end state or outcome and bare this in mind – any process solving model is made more effective by knowing what you are moving towards. Create a quadrant made up of the four categories of a SWOT analysis and ask participants to generate ideas based on each of those quadrants.

Once you have those ideas assembled in their quadrants, cluster them together based on their affinity with other ideas. These clusters are then used to facilitate group conversations and move things forward. 

SWOT analysis   #gamestorming   #problem solving   #action   #meeting facilitation   The SWOT Analysis is a long-standing technique of looking at what we have, with respect to the desired end state, as well as what we could improve on. It gives us an opportunity to gauge approaching opportunities and dangers, and assess the seriousness of the conditions that affect our future. When we understand those conditions, we can influence what comes next.

14. Agreement-Certainty Matrix

Not every problem-solving approach is right for every challenge, and deciding on the right method for the challenge at hand is a key part of being an effective team.

The Agreement Certainty matrix helps teams align on the nature of the challenges facing them. By sorting problems from simple to chaotic, your team can understand what methods are suitable for each problem and what they can do to ensure effective results. 

If you are already using Liberating Structures techniques as part of your problem-solving strategy, the Agreement-Certainty Matrix can be an invaluable addition to your process. We’ve found it particularly if you are having issues with recurring problems in your organization and want to go deeper in understanding the root cause. 

Agreement-Certainty Matrix   #issue analysis   #liberating structures   #problem solving   You can help individuals or groups avoid the frequent mistake of trying to solve a problem with methods that are not adapted to the nature of their challenge. The combination of two questions makes it possible to easily sort challenges into four categories: simple, complicated, complex , and chaotic .  A problem is simple when it can be solved reliably with practices that are easy to duplicate.  It is complicated when experts are required to devise a sophisticated solution that will yield the desired results predictably.  A problem is complex when there are several valid ways to proceed but outcomes are not predictable in detail.  Chaotic is when the context is too turbulent to identify a path forward.  A loose analogy may be used to describe these differences: simple is like following a recipe, complicated like sending a rocket to the moon, complex like raising a child, and chaotic is like the game “Pin the Tail on the Donkey.”  The Liberating Structures Matching Matrix in Chapter 5 can be used as the first step to clarify the nature of a challenge and avoid the mismatches between problems and solutions that are frequently at the root of chronic, recurring problems.

Organizing and charting a team’s progress can be important in ensuring its success. SQUID (Sequential Question and Insight Diagram) is a great model that allows a team to effectively switch between giving questions and answers and develop the skills they need to stay on track throughout the process. 

Begin with two different colored sticky notes – one for questions and one for answers – and with your central topic (the head of the squid) on the board. Ask the group to first come up with a series of questions connected to their best guess of how to approach the topic. Ask the group to come up with answers to those questions, fix them to the board and connect them with a line. After some discussion, go back to question mode by responding to the generated answers or other points on the board.

It’s rewarding to see a diagram grow throughout the exercise, and a completed SQUID can provide a visual resource for future effort and as an example for other teams.

SQUID   #gamestorming   #project planning   #issue analysis   #problem solving   When exploring an information space, it’s important for a group to know where they are at any given time. By using SQUID, a group charts out the territory as they go and can navigate accordingly. SQUID stands for Sequential Question and Insight Diagram.

16. Speed Boat

To continue with our nautical theme, Speed Boat is a short and sweet activity that can help a team quickly identify what employees, clients or service users might have a problem with and analyze what might be standing in the way of achieving a solution.

Methods that allow for a group to make observations, have insights and obtain those eureka moments quickly are invaluable when trying to solve complex problems.

In Speed Boat, the approach is to first consider what anchors and challenges might be holding an organization (or boat) back. Bonus points if you are able to identify any sharks in the water and develop ideas that can also deal with competitors!   

Speed Boat   #gamestorming   #problem solving   #action   Speedboat is a short and sweet way to identify what your employees or clients don’t like about your product/service or what’s standing in the way of a desired goal.

17. The Journalistic Six

Some of the most effective ways of solving problems is by encouraging teams to be more inclusive and diverse in their thinking.

Based on the six key questions journalism students are taught to answer in articles and news stories, The Journalistic Six helps create teams to see the whole picture. By using who, what, when, where, why, and how to facilitate the conversation and encourage creative thinking, your team can make sure that the problem identification and problem analysis stages of the are covered exhaustively and thoughtfully. Reporter’s notebook and dictaphone optional.

The Journalistic Six – Who What When Where Why How   #idea generation   #issue analysis   #problem solving   #online   #creative thinking   #remote-friendly   A questioning method for generating, explaining, investigating ideas.

18. LEGO Challenge

Now for an activity that is a little out of the (toy) box. LEGO Serious Play is a facilitation methodology that can be used to improve creative thinking and problem-solving skills. 

The LEGO Challenge includes giving each member of the team an assignment that is hidden from the rest of the group while they create a structure without speaking.

What the LEGO challenge brings to the table is a fun working example of working with stakeholders who might not be on the same page to solve problems. Also, it’s LEGO! Who doesn’t love LEGO! 

LEGO Challenge   #hyperisland   #team   A team-building activity in which groups must work together to build a structure out of LEGO, but each individual has a secret “assignment” which makes the collaborative process more challenging. It emphasizes group communication, leadership dynamics, conflict, cooperation, patience and problem solving strategy.

19. What, So What, Now What?

If not carefully managed, the problem identification and problem analysis stages of the problem-solving process can actually create more problems and misunderstandings.

The What, So What, Now What? problem-solving activity is designed to help collect insights and move forward while also eliminating the possibility of disagreement when it comes to identifying, clarifying, and analyzing organizational or work problems. 

Facilitation is all about bringing groups together so that might work on a shared goal and the best problem-solving strategies ensure that teams are aligned in purpose, if not initially in opinion or insight.

Throughout the three steps of this game, you give everyone on a team to reflect on a problem by asking what happened, why it is important, and what actions should then be taken. 

This can be a great activity for bringing our individual perceptions about a problem or challenge and contextualizing it in a larger group setting. This is one of the most important problem-solving skills you can bring to your organization.

W³ – What, So What, Now What?   #issue analysis   #innovation   #liberating structures   You can help groups reflect on a shared experience in a way that builds understanding and spurs coordinated action while avoiding unproductive conflict. It is possible for every voice to be heard while simultaneously sifting for insights and shaping new direction. Progressing in stages makes this practical—from collecting facts about What Happened to making sense of these facts with So What and finally to what actions logically follow with Now What . The shared progression eliminates most of the misunderstandings that otherwise fuel disagreements about what to do. Voila!

20. Journalists  

Problem analysis can be one of the most important and decisive stages of all problem-solving tools. Sometimes, a team can become bogged down in the details and are unable to move forward.

Journalists is an activity that can avoid a group from getting stuck in the problem identification or problem analysis stages of the process.

In Journalists, the group is invited to draft the front page of a fictional newspaper and figure out what stories deserve to be on the cover and what headlines those stories will have. By reframing how your problems and challenges are approached, you can help a team move productively through the process and be better prepared for the steps to follow.

Journalists   #vision   #big picture   #issue analysis   #remote-friendly   This is an exercise to use when the group gets stuck in details and struggles to see the big picture. Also good for defining a vision.

Problem-solving techniques for developing solutions 

The success of any problem-solving process can be measured by the solutions it produces. After you’ve defined the issue, explored existing ideas, and ideated, it’s time to narrow down to the correct solution.

Use these problem-solving techniques when you want to help your team find consensus, compare possible solutions, and move towards taking action on a particular problem.

  • Improved Solutions
  • Four-Step Sketch
  • 15% Solutions
  • How-Now-Wow matrix
  • Impact Effort Matrix

21. Mindspin  

Brainstorming is part of the bread and butter of the problem-solving process and all problem-solving strategies benefit from getting ideas out and challenging a team to generate solutions quickly. 

With Mindspin, participants are encouraged not only to generate ideas but to do so under time constraints and by slamming down cards and passing them on. By doing multiple rounds, your team can begin with a free generation of possible solutions before moving on to developing those solutions and encouraging further ideation. 

This is one of our favorite problem-solving activities and can be great for keeping the energy up throughout the workshop. Remember the importance of helping people become engaged in the process – energizing problem-solving techniques like Mindspin can help ensure your team stays engaged and happy, even when the problems they’re coming together to solve are complex. 

MindSpin   #teampedia   #idea generation   #problem solving   #action   A fast and loud method to enhance brainstorming within a team. Since this activity has more than round ideas that are repetitive can be ruled out leaving more creative and innovative answers to the challenge.

22. Improved Solutions

After a team has successfully identified a problem and come up with a few solutions, it can be tempting to call the work of the problem-solving process complete. That said, the first solution is not necessarily the best, and by including a further review and reflection activity into your problem-solving model, you can ensure your group reaches the best possible result. 

One of a number of problem-solving games from Thiagi Group, Improved Solutions helps you go the extra mile and develop suggested solutions with close consideration and peer review. By supporting the discussion of several problems at once and by shifting team roles throughout, this problem-solving technique is a dynamic way of finding the best solution. 

Improved Solutions   #creativity   #thiagi   #problem solving   #action   #team   You can improve any solution by objectively reviewing its strengths and weaknesses and making suitable adjustments. In this creativity framegame, you improve the solutions to several problems. To maintain objective detachment, you deal with a different problem during each of six rounds and assume different roles (problem owner, consultant, basher, booster, enhancer, and evaluator) during each round. At the conclusion of the activity, each player ends up with two solutions to her problem.

23. Four Step Sketch

Creative thinking and visual ideation does not need to be confined to the opening stages of your problem-solving strategies. Exercises that include sketching and prototyping on paper can be effective at the solution finding and development stage of the process, and can be great for keeping a team engaged. 

By going from simple notes to a crazy 8s round that involves rapidly sketching 8 variations on their ideas before then producing a final solution sketch, the group is able to iterate quickly and visually. Problem-solving techniques like Four-Step Sketch are great if you have a group of different thinkers and want to change things up from a more textual or discussion-based approach.

Four-Step Sketch   #design sprint   #innovation   #idea generation   #remote-friendly   The four-step sketch is an exercise that helps people to create well-formed concepts through a structured process that includes: Review key information Start design work on paper,  Consider multiple variations , Create a detailed solution . This exercise is preceded by a set of other activities allowing the group to clarify the challenge they want to solve. See how the Four Step Sketch exercise fits into a Design Sprint

24. 15% Solutions

Some problems are simpler than others and with the right problem-solving activities, you can empower people to take immediate actions that can help create organizational change. 

Part of the liberating structures toolkit, 15% solutions is a problem-solving technique that focuses on finding and implementing solutions quickly. A process of iterating and making small changes quickly can help generate momentum and an appetite for solving complex problems.

Problem-solving strategies can live and die on whether people are onboard. Getting some quick wins is a great way of getting people behind the process.   

It can be extremely empowering for a team to realize that problem-solving techniques can be deployed quickly and easily and delineate between things they can positively impact and those things they cannot change. 

15% Solutions   #action   #liberating structures   #remote-friendly   You can reveal the actions, however small, that everyone can do immediately. At a minimum, these will create momentum, and that may make a BIG difference.  15% Solutions show that there is no reason to wait around, feel powerless, or fearful. They help people pick it up a level. They get individuals and the group to focus on what is within their discretion instead of what they cannot change.  With a very simple question, you can flip the conversation to what can be done and find solutions to big problems that are often distributed widely in places not known in advance. Shifting a few grains of sand may trigger a landslide and change the whole landscape.

25. How-Now-Wow Matrix

The problem-solving process is often creative, as complex problems usually require a change of thinking and creative response in order to find the best solutions. While it’s common for the first stages to encourage creative thinking, groups can often gravitate to familiar solutions when it comes to the end of the process. 

When selecting solutions, you don’t want to lose your creative energy! The How-Now-Wow Matrix from Gamestorming is a great problem-solving activity that enables a group to stay creative and think out of the box when it comes to selecting the right solution for a given problem.

Problem-solving techniques that encourage creative thinking and the ideation and selection of new solutions can be the most effective in organisational change. Give the How-Now-Wow Matrix a go, and not just for how pleasant it is to say out loud. 

How-Now-Wow Matrix   #gamestorming   #idea generation   #remote-friendly   When people want to develop new ideas, they most often think out of the box in the brainstorming or divergent phase. However, when it comes to convergence, people often end up picking ideas that are most familiar to them. This is called a ‘creative paradox’ or a ‘creadox’. The How-Now-Wow matrix is an idea selection tool that breaks the creadox by forcing people to weigh each idea on 2 parameters.

26. Impact and Effort Matrix

All problem-solving techniques hope to not only find solutions to a given problem or challenge but to find the best solution. When it comes to finding a solution, groups are invited to put on their decision-making hats and really think about how a proposed idea would work in practice. 

The Impact and Effort Matrix is one of the problem-solving techniques that fall into this camp, empowering participants to first generate ideas and then categorize them into a 2×2 matrix based on impact and effort.

Activities that invite critical thinking while remaining simple are invaluable. Use the Impact and Effort Matrix to move from ideation and towards evaluating potential solutions before then committing to them. 

Impact and Effort Matrix   #gamestorming   #decision making   #action   #remote-friendly   In this decision-making exercise, possible actions are mapped based on two factors: effort required to implement and potential impact. Categorizing ideas along these lines is a useful technique in decision making, as it obliges contributors to balance and evaluate suggested actions before committing to them.

27. Dotmocracy

If you’ve followed each of the problem-solving steps with your group successfully, you should move towards the end of your process with heaps of possible solutions developed with a specific problem in mind. But how do you help a group go from ideation to putting a solution into action? 

Dotmocracy – or Dot Voting -is a tried and tested method of helping a team in the problem-solving process make decisions and put actions in place with a degree of oversight and consensus. 

One of the problem-solving techniques that should be in every facilitator’s toolbox, Dot Voting is fast and effective and can help identify the most popular and best solutions and help bring a group to a decision effectively. 

Dotmocracy   #action   #decision making   #group prioritization   #hyperisland   #remote-friendly   Dotmocracy is a simple method for group prioritization or decision-making. It is not an activity on its own, but a method to use in processes where prioritization or decision-making is the aim. The method supports a group to quickly see which options are most popular or relevant. The options or ideas are written on post-its and stuck up on a wall for the whole group to see. Each person votes for the options they think are the strongest, and that information is used to inform a decision.

All facilitators know that warm-ups and icebreakers are useful for any workshop or group process. Problem-solving workshops are no different.

Use these problem-solving techniques to warm up a group and prepare them for the rest of the process. Activating your group by tapping into some of the top problem-solving skills can be one of the best ways to see great outcomes from your session.

  • Check-in/Check-out
  • Doodling Together
  • Show and Tell
  • Constellations
  • Draw a Tree

28. Check-in / Check-out

Solid processes are planned from beginning to end, and the best facilitators know that setting the tone and establishing a safe, open environment can be integral to a successful problem-solving process.

Check-in / Check-out is a great way to begin and/or bookend a problem-solving workshop. Checking in to a session emphasizes that everyone will be seen, heard, and expected to contribute. 

If you are running a series of meetings, setting a consistent pattern of checking in and checking out can really help your team get into a groove. We recommend this opening-closing activity for small to medium-sized groups though it can work with large groups if they’re disciplined!

Check-in / Check-out   #team   #opening   #closing   #hyperisland   #remote-friendly   Either checking-in or checking-out is a simple way for a team to open or close a process, symbolically and in a collaborative way. Checking-in/out invites each member in a group to be present, seen and heard, and to express a reflection or a feeling. Checking-in emphasizes presence, focus and group commitment; checking-out emphasizes reflection and symbolic closure.

29. Doodling Together  

Thinking creatively and not being afraid to make suggestions are important problem-solving skills for any group or team, and warming up by encouraging these behaviors is a great way to start. 

Doodling Together is one of our favorite creative ice breaker games – it’s quick, effective, and fun and can make all following problem-solving steps easier by encouraging a group to collaborate visually. By passing cards and adding additional items as they go, the workshop group gets into a groove of co-creation and idea development that is crucial to finding solutions to problems. 

Doodling Together   #collaboration   #creativity   #teamwork   #fun   #team   #visual methods   #energiser   #icebreaker   #remote-friendly   Create wild, weird and often funny postcards together & establish a group’s creative confidence.

30. Show and Tell

You might remember some version of Show and Tell from being a kid in school and it’s a great problem-solving activity to kick off a session.

Asking participants to prepare a little something before a workshop by bringing an object for show and tell can help them warm up before the session has even begun! Games that include a physical object can also help encourage early engagement before moving onto more big-picture thinking.

By asking your participants to tell stories about why they chose to bring a particular item to the group, you can help teams see things from new perspectives and see both differences and similarities in the way they approach a topic. Great groundwork for approaching a problem-solving process as a team! 

Show and Tell   #gamestorming   #action   #opening   #meeting facilitation   Show and Tell taps into the power of metaphors to reveal players’ underlying assumptions and associations around a topic The aim of the game is to get a deeper understanding of stakeholders’ perspectives on anything—a new project, an organizational restructuring, a shift in the company’s vision or team dynamic.

31. Constellations

Who doesn’t love stars? Constellations is a great warm-up activity for any workshop as it gets people up off their feet, energized, and ready to engage in new ways with established topics. It’s also great for showing existing beliefs, biases, and patterns that can come into play as part of your session.

Using warm-up games that help build trust and connection while also allowing for non-verbal responses can be great for easing people into the problem-solving process and encouraging engagement from everyone in the group. Constellations is great in large spaces that allow for movement and is definitely a practical exercise to allow the group to see patterns that are otherwise invisible. 

Constellations   #trust   #connection   #opening   #coaching   #patterns   #system   Individuals express their response to a statement or idea by standing closer or further from a central object. Used with teams to reveal system, hidden patterns, perspectives.

32. Draw a Tree

Problem-solving games that help raise group awareness through a central, unifying metaphor can be effective ways to warm-up a group in any problem-solving model.

Draw a Tree is a simple warm-up activity you can use in any group and which can provide a quick jolt of energy. Start by asking your participants to draw a tree in just 45 seconds – they can choose whether it will be abstract or realistic. 

Once the timer is up, ask the group how many people included the roots of the tree and use this as a means to discuss how we can ignore important parts of any system simply because they are not visible.

All problem-solving strategies are made more effective by thinking of problems critically and by exposing things that may not normally come to light. Warm-up games like Draw a Tree are great in that they quickly demonstrate some key problem-solving skills in an accessible and effective way.

Draw a Tree   #thiagi   #opening   #perspectives   #remote-friendly   With this game you can raise awarness about being more mindful, and aware of the environment we live in.

Each step of the problem-solving workshop benefits from an intelligent deployment of activities, games, and techniques. Bringing your session to an effective close helps ensure that solutions are followed through on and that you also celebrate what has been achieved.

Here are some problem-solving activities you can use to effectively close a workshop or meeting and ensure the great work you’ve done can continue afterward.

  • One Breath Feedback
  • Who What When Matrix
  • Response Cards

How do I conclude a problem-solving process?

All good things must come to an end. With the bulk of the work done, it can be tempting to conclude your workshop swiftly and without a moment to debrief and align. This can be problematic in that it doesn’t allow your team to fully process the results or reflect on the process.

At the end of an effective session, your team will have gone through a process that, while productive, can be exhausting. It’s important to give your group a moment to take a breath, ensure that they are clear on future actions, and provide short feedback before leaving the space. 

The primary purpose of any problem-solving method is to generate solutions and then implement them. Be sure to take the opportunity to ensure everyone is aligned and ready to effectively implement the solutions you produced in the workshop.

Remember that every process can be improved and by giving a short moment to collect feedback in the session, you can further refine your problem-solving methods and see further success in the future too.

33. One Breath Feedback

Maintaining attention and focus during the closing stages of a problem-solving workshop can be tricky and so being concise when giving feedback can be important. It’s easy to incur “death by feedback” should some team members go on for too long sharing their perspectives in a quick feedback round. 

One Breath Feedback is a great closing activity for workshops. You give everyone an opportunity to provide feedback on what they’ve done but only in the space of a single breath. This keeps feedback short and to the point and means that everyone is encouraged to provide the most important piece of feedback to them. 

One breath feedback   #closing   #feedback   #action   This is a feedback round in just one breath that excels in maintaining attention: each participants is able to speak during just one breath … for most people that’s around 20 to 25 seconds … unless of course you’ve been a deep sea diver in which case you’ll be able to do it for longer.

34. Who What When Matrix 

Matrices feature as part of many effective problem-solving strategies and with good reason. They are easily recognizable, simple to use, and generate results.

The Who What When Matrix is a great tool to use when closing your problem-solving session by attributing a who, what and when to the actions and solutions you have decided upon. The resulting matrix is a simple, easy-to-follow way of ensuring your team can move forward. 

Great solutions can’t be enacted without action and ownership. Your problem-solving process should include a stage for allocating tasks to individuals or teams and creating a realistic timeframe for those solutions to be implemented or checked out. Use this method to keep the solution implementation process clear and simple for all involved. 

Who/What/When Matrix   #gamestorming   #action   #project planning   With Who/What/When matrix, you can connect people with clear actions they have defined and have committed to.

35. Response cards

Group discussion can comprise the bulk of most problem-solving activities and by the end of the process, you might find that your team is talked out! 

Providing a means for your team to give feedback with short written notes can ensure everyone is head and can contribute without the need to stand up and talk. Depending on the needs of the group, giving an alternative can help ensure everyone can contribute to your problem-solving model in the way that makes the most sense for them.

Response Cards is a great way to close a workshop if you are looking for a gentle warm-down and want to get some swift discussion around some of the feedback that is raised. 

Response Cards   #debriefing   #closing   #structured sharing   #questions and answers   #thiagi   #action   It can be hard to involve everyone during a closing of a session. Some might stay in the background or get unheard because of louder participants. However, with the use of Response Cards, everyone will be involved in providing feedback or clarify questions at the end of a session.

Save time and effort discovering the right solutions

A structured problem solving process is a surefire way of solving tough problems, discovering creative solutions and driving organizational change. But how can you design for successful outcomes?

With SessionLab, it’s easy to design engaging workshops that deliver results. Drag, drop and reorder blocks  to build your agenda. When you make changes or update your agenda, your session  timing   adjusts automatically , saving you time on manual adjustments.

Collaborating with stakeholders or clients? Share your agenda with a single click and collaborate in real-time. No more sending documents back and forth over email.

Explore  how to use SessionLab  to design effective problem solving workshops or  watch this five minute video  to see the planner in action!

what is a complex problem solver

Over to you

The problem-solving process can often be as complicated and multifaceted as the problems they are set-up to solve. With the right problem-solving techniques and a mix of creative exercises designed to guide discussion and generate purposeful ideas, we hope we’ve given you the tools to find the best solutions as simply and easily as possible.

Is there a problem-solving technique that you are missing here? Do you have a favorite activity or method you use when facilitating? Let us know in the comments below, we’d love to hear from you! 

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thank you very much for these excellent techniques

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Certainly wonderful article, very detailed. Shared!

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How to master the seven-step problem-solving process

In this episode of the McKinsey Podcast , Simon London speaks with Charles Conn, CEO of venture-capital firm Oxford Sciences Innovation, and McKinsey senior partner Hugo Sarrazin about the complexities of different problem-solving strategies.

Podcast transcript

Simon London: Hello, and welcome to this episode of the McKinsey Podcast , with me, Simon London. What’s the number-one skill you need to succeed professionally? Salesmanship, perhaps? Or a facility with statistics? Or maybe the ability to communicate crisply and clearly? Many would argue that at the very top of the list comes problem solving: that is, the ability to think through and come up with an optimal course of action to address any complex challenge—in business, in public policy, or indeed in life.

Looked at this way, it’s no surprise that McKinsey takes problem solving very seriously, testing for it during the recruiting process and then honing it, in McKinsey consultants, through immersion in a structured seven-step method. To discuss the art of problem solving, I sat down in California with McKinsey senior partner Hugo Sarrazin and also with Charles Conn. Charles is a former McKinsey partner, entrepreneur, executive, and coauthor of the book Bulletproof Problem Solving: The One Skill That Changes Everything [John Wiley & Sons, 2018].

Charles and Hugo, welcome to the podcast. Thank you for being here.

Hugo Sarrazin: Our pleasure.

Charles Conn: It’s terrific to be here.

Simon London: Problem solving is a really interesting piece of terminology. It could mean so many different things. I have a son who’s a teenage climber. They talk about solving problems. Climbing is problem solving. Charles, when you talk about problem solving, what are you talking about?

Charles Conn: For me, problem solving is the answer to the question “What should I do?” It’s interesting when there’s uncertainty and complexity, and when it’s meaningful because there are consequences. Your son’s climbing is a perfect example. There are consequences, and it’s complicated, and there’s uncertainty—can he make that grab? I think we can apply that same frame almost at any level. You can think about questions like “What town would I like to live in?” or “Should I put solar panels on my roof?”

You might think that’s a funny thing to apply problem solving to, but in my mind it’s not fundamentally different from business problem solving, which answers the question “What should my strategy be?” Or problem solving at the policy level: “How do we combat climate change?” “Should I support the local school bond?” I think these are all part and parcel of the same type of question, “What should I do?”

I’m a big fan of structured problem solving. By following steps, we can more clearly understand what problem it is we’re solving, what are the components of the problem that we’re solving, which components are the most important ones for us to pay attention to, which analytic techniques we should apply to those, and how we can synthesize what we’ve learned back into a compelling story. That’s all it is, at its heart.

I think sometimes when people think about seven steps, they assume that there’s a rigidity to this. That’s not it at all. It’s actually to give you the scope for creativity, which often doesn’t exist when your problem solving is muddled.

Simon London: You were just talking about the seven-step process. That’s what’s written down in the book, but it’s a very McKinsey process as well. Without getting too deep into the weeds, let’s go through the steps, one by one. You were just talking about problem definition as being a particularly important thing to get right first. That’s the first step. Hugo, tell us about that.

Hugo Sarrazin: It is surprising how often people jump past this step and make a bunch of assumptions. The most powerful thing is to step back and ask the basic questions—“What are we trying to solve? What are the constraints that exist? What are the dependencies?” Let’s make those explicit and really push the thinking and defining. At McKinsey, we spend an enormous amount of time in writing that little statement, and the statement, if you’re a logic purist, is great. You debate. “Is it an ‘or’? Is it an ‘and’? What’s the action verb?” Because all these specific words help you get to the heart of what matters.

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Simon London: So this is a concise problem statement.

Hugo Sarrazin: Yeah. It’s not like “Can we grow in Japan?” That’s interesting, but it is “What, specifically, are we trying to uncover in the growth of a product in Japan? Or a segment in Japan? Or a channel in Japan?” When you spend an enormous amount of time, in the first meeting of the different stakeholders, debating this and having different people put forward what they think the problem definition is, you realize that people have completely different views of why they’re here. That, to me, is the most important step.

Charles Conn: I would agree with that. For me, the problem context is critical. When we understand “What are the forces acting upon your decision maker? How quickly is the answer needed? With what precision is the answer needed? Are there areas that are off limits or areas where we would particularly like to find our solution? Is the decision maker open to exploring other areas?” then you not only become more efficient, and move toward what we call the critical path in problem solving, but you also make it so much more likely that you’re not going to waste your time or your decision maker’s time.

How often do especially bright young people run off with half of the idea about what the problem is and start collecting data and start building models—only to discover that they’ve really gone off half-cocked.

Hugo Sarrazin: Yeah.

Charles Conn: And in the wrong direction.

Simon London: OK. So step one—and there is a real art and a structure to it—is define the problem. Step two, Charles?

Charles Conn: My favorite step is step two, which is to use logic trees to disaggregate the problem. Every problem we’re solving has some complexity and some uncertainty in it. The only way that we can really get our team working on the problem is to take the problem apart into logical pieces.

What we find, of course, is that the way to disaggregate the problem often gives you an insight into the answer to the problem quite quickly. I love to do two or three different cuts at it, each one giving a bit of a different insight into what might be going wrong. By doing sensible disaggregations, using logic trees, we can figure out which parts of the problem we should be looking at, and we can assign those different parts to team members.

Simon London: What’s a good example of a logic tree on a sort of ratable problem?

Charles Conn: Maybe the easiest one is the classic profit tree. Almost in every business that I would take a look at, I would start with a profit or return-on-assets tree. In its simplest form, you have the components of revenue, which are price and quantity, and the components of cost, which are cost and quantity. Each of those can be broken out. Cost can be broken into variable cost and fixed cost. The components of price can be broken into what your pricing scheme is. That simple tree often provides insight into what’s going on in a business or what the difference is between that business and the competitors.

If we add the leg, which is “What’s the asset base or investment element?”—so profit divided by assets—then we can ask the question “Is the business using its investments sensibly?” whether that’s in stores or in manufacturing or in transportation assets. I hope we can see just how simple this is, even though we’re describing it in words.

When I went to work with Gordon Moore at the Moore Foundation, the problem that he asked us to look at was “How can we save Pacific salmon?” Now, that sounds like an impossible question, but it was amenable to precisely the same type of disaggregation and allowed us to organize what became a 15-year effort to improve the likelihood of good outcomes for Pacific salmon.

Simon London: Now, is there a danger that your logic tree can be impossibly large? This, I think, brings us onto the third step in the process, which is that you have to prioritize.

Charles Conn: Absolutely. The third step, which we also emphasize, along with good problem definition, is rigorous prioritization—we ask the questions “How important is this lever or this branch of the tree in the overall outcome that we seek to achieve? How much can I move that lever?” Obviously, we try and focus our efforts on ones that have a big impact on the problem and the ones that we have the ability to change. With salmon, ocean conditions turned out to be a big lever, but not one that we could adjust. We focused our attention on fish habitats and fish-harvesting practices, which were big levers that we could affect.

People spend a lot of time arguing about branches that are either not important or that none of us can change. We see it in the public square. When we deal with questions at the policy level—“Should you support the death penalty?” “How do we affect climate change?” “How can we uncover the causes and address homelessness?”—it’s even more important that we’re focusing on levers that are big and movable.

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Simon London: Let’s move swiftly on to step four. You’ve defined your problem, you disaggregate it, you prioritize where you want to analyze—what you want to really look at hard. Then you got to the work plan. Now, what does that mean in practice?

Hugo Sarrazin: Depending on what you’ve prioritized, there are many things you could do. It could be breaking the work among the team members so that people have a clear piece of the work to do. It could be defining the specific analyses that need to get done and executed, and being clear on time lines. There’s always a level-one answer, there’s a level-two answer, there’s a level-three answer. Without being too flippant, I can solve any problem during a good dinner with wine. It won’t have a whole lot of backing.

Simon London: Not going to have a lot of depth to it.

Hugo Sarrazin: No, but it may be useful as a starting point. If the stakes are not that high, that could be OK. If it’s really high stakes, you may need level three and have the whole model validated in three different ways. You need to find a work plan that reflects the level of precision, the time frame you have, and the stakeholders you need to bring along in the exercise.

Charles Conn: I love the way you’ve described that, because, again, some people think of problem solving as a linear thing, but of course what’s critical is that it’s iterative. As you say, you can solve the problem in one day or even one hour.

Charles Conn: We encourage our teams everywhere to do that. We call it the one-day answer or the one-hour answer. In work planning, we’re always iterating. Every time you see a 50-page work plan that stretches out to three months, you know it’s wrong. It will be outmoded very quickly by that learning process that you described. Iterative problem solving is a critical part of this. Sometimes, people think work planning sounds dull, but it isn’t. It’s how we know what’s expected of us and when we need to deliver it and how we’re progressing toward the answer. It’s also the place where we can deal with biases. Bias is a feature of every human decision-making process. If we design our team interactions intelligently, we can avoid the worst sort of biases.

Simon London: Here we’re talking about cognitive biases primarily, right? It’s not that I’m biased against you because of your accent or something. These are the cognitive biases that behavioral sciences have shown we all carry around, things like anchoring, overoptimism—these kinds of things.

Both: Yeah.

Charles Conn: Availability bias is the one that I’m always alert to. You think you’ve seen the problem before, and therefore what’s available is your previous conception of it—and we have to be most careful about that. In any human setting, we also have to be careful about biases that are based on hierarchies, sometimes called sunflower bias. I’m sure, Hugo, with your teams, you make sure that the youngest team members speak first. Not the oldest team members, because it’s easy for people to look at who’s senior and alter their own creative approaches.

Hugo Sarrazin: It’s helpful, at that moment—if someone is asserting a point of view—to ask the question “This was true in what context?” You’re trying to apply something that worked in one context to a different one. That can be deadly if the context has changed, and that’s why organizations struggle to change. You promote all these people because they did something that worked well in the past, and then there’s a disruption in the industry, and they keep doing what got them promoted even though the context has changed.

Simon London: Right. Right.

Hugo Sarrazin: So it’s the same thing in problem solving.

Charles Conn: And it’s why diversity in our teams is so important. It’s one of the best things about the world that we’re in now. We’re likely to have people from different socioeconomic, ethnic, and national backgrounds, each of whom sees problems from a slightly different perspective. It is therefore much more likely that the team will uncover a truly creative and clever approach to problem solving.

Simon London: Let’s move on to step five. You’ve done your work plan. Now you’ve actually got to do the analysis. The thing that strikes me here is that the range of tools that we have at our disposal now, of course, is just huge, particularly with advances in computation, advanced analytics. There’s so many things that you can apply here. Just talk about the analysis stage. How do you pick the right tools?

Charles Conn: For me, the most important thing is that we start with simple heuristics and explanatory statistics before we go off and use the big-gun tools. We need to understand the shape and scope of our problem before we start applying these massive and complex analytical approaches.

Simon London: Would you agree with that?

Hugo Sarrazin: I agree. I think there are so many wonderful heuristics. You need to start there before you go deep into the modeling exercise. There’s an interesting dynamic that’s happening, though. In some cases, for some types of problems, it is even better to set yourself up to maximize your learning. Your problem-solving methodology is test and learn, test and learn, test and learn, and iterate. That is a heuristic in itself, the A/B testing that is used in many parts of the world. So that’s a problem-solving methodology. It’s nothing different. It just uses technology and feedback loops in a fast way. The other one is exploratory data analysis. When you’re dealing with a large-scale problem, and there’s so much data, I can get to the heuristics that Charles was talking about through very clever visualization of data.

You test with your data. You need to set up an environment to do so, but don’t get caught up in neural-network modeling immediately. You’re testing, you’re checking—“Is the data right? Is it sound? Does it make sense?”—before you launch too far.

Simon London: You do hear these ideas—that if you have a big enough data set and enough algorithms, they’re going to find things that you just wouldn’t have spotted, find solutions that maybe you wouldn’t have thought of. Does machine learning sort of revolutionize the problem-solving process? Or are these actually just other tools in the toolbox for structured problem solving?

Charles Conn: It can be revolutionary. There are some areas in which the pattern recognition of large data sets and good algorithms can help us see things that we otherwise couldn’t see. But I do think it’s terribly important we don’t think that this particular technique is a substitute for superb problem solving, starting with good problem definition. Many people use machine learning without understanding algorithms that themselves can have biases built into them. Just as 20 years ago, when we were doing statistical analysis, we knew that we needed good model definition, we still need a good understanding of our algorithms and really good problem definition before we launch off into big data sets and unknown algorithms.

Simon London: Step six. You’ve done your analysis.

Charles Conn: I take six and seven together, and this is the place where young problem solvers often make a mistake. They’ve got their analysis, and they assume that’s the answer, and of course it isn’t the answer. The ability to synthesize the pieces that came out of the analysis and begin to weave those into a story that helps people answer the question “What should I do?” This is back to where we started. If we can’t synthesize, and we can’t tell a story, then our decision maker can’t find the answer to “What should I do?”

Simon London: But, again, these final steps are about motivating people to action, right?

Charles Conn: Yeah.

Simon London: I am slightly torn about the nomenclature of problem solving because it’s on paper, right? Until you motivate people to action, you actually haven’t solved anything.

Charles Conn: I love this question because I think decision-making theory, without a bias to action, is a waste of time. Everything in how I approach this is to help people take action that makes the world better.

Simon London: Hence, these are absolutely critical steps. If you don’t do this well, you’ve just got a bunch of analysis.

Charles Conn: We end up in exactly the same place where we started, which is people speaking across each other, past each other in the public square, rather than actually working together, shoulder to shoulder, to crack these important problems.

Simon London: In the real world, we have a lot of uncertainty—arguably, increasing uncertainty. How do good problem solvers deal with that?

Hugo Sarrazin: At every step of the process. In the problem definition, when you’re defining the context, you need to understand those sources of uncertainty and whether they’re important or not important. It becomes important in the definition of the tree.

You need to think carefully about the branches of the tree that are more certain and less certain as you define them. They don’t have equal weight just because they’ve got equal space on the page. Then, when you’re prioritizing, your prioritization approach may put more emphasis on things that have low probability but huge impact—or, vice versa, may put a lot of priority on things that are very likely and, hopefully, have a reasonable impact. You can introduce that along the way. When you come back to the synthesis, you just need to be nuanced about what you’re understanding, the likelihood.

Often, people lack humility in the way they make their recommendations: “This is the answer.” They’re very precise, and I think we would all be well-served to say, “This is a likely answer under the following sets of conditions” and then make the level of uncertainty clearer, if that is appropriate. It doesn’t mean you’re always in the gray zone; it doesn’t mean you don’t have a point of view. It just means that you can be explicit about the certainty of your answer when you make that recommendation.

Simon London: So it sounds like there is an underlying principle: “Acknowledge and embrace the uncertainty. Don’t pretend that it isn’t there. Be very clear about what the uncertainties are up front, and then build that into every step of the process.”

Hugo Sarrazin: Every step of the process.

Simon London: Yeah. We have just walked through a particular structured methodology for problem solving. But, of course, this is not the only structured methodology for problem solving. One that is also very well-known is design thinking, which comes at things very differently. So, Hugo, I know you have worked with a lot of designers. Just give us a very quick summary. Design thinking—what is it, and how does it relate?

Hugo Sarrazin: It starts with an incredible amount of empathy for the user and uses that to define the problem. It does pause and go out in the wild and spend an enormous amount of time seeing how people interact with objects, seeing the experience they’re getting, seeing the pain points or joy—and uses that to infer and define the problem.

Simon London: Problem definition, but out in the world.

Hugo Sarrazin: With an enormous amount of empathy. There’s a huge emphasis on empathy. Traditional, more classic problem solving is you define the problem based on an understanding of the situation. This one almost presupposes that we don’t know the problem until we go see it. The second thing is you need to come up with multiple scenarios or answers or ideas or concepts, and there’s a lot of divergent thinking initially. That’s slightly different, versus the prioritization, but not for long. Eventually, you need to kind of say, “OK, I’m going to converge again.” Then you go and you bring things back to the customer and get feedback and iterate. Then you rinse and repeat, rinse and repeat. There’s a lot of tactile building, along the way, of prototypes and things like that. It’s very iterative.

Simon London: So, Charles, are these complements or are these alternatives?

Charles Conn: I think they’re entirely complementary, and I think Hugo’s description is perfect. When we do problem definition well in classic problem solving, we are demonstrating the kind of empathy, at the very beginning of our problem, that design thinking asks us to approach. When we ideate—and that’s very similar to the disaggregation, prioritization, and work-planning steps—we do precisely the same thing, and often we use contrasting teams, so that we do have divergent thinking. The best teams allow divergent thinking to bump them off whatever their initial biases in problem solving are. For me, design thinking gives us a constant reminder of creativity, empathy, and the tactile nature of problem solving, but it’s absolutely complementary, not alternative.

Simon London: I think, in a world of cross-functional teams, an interesting question is do people with design-thinking backgrounds really work well together with classical problem solvers? How do you make that chemistry happen?

Hugo Sarrazin: Yeah, it is not easy when people have spent an enormous amount of time seeped in design thinking or user-centric design, whichever word you want to use. If the person who’s applying classic problem-solving methodology is very rigid and mechanical in the way they’re doing it, there could be an enormous amount of tension. If there’s not clarity in the role and not clarity in the process, I think having the two together can be, sometimes, problematic.

The second thing that happens often is that the artifacts the two methodologies try to gravitate toward can be different. Classic problem solving often gravitates toward a model; design thinking migrates toward a prototype. Rather than writing a big deck with all my supporting evidence, they’ll bring an example, a thing, and that feels different. Then you spend your time differently to achieve those two end products, so that’s another source of friction.

Now, I still think it can be an incredibly powerful thing to have the two—if there are the right people with the right mind-set, if there is a team that is explicit about the roles, if we’re clear about the kind of outcomes we are attempting to bring forward. There’s an enormous amount of collaborativeness and respect.

Simon London: But they have to respect each other’s methodology and be prepared to flex, maybe, a little bit, in how this process is going to work.

Hugo Sarrazin: Absolutely.

Simon London: The other area where, it strikes me, there could be a little bit of a different sort of friction is this whole concept of the day-one answer, which is what we were just talking about in classical problem solving. Now, you know that this is probably not going to be your final answer, but that’s how you begin to structure the problem. Whereas I would imagine your design thinkers—no, they’re going off to do their ethnographic research and get out into the field, potentially for a long time, before they come back with at least an initial hypothesis.

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Hugo Sarrazin: That is a great callout, and that’s another difference. Designers typically will like to soak into the situation and avoid converging too quickly. There’s optionality and exploring different options. There’s a strong belief that keeps the solution space wide enough that you can come up with more radical ideas. If there’s a large design team or many designers on the team, and you come on Friday and say, “What’s our week-one answer?” they’re going to struggle. They’re not going to be comfortable, naturally, to give that answer. It doesn’t mean they don’t have an answer; it’s just not where they are in their thinking process.

Simon London: I think we are, sadly, out of time for today. But Charles and Hugo, thank you so much.

Charles Conn: It was a pleasure to be here, Simon.

Hugo Sarrazin: It was a pleasure. Thank you.

Simon London: And thanks, as always, to you, our listeners, for tuning into this episode of the McKinsey Podcast . If you want to learn more about problem solving, you can find the book, Bulletproof Problem Solving: The One Skill That Changes Everything , online or order it through your local bookstore. To learn more about McKinsey, you can of course find us at McKinsey.com.

Charles Conn is CEO of Oxford Sciences Innovation and an alumnus of McKinsey’s Sydney office. Hugo Sarrazin is a senior partner in the Silicon Valley office, where Simon London, a member of McKinsey Publishing, is also based.

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Intelligence, Creativity, and Wisdom: A Case for Complex Problem Solving?

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This chapter covers the roles that intelligence, creativity, and wisdom play during problem solving as an integral competency that is needed to master challenges in the twenty-first century. We suggest that problem solving requires a set of skills that are strongly intertwined with all three concepts: intelligence, creativity, and wisdom.

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Ardelt, M. (2004). Wisdom as expert knowledge system: A critical review of a contemporary operationalization of an ancient concept. Human Development, 47 (5), 257–285.

Article   Google Scholar  

Autor, D. H., Levy, F., & Murnane, R. J. (2003). The skill content of recent technological change: An empirical exploration. The Quarterly Journal of Economics. https://doi.org/10.1162/003355303322552801

Azevedo, R. (2009). Theoretical, conceptual, methodological, and instructional issues in research on metacognition and self-regulated learning: A discussion. Metacognition and Learning. https://doi.org/10.1007/s11409-009-9035-7

Baker, R., & Yacef, K. (2009). Journal of Educational Data Mining JEDM. JEDM | Journal of Educational Data Mining, 1 (1), 3–17.

Google Scholar  

Baltes, P. B., & Smith, J. (2008). The fascination of wisdom: Its nature, ontogeny, and function. Perspectives on Psychological Science: A Journal of the Association for Psychological Science, 3 (1), 56–64.

Article   PubMed   Google Scholar  

Berardi-Coletta, B., Buyer, L. S., Dominowski, R. L., & Rellinger, E. R. (1995). Metacognition and problem solving: A process-oriented approach. Journal of Experimental Psychology. Learning, Memory, and Cognition, 21 (1), 205–223.

Blech, C., & Funke, J. (2010). You cannot have your cake and eat it, too: How induced goal conflicts affect complex problem solving. The Open Psychology Journal, 3 (1), 42–53.

Boring, E. G. (1923). Intelligence as the tests test it. New Republic , 210–214.

Care, E., Griffin, P., & Wilson, M. (2018). Assessment and teaching of 21st century skills research and applications. Educational Assessment in an Information Age, January. https://doi.org/10.1007/978-3-319-65368-6

Cascio, W. F. (1995). Whither industrial and organizational psychology in a changing world of work? The American Psychologist, 50 (11), 928–939.

Cornoldi, C., Carretti, B., Drusi, S., & Tencati, C. (2015). Improving problem solving in primary school students: The effect of a training programme focusing on metacognition and working memory. The British Journal of Educational Psychology, 85 (3), 424–439.

Cropley, A. (2006). In praise of convergent thinking. Creativity Research Journal, 18 (3), 391–404.

Csapó, B., & Funke, J. (2017). The nature of problem solving. Using research to inspire 21st century learning . OECD Publishing.

Danner, D., Hagemann, D., Holt, D. V., Hager, M., Schankin, A., Wüstenberg, S., & Funke, J. (2011). Measuring performance in dynamic decision making. Journal of Individual Differences, 32 (4), 225–233.

Fischer, A., Greiff, S., & Funke, J. (2011). The process of solving complex problems. The Journal of Problem Solving, 4 (1). https://doi.org/10.7771/1932-6246.1118

Flavell, J. H. (1979). Metacognition and cognitive monitoring. The American Psychologist, 34 (10), 906–911.

Forthmann, B., Beaty, R. E., & Johnson, D. R. (2022). Semantic spaces are not created equal—How should we weigh them in the Sequel? European Journal of Psychological Assessment: Official Organ of the European Association of Psychological Assessment . https://doi.org/10.1027/1015-5759/a000723

Funke, J. (2001). Dynamic systems as tools for analysing human judgement. Thinking and Reasoning, 7 (1), 69–89.

Funke, J. (2019). Problem solving. In R. J. Sternberg & J. Funke (Eds.), The psychology of human thought: An introduction (pp. 155–176). Heidelberg University.

Gobert, J. D., Sao Pedro, M., Raziuddin, J., & Baker, R. S. (2013). From log files to assessment metrics: Measuring students’ science inquiry skills using educational data mining. Journal of the Learning Sciences, 22 (4), 521–563.

Goldstein, S., Princiotta, D., & Naglieri, J. A. (2015). Handbook of intelligence: Evolutionary theory, historical perspective, and current concepts . Springer.

Gottschling, J., Krieger, F., & Greiff, S. (2022). The fight against infectious diseases: The essential role of higher-order thinking and problem-solving. Journal of Intelligence, 10 (1). https://doi.org/10.1016/j.intell.2011.11.003

Greiff, S., Wüstenberg, S., & Avvisati, F. (2015). Computer-generated log-file analyses as a window into students’ minds? A showcase study based on the PISA 2012 assessment of problem solving. Computers and Education, 91 , 92–105.

Greiff, S., Wüstenberg, S., Csapó, B., Demetriou, A., Hautamäki, J., Graesser, A. C., & Martin, R. (2014). Domain-general problem solving skills and education in the 21st century. Educational Research Review, 13 , 74–83.

Greiff, S., Wüstenberg, S., & Funke, J. (2012). Dynamic problem solving: A new assessment perspective. Applied Psychological Measurement, 36 (3), 189–213.

Greiff, S., Wüstenberg, S., Molnár, G., Fischer, A., Funke, J., & Csapó, B. (2013). Complex problem solving in educational contexts-something beyond g : Concept, assessment, measurement invariance, and construct validity. Journal of Educational Psychology, 105 (2), 364–379.

Guilford, J. P. (1950). Creativity. American Psychologist, 5 , 444–454.

Horn, J. L., & Cattell, R. B. (1966). Refinement and test of the theory of fluid and crystallized general intelligences. Journal of Educational Psychology, 57 (5), 253.

Lotz, C., Scherer, R., Greiff, S., & Sparfeldt, J. R. (2017, October). Intelligence in action—Effective strategic behaviors while solving complex problems. Intelligence, 64 , 98–112.

Lubart, T. I. (1994). Creativity . In R. J. Sternberg (Ed.), Thinking and problem solving (pp. 290–332). Academic Press.

Mayer, R. E., & Wittrock, M. C. (2006). Problem solving. In P. A. Alexander & P. H. Winne (Eds.), Handbook of educational psychology (2nd ed., pp. 287–299). Routledge.

McGrew, K. S. (2009). CHC theory and the human cognitive abilities project: Standing on the shoulders of the giants of psychometric intelligence research. Intelligence, 37 (1), 1–10.

Mihalca, L., Mengelkamp, C., & Schnotz, W. (2017). Accuracy of metacognitive judgments as a moderator of learner control effectiveness in problem-solving tasks. Metacognition and Learning, 12 , 357–379.

Neisser, U., Boodoo, G., Bouchard, T. J., Jr., Boykin, A. W., Brody, N., Ceci, S. J., Halpern, D. F., Loehlin, J. C., Perloff, R., Sternberg, R. J., & Urbina, S. (1996). Intelligence: Knowns and unknowns. The American Psychologist, 51 (2), 77–101.

Nicolay, B., Krieger, F., Stadler, M., Gobert, J., & Greiff, S. (2021). Lost in transition—Learning analytics on the transfer from knowledge acquisition to knowledge application in complex problem solving. Computers in Human Behavior, 115 . https://doi.org/10.1016/j.chb.2020.106594

OECD (2013). PISA 2012 assessment and analytical framework . OECD Publishing.

Book   Google Scholar  

OECD (2014). PISA 2012 Results: Creative Problem Solving: Students’ Skills in Tackling Real-Life Problems (Volume V). OECD publishing.

Osman, M. (2010). Controlling uncertainty: A review of human behavior in complex dynamic environments. Psychological Bulletin, 136 (1), 65–86.

Plucker, J. A., Beghetto, R. A., & Dow, G. T. (2004). Why isn’t creativity more important to educational psychologists? Potentials, pitfalls, and future directions in creativity research. Educational Psychologist, 39 , 83–96.

Popper, K. (1999). All life is problem solving . Routledge.

Roth, B., Romeyke, S., Spinath, F. M., Domnick, F., Schäfer, S., & Becker, N. (2015). Intelligence and school grades: A meta-analysis. Intelligence, 53 , 118–137.

Schmidt, F. L., & Hunter, J. (2004). General mental ability in the world of work: Occupational attainment and job performance. Journal of Personality and Social Psychology, 86 (1), 162–173. https://doi.org/10.1037/0022-3514.86.1.162

Schneider, W. J., & McGrew, K. S. (2018). The Cattell–Horn–Carroll theory of cognitive abilities. In D. P. Flanagan & E. M. McDonough (Eds.), Contemporary intellectual assessment: Theories, tests, and issues (pp. 73–163). The Guilford Press.

Schweizer, F., Wüstenberg, S., & Greiff, S. (2013). Validity of the MicroDYN approach: Complex problem solving predicts school grades beyond working memory capacity. Learning and Individual Differences, 24 , 42–52.

Spearman, C. (1904). ‘General Intelligence’, objectively determined and measured. The American Journal of Psychology, 15 (2), 201–292.

Spearman, C. (1927). The abilities of man: Their nature and measurement . Macmillan and Co..

Stadler, M., Becker, N., Gödker, M., Leutner, D., & Greiff, S. (2015). Complex problem solving and intelligence: A meta-analysis. Intelligence, 53 , 92–101.

Stanovich, K. E. (2009). What intelligence tests miss . Yale University Press.

Sternberg, R. J. (2001). Why schools should teach for wisdom: The balance theory of wisdom in educational settings. Educational Psychologist, 36 (4), 227–245.

Sternberg, R. J. (2003). Wisdom, intelligence, and creativity synthesized . Cambridge University Press.

Sternberg, R. J. (2021). Adaptive intelligence: How to survive and thrive in a world of uncertainty . Cambridge University Press.

Sternberg, R. J. (2022). Meta-intelligence: Understanding, control, and coordination of higher cognitive processes. In R. M. Holm-Hadulla, J. Funke, & M. Wink (Eds.), Intelligence—Theories and applications (pp. 339–349). Springer International Publishing.

Chapter   Google Scholar  

Sternberg, R. J., Glaveanu, V., Karami, S., Kaufman, J. C., Phillipson, S. N., & Preiss, D. D. (2021). Meta-intelligence: Understanding, control, and interactivity between creative, analytical, practical, and wisdom-based approaches in problem solving. Journal of Intelligence, 9 (2). https://doi.org/10.3390/jintelligence9020019

Sternberg, R. J., & Glück, J. (2022). The psychology of wisdom: An introduction . Cambridge University Press.

Sternberg, R. J., & Lubart, T. I. (1995). Defying the crowd: Cultivating creativity in a culture of conformity . Free Press.

Stylianou, D. A. (2002). On the interaction of visualization and analysis: The negotiation of a visual representation in expert problem solving. The Journal of Mathematical Behavior, 21 (3), 303–317.

Thurstone, L. L. (1938). Primary mental abilities. Psychometric monograph no. 1 . University of Chicago Press.

Thurstone, L. L., & Thurstone, T. G. (1941). Factorial studies of intelligence . University of Chicago Press.

Veenman, M. V. J., Van Hout-Wolters, B. H. A. M., & Afflerbach, P. (2006). Metacognition and learning: conceptual and methodological considerations. Metacognition and Learning. https://doi.org/10.1007/s11409-006-6893-0

Winne, P. H., & Baker, R. S. (2013). The potentials of educational data mining for researching metacognition, motivation and self-regulated learning. Journal of Educational Data Mining, 5 (1), 1–8.

Wu, H., & Molnár, G. (2021). Logfile analyses of successful and unsuccessful strategy use in complex problem-solving: A cross-national comparison study. European Journal of Psychology of Education . https://doi.org/10.1007/s10212-020-00516-y

Wüstenberg, S., Greiff, S., & Funke, J. (2012). Complex problem solving—More than reasoning? Intelligence, 40 (1), 1–14.

Zohar, A., & Barzilai, S. (2013). A review of research on metacognition in science education: Current and future directions. Studies in Science Education. https://doi.org/10.1080/03057267.2013.847261

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Krieger, F., Greiff, S. (2023). Intelligence, Creativity, and Wisdom: A Case for Complex Problem Solving?. In: Sternberg, R.J., Kaufman, J.C., Karami, S. (eds) Intelligence, Creativity, and Wisdom. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-031-26772-7_10

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Systems thinking was designed to improve people's ability to manage organizations comprehensively in a volatile global environment. It offers managers a framework for understanding complex situations and the dynamics those situations produce. Systems thinking is a response to the rapid changes in technology, population, and economic activity that are transforming the world, and as a way to deal with the ever-increasing complexity of today's business.

Senior managers can use systems thinking to design policies that lead their organizations to high performance. The program is intended to give participants the tools and confidence to manage organizations with full understanding and solid strategy.

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This complex problem-solving course introduces participants to MIT's unique, powerful, and integrative System Dynamics approach to assess problems that will not go away and to produce the results they want. Through exercises and simulation models, participants experience the long-term side effects and impacts of decisions and understand the ways in which performance is tied to structures and policies.

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What Is Problem Solving? How Software Engineers Approach Complex Challenges

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From debugging an existing system to designing an entirely new software application, a day in the life of a software engineer is filled with various challenges and complexities. The one skill that glues these disparate tasks together and makes them manageable? Problem solving . 

Throughout this blog post, we’ll explore why problem-solving skills are so critical for software engineers, delve into the techniques they use to address complex challenges, and discuss how hiring managers can identify these skills during the hiring process. 

What Is Problem Solving?

But what exactly is problem solving in the context of software engineering? How does it work, and why is it so important?

Problem solving, in the simplest terms, is the process of identifying a problem, analyzing it, and finding the most effective solution to overcome it. For software engineers, this process is deeply embedded in their daily workflow. It could be something as simple as figuring out why a piece of code isn’t working as expected, or something as complex as designing the architecture for a new software system. 

In a world where technology is evolving at a blistering pace, the complexity and volume of problems that software engineers face are also growing. As such, the ability to tackle these issues head-on and find innovative solutions is not only a handy skill — it’s a necessity. 

The Importance of Problem-Solving Skills for Software Engineers

Problem-solving isn’t just another ability that software engineers pull out of their toolkits when they encounter a bug or a system failure. It’s a constant, ongoing process that’s intrinsic to every aspect of their work. Let’s break down why this skill is so critical.

Driving Development Forward

Without problem solving, software development would hit a standstill. Every new feature, every optimization, and every bug fix is a problem that needs solving. Whether it’s a performance issue that needs diagnosing or a user interface that needs improving, the capacity to tackle and solve these problems is what keeps the wheels of development turning.

It’s estimated that 60% of software development lifecycle costs are related to maintenance tasks, including debugging and problem solving. This highlights how pivotal this skill is to the everyday functioning and advancement of software systems.

Innovation and Optimization

The importance of problem solving isn’t confined to reactive scenarios; it also plays a major role in proactive, innovative initiatives . Software engineers often need to think outside the box to come up with creative solutions, whether it’s optimizing an algorithm to run faster or designing a new feature to meet customer needs. These are all forms of problem solving.

Consider the development of the modern smartphone. It wasn’t born out of a pre-existing issue but was a solution to a problem people didn’t realize they had — a device that combined communication, entertainment, and productivity into one handheld tool.

Increasing Efficiency and Productivity

Good problem-solving skills can save a lot of time and resources. Effective problem-solvers are adept at dissecting an issue to understand its root cause, thus reducing the time spent on trial and error. This efficiency means projects move faster, releases happen sooner, and businesses stay ahead of their competition.

Improving Software Quality

Problem solving also plays a significant role in enhancing the quality of the end product. By tackling the root causes of bugs and system failures, software engineers can deliver reliable, high-performing software. This is critical because, according to the Consortium for Information and Software Quality, poor quality software in the U.S. in 2022 cost at least $2.41 trillion in operational issues, wasted developer time, and other related problems.

Problem-Solving Techniques in Software Engineering

So how do software engineers go about tackling these complex challenges? Let’s explore some of the key problem-solving techniques, theories, and processes they commonly use.

Decomposition

Breaking down a problem into smaller, manageable parts is one of the first steps in the problem-solving process. It’s like dealing with a complicated puzzle. You don’t try to solve it all at once. Instead, you separate the pieces, group them based on similarities, and then start working on the smaller sets. This method allows software engineers to handle complex issues without being overwhelmed and makes it easier to identify where things might be going wrong.

Abstraction

In the realm of software engineering, abstraction means focusing on the necessary information only and ignoring irrelevant details. It is a way of simplifying complex systems to make them easier to understand and manage. For instance, a software engineer might ignore the details of how a database works to focus on the information it holds and how to retrieve or modify that information.

Algorithmic Thinking

At its core, software engineering is about creating algorithms — step-by-step procedures to solve a problem or accomplish a goal. Algorithmic thinking involves conceiving and expressing these procedures clearly and accurately and viewing every problem through an algorithmic lens. A well-designed algorithm not only solves the problem at hand but also does so efficiently, saving computational resources.

Parallel Thinking

Parallel thinking is a structured process where team members think in the same direction at the same time, allowing for more organized discussion and collaboration. It’s an approach popularized by Edward de Bono with the “ Six Thinking Hats ” technique, where each “hat” represents a different style of thinking.

In the context of software engineering, parallel thinking can be highly effective for problem solving. For instance, when dealing with a complex issue, the team can use the “White Hat” to focus solely on the data and facts about the problem, then the “Black Hat” to consider potential problems with a proposed solution, and so on. This structured approach can lead to more comprehensive analysis and more effective solutions, and it ensures that everyone’s perspectives are considered.

This is the process of identifying and fixing errors in code . Debugging involves carefully reviewing the code, reproducing and analyzing the error, and then making necessary modifications to rectify the problem. It’s a key part of maintaining and improving software quality.

Testing and Validation

Testing is an essential part of problem solving in software engineering. Engineers use a variety of tests to verify that their code works as expected and to uncover any potential issues. These range from unit tests that check individual components of the code to integration tests that ensure the pieces work well together. Validation, on the other hand, ensures that the solution not only works but also fulfills the intended requirements and objectives.

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Evaluating Problem-Solving Skills

We’ve examined the importance of problem-solving in the work of a software engineer and explored various techniques software engineers employ to approach complex challenges. Now, let’s delve into how hiring teams can identify and evaluate problem-solving skills during the hiring process.

Recognizing Problem-Solving Skills in Candidates

How can you tell if a candidate is a good problem solver? Look for these indicators:

  • Previous Experience: A history of dealing with complex, challenging projects is often a good sign. Ask the candidate to discuss a difficult problem they faced in a previous role and how they solved it.
  • Problem-Solving Questions: During interviews, pose hypothetical scenarios or present real problems your company has faced. Ask candidates to explain how they would tackle these issues. You’re not just looking for a correct solution but the thought process that led them there.
  • Technical Tests: Coding challenges and other technical tests can provide insight into a candidate’s problem-solving abilities. Consider leveraging a platform for assessing these skills in a realistic, job-related context.

Assessing Problem-Solving Skills

Once you’ve identified potential problem solvers, here are a few ways you can assess their skills:

  • Solution Effectiveness: Did the candidate solve the problem? How efficient and effective is their solution?
  • Approach and Process: Go beyond whether or not they solved the problem and examine how they arrived at their solution. Did they break the problem down into manageable parts? Did they consider different perspectives and possibilities?
  • Communication: A good problem solver can explain their thought process clearly. Can the candidate effectively communicate how they arrived at their solution and why they chose it?
  • Adaptability: Problem-solving often involves a degree of trial and error. How does the candidate handle roadblocks? Do they adapt their approach based on new information or feedback?

Hiring managers play a crucial role in identifying and fostering problem-solving skills within their teams. By focusing on these abilities during the hiring process, companies can build teams that are more capable, innovative, and resilient.

Key Takeaways

As you can see, problem solving plays a pivotal role in software engineering. Far from being an occasional requirement, it is the lifeblood that drives development forward, catalyzes innovation, and delivers of quality software. 

By leveraging problem-solving techniques, software engineers employ a powerful suite of strategies to overcome complex challenges. But mastering these techniques isn’t simple feat. It requires a learning mindset, regular practice, collaboration, reflective thinking, resilience, and a commitment to staying updated with industry trends. 

For hiring managers and team leads, recognizing these skills and fostering a culture that values and nurtures problem solving is key. It’s this emphasis on problem solving that can differentiate an average team from a high-performing one and an ordinary product from an industry-leading one.

At the end of the day, software engineering is fundamentally about solving problems — problems that matter to businesses, to users, and to the wider society. And it’s the proficient problem solvers who stand at the forefront of this dynamic field, turning challenges into opportunities, and ideas into reality.

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Complex Problem Solving: What It Is and What It Is Not

Affiliations.

  • 1 Department of Psychology, University of BambergBamberg, Germany.
  • 2 Department of Psychology, Heidelberg UniversityHeidelberg, Germany.
  • PMID: 28744242
  • PMCID: PMC5504467
  • DOI: 10.3389/fpsyg.2017.01153

Computer-simulated scenarios have been part of psychological research on problem solving for more than 40 years. The shift in emphasis from simple toy problems to complex, more real-life oriented problems has been accompanied by discussions about the best ways to assess the process of solving complex problems. Psychometric issues such as reliable assessments and addressing correlations with other instruments have been in the foreground of these discussions and have left the content validity of complex problem solving in the background. In this paper, we return the focus to content issues and address the important features that define complex problems.

Keywords: MicroDYN; assessment; complex problem solving; definition; validity.

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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."

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

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  • 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.

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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."

March 12, 2024

The Simplest Math Problem Could Be Unsolvable

The Collatz conjecture has plagued mathematicians for decades—so much so that professors warn their students away from it

By Manon Bischoff

Close up of lightbulb sparkling with teal color outline on black background

Mathematicians have been hoping for a flash of insight to solve the Collatz conjecture.

James Brey/Getty Images

At first glance, the problem seems ridiculously simple. And yet experts have been searching for a solution in vain for decades. According to mathematician Jeffrey Lagarias, number theorist Shizuo Kakutani told him that during the cold war, “for about a month everybody at Yale [University] worked on it, with no result. A similar phenomenon happened when I mentioned it at the University of Chicago. A joke was made that this problem was part of a conspiracy to slow down mathematical research in the U.S.”

The Collatz conjecture—the vexing puzzle Kakutani described—is one of those supposedly simple problems that people tend to get lost in. For this reason, experienced professors often warn their ambitious students not to get bogged down in it and lose sight of their actual research.

The conjecture itself can be formulated so simply that even primary school students understand it. Take a natural number. If it is odd, multiply it by 3 and add 1; if it is even, divide it by 2. Proceed in the same way with the result x : if x is odd, you calculate 3 x + 1; otherwise calculate x / 2. Repeat these instructions as many times as possible, and, according to the conjecture, you will always end up with the number 1.

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For example: If you start with 5, you have to calculate 5 x 3 + 1, which results in 16. Because 16 is an even number, you have to halve it, which gives you 8. Then 8 / 2 = 4, which, when divided by 2, is 2—and 2 / 2 = 1. The process of iterative calculation brings you to the end after five steps.

Of course, you can also continue calculating with 1, which gives you 4, then 2 and then 1 again. The calculation rule leads you into an inescapable loop. Therefore 1 is seen as the end point of the procedure.

Bubbles with numbers and arrows show Collatz conjecture sequences

Following iterative calculations, you can begin with any of the numbers above and will ultimately reach 1.

Credit: Keenan Pepper/Public domain via Wikimedia Commons

It’s really fun to go through the iterative calculation rule for different numbers and look at the resulting sequences. If you start with 6: 6 → 3 → 10 → 5 → 16 → 8 → 4 → 2 → 1. Or 42: 42 → 21 → 64 → 32 → 16 → 8 → 4 → 2 → 1. No matter which number you start with, you always seem to end up with 1. There are some numbers, such as 27, where it takes quite a long time (27 → 82 → 41 → 124 → 62 → 31 → 94 → 47 → 142 → 71 → 214 → 107 → 322 → 161 → 484 → 242 → 121 → 364 → 182 → 91 → 274 → ...), but so far the result has always been 1. (Admittedly, you have to be patient with the starting number 27, which requires 111 steps.)

But strangely there is still no mathematical proof that the Collatz conjecture is true. And that absence has mystified mathematicians for years.

The origin of the Collatz conjecture is uncertain, which is why this hypothesis is known by many different names. Experts speak of the Syracuse problem, the Ulam problem, the 3 n + 1 conjecture, the Hasse algorithm or the Kakutani problem.

German mathematician Lothar Collatz became interested in iterative functions during his mathematics studies and investigated them. In the early 1930s he also published specialist articles on the subject , but the explicit calculation rule for the problem named after him was not among them. In the 1950s and 1960s the Collatz conjecture finally gained notoriety when mathematicians Helmut Hasse and Shizuo Kakutani, among others, disseminated it to various universities, including Syracuse University.

Like a siren song, this seemingly simple conjecture captivated the experts. For decades they have been looking for proof that after repeating the Collatz procedure a finite number of times, you end up with 1. The reason for this persistence is not just the simplicity of the problem: the Collatz conjecture is related to other important questions in mathematics. For example, such iterative functions appear in dynamic systems, such as models that describe the orbits of planets. The conjecture is also related to the Riemann conjecture, one of the oldest problems in number theory.

Empirical Evidence for the Collatz Conjecture

In 2019 and 2020 researchers checked all numbers below 2 68 , or about 3 x 10 20 numbers in the sequence, in a collaborative computer science project . All numbers in that set fulfill the Collatz conjecture as initial values. But that doesn’t mean that there isn’t an outlier somewhere. There could be a starting value that, after repeated Collatz procedures, yields ever larger values that eventually rise to infinity. This scenario seems unlikely, however, if the problem is examined statistically.

An odd number n is increased to 3 n + 1 after the first step of the iteration, but the result is inevitably even and is therefore halved in the following step. In half of all cases, the halving produces an odd number, which must therefore be increased to 3 n + 1 again, whereupon an even result is obtained again. If the result of the second step is even again, however, you have to divide the new number by 2 twice in every fourth case. In every eighth case, you must divide it by 2 three times, and so on.

In order to evaluate the long-term behavior of this sequence of numbers , Lagarias calculated the geometric mean from these considerations in 1985 and obtained the following result: ( 3 / 2 ) 1/2 x ( 3 ⁄ 4 ) 1/4 x ( 3 ⁄ 8 ) 1/8 · ... = 3 ⁄ 4 . This shows that the sequence elements shrink by an average factor of 3 ⁄ 4 at each step of the iterative calculation rule. It is therefore extremely unlikely that there is a starting value that grows to infinity as a result of the procedure.

There could be a starting value, however, that ends in a loop that is not 4 → 2 → 1. That loop could include significantly more numbers, such that 1 would never be reached.

Such “nontrivial” loops can be found, for example, if you also allow negative integers for the Collatz conjecture: in this case, the iterative calculation rule can end not only at –2 → –1 → –2 → ... but also at –5 → –14 → –7 → –20 → –10 → –5 → ... or –17 → –50 → ... → –17 →.... If we restrict ourselves to natural numbers, no nontrivial loops are known to date—which does not mean that they do not exist. Experts have now been able to show that such a loop in the Collatz problem, however, would have to consist of at least 186 billion numbers .

A plot lays out the starting number of the Collatz sequence on the x-axis with the total length of the completed sequence on the y-axis

The length of the Collatz sequences for all numbers from 1 to 9,999 varies greatly.

Credit: Cirne/Public domain via Wikimedia Commons

Even if that sounds unlikely, it doesn’t have to be. In mathematics there are many examples where certain laws only break down after many iterations are considered. For instance,the prime number theorem overestimates the number of primes for only about 10 316 numbers. After that point, the prime number set underestimates the actual number of primes.

Something similar could occur with the Collatz conjecture: perhaps there is a huge number hidden deep in the number line that breaks the pattern observed so far.

A Proof for Almost All Numbers

Mathematicians have been searching for a conclusive proof for decades. The greatest progress was made in 2019 by Fields Medalist Terence Tao of the University of California, Los Angeles, when he proved that almost all starting values of natural numbers eventually end up at a value close to 1.

“Almost all” has a precise mathematical meaning: if you randomly select a natural number as a starting value, it has a 100 percent probability of ending up at 1. ( A zero-probability event, however, is not necessarily an impossible one .) That’s “about as close as one can get to the Collatz conjecture without actually solving it,” Tao said in a talk he gave in 2020 . Unfortunately, Tao’s method cannot generalize to all figures because it is based on statistical considerations.

All other approaches have led to a dead end as well. Perhaps that means the Collatz conjecture is wrong. “Maybe we should be spending more energy looking for counterexamples than we’re currently spending,” said mathematician Alex Kontorovich of Rutgers University in a video on the Veritasium YouTube channel .

Perhaps the Collatz conjecture will be determined true or false in the coming years. But there is another possibility: perhaps it truly is a problem that cannot be proven with available mathematical tools. In fact, in 1987 the late mathematician John Horton Conway investigated a generalization of the Collatz conjecture and found that iterative functions have properties that are unprovable. Perhaps this also applies to the Collatz conjecture. As simple as it may seem, it could be doomed to remain unsolved forever.

This article originally appeared in Spektrum der Wissenschaft and was reproduced with permission.

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Complex Problem Solving: What It Is and What It Is Not

Dietrich dörner.

1 Department of Psychology, University of Bamberg, Bamberg, Germany

Joachim Funke

2 Department of Psychology, Heidelberg University, Heidelberg, Germany

Computer-simulated scenarios have been part of psychological research on problem solving for more than 40 years. The shift in emphasis from simple toy problems to complex, more real-life oriented problems has been accompanied by discussions about the best ways to assess the process of solving complex problems. Psychometric issues such as reliable assessments and addressing correlations with other instruments have been in the foreground of these discussions and have left the content validity of complex problem solving in the background. In this paper, we return the focus to content issues and address the important features that define complex problems.

Succeeding in the 21st century requires many competencies, including creativity, life-long learning, and collaboration skills (e.g., National Research Council, 2011 ; Griffin and Care, 2015 ), to name only a few. One competence that seems to be of central importance is the ability to solve complex problems ( Mainzer, 2009 ). Mainzer quotes the Nobel prize winner Simon (1957) who wrote as early as 1957:

The capacity of the human mind for formulating and solving complex problems is very small compared with the size of the problem whose solution is required for objectively rational behavior in the real world or even for a reasonable approximation to such objective rationality. (p. 198)

The shift from well-defined to ill-defined problems came about as a result of a disillusion with the “general problem solver” ( Newell et al., 1959 ): The general problem solver was a computer software intended to solve all kind of problems that can be expressed through well-formed formulas. However, it soon became clear that this procedure was in fact a “special problem solver” that could only solve well-defined problems in a closed space. But real-world problems feature open boundaries and have no well-determined solution. In fact, the world is full of wicked problems and clumsy solutions ( Verweij and Thompson, 2006 ). As a result, solving well-defined problems and solving ill-defined problems requires different cognitive processes ( Schraw et al., 1995 ; but see Funke, 2010 ).

Well-defined problems have a clear set of means for reaching a precisely described goal state. For example: in a match-stick arithmetic problem, a person receives a false arithmetic expression constructed out of matchsticks (e.g., IV = III + III). According to the instructions, moving one of the matchsticks will make the equations true. Here, both the problem (find the appropriate stick to move) and the goal state (true arithmetic expression; solution is: VI = III + III) are defined clearly.

Ill-defined problems have no clear problem definition, their goal state is not defined clearly, and the means of moving towards the (diffusely described) goal state are not clear. For example: The goal state for solving the political conflict in the near-east conflict between Israel and Palestine is not clearly defined (living in peaceful harmony with each other?) and even if the conflict parties would agree on a two-state solution, this goal again leaves many issues unresolved. This type of problem is called a “complex problem” and is of central importance to this paper. All psychological processes that occur within individual persons and deal with the handling of such ill-defined complex problems will be subsumed under the umbrella term “complex problem solving” (CPS).

Systematic research on CPS started in the 1970s with observations of the behavior of participants who were confronted with computer simulated microworlds. For example, in one of those microworlds participants assumed the role of executives who were tasked to manage a company over a certain period of time (see Brehmer and Dörner, 1993 , for a discussion of this methodology). Today, CPS is an established concept and has even influenced large-scale assessments such as PISA (“Programme for International Student Assessment”), organized by the Organization for Economic Cooperation and Development ( OECD, 2014 ). According to the World Economic Forum, CPS is one of the most important competencies required in the future ( World Economic Forum, 2015 ). Numerous articles on the subject have been published in recent years, documenting the increasing research activity relating to this field. In the following collection of papers we list only those published in 2010 and later: theoretical papers ( Blech and Funke, 2010 ; Funke, 2010 ; Knauff and Wolf, 2010 ; Leutner et al., 2012 ; Selten et al., 2012 ; Wüstenberg et al., 2012 ; Greiff et al., 2013b ; Fischer and Neubert, 2015 ; Schoppek and Fischer, 2015 ), papers about measurement issues ( Danner et al., 2011a ; Greiff et al., 2012 , 2015a ; Alison et al., 2013 ; Gobert et al., 2015 ; Greiff and Fischer, 2013 ; Herde et al., 2016 ; Stadler et al., 2016 ), papers about applications ( Fischer and Neubert, 2015 ; Ederer et al., 2016 ; Tremblay et al., 2017 ), papers about differential effects ( Barth and Funke, 2010 ; Danner et al., 2011b ; Beckmann and Goode, 2014 ; Greiff and Neubert, 2014 ; Scherer et al., 2015 ; Meißner et al., 2016 ; Wüstenberg et al., 2016 ), one paper about developmental effects ( Frischkorn et al., 2014 ), one paper with a neuroscience background ( Osman, 2012 ) 1 , papers about cultural differences ( Güss and Dörner, 2011 ; Sonnleitner et al., 2014 ; Güss et al., 2015 ), papers about validity issues ( Goode and Beckmann, 2010 ; Greiff et al., 2013c ; Schweizer et al., 2013 ; Mainert et al., 2015 ; Funke et al., 2017 ; Greiff et al., 2017 , 2015b ; Kretzschmar et al., 2016 ; Kretzschmar, 2017 ), review papers and meta-analyses ( Osman, 2010 ; Stadler et al., 2015 ), and finally books ( Qudrat-Ullah, 2015 ; Csapó and Funke, 2017b ) and book chapters ( Funke, 2012 ; Hotaling et al., 2015 ; Funke and Greiff, 2017 ; Greiff and Funke, 2017 ; Csapó and Funke, 2017a ; Fischer et al., 2017 ; Molnàr et al., 2017 ; Tobinski and Fritz, 2017 ; Viehrig et al., 2017 ). In addition, a new “Journal of Dynamic Decision Making” (JDDM) has been launched ( Fischer et al., 2015 , 2016 ) to give the field an open-access outlet for research and discussion.

This paper aims to clarify aspects of validity: what should be meant by the term CPS and what not? This clarification seems necessary because misunderstandings in recent publications provide – from our point of view – a potentially misleading picture of the construct. We start this article with a historical review before attempting to systematize different positions. We conclude with a working definition.

Historical Review

The concept behind CPS goes back to the German phrase “komplexes Problemlösen” (CPS; the term “komplexes Problemlösen” was used as a book title by Funke, 1986 ). The concept was introduced in Germany by Dörner and colleagues in the mid-1970s (see Dörner et al., 1975 ; Dörner, 1975 ) for the first time. The German phrase was later translated to CPS in the titles of two edited volumes by Sternberg and Frensch (1991) and Frensch and Funke (1995a) that collected papers from different research traditions. Even though it looks as though the term was coined in the 1970s, Edwards (1962) used the term “dynamic decision making” to describe decisions that come in a sequence. He compared static with dynamic decision making, writing:

  • simple  In dynamic situations, a new complication not found in the static situations arises. The environment in which the decision is set may be changing, either as a function of the sequence of decisions, or independently of them, or both. It is this possibility of an environment which changes while you collect information about it which makes the task of dynamic decision theory so difficult and so much fun. (p. 60)

The ability to solve complex problems is typically measured via dynamic systems that contain several interrelated variables that participants need to alter. Early work (see, e.g., Dörner, 1980 ) used a simulation scenario called “Lohhausen” that contained more than 2000 variables that represented the activities of a small town: Participants had to take over the role of a mayor for a simulated period of 10 years. The simulation condensed these ten years to ten hours in real time. Later, researchers used smaller dynamic systems as scenarios either based on linear equations (see, e.g., Funke, 1993 ) or on finite state automata (see, e.g., Buchner and Funke, 1993 ). In these contexts, CPS consisted of the identification and control of dynamic task environments that were previously unknown to the participants. Different task environments came along with different degrees of fidelity ( Gray, 2002 ).

According to Funke (2012) , the typical attributes of complex systems are (a) complexity of the problem situation which is usually represented by the sheer number of involved variables; (b) connectivity and mutual dependencies between involved variables; (c) dynamics of the situation, which reflects the role of time and developments within a system; (d) intransparency (in part or full) about the involved variables and their current values; and (e) polytely (greek term for “many goals”), representing goal conflicts on different levels of analysis. This mixture of features is similar to what is called VUCA (volatility, uncertainty, complexity, ambiguity) in modern approaches to management (e.g., Mack et al., 2016 ).

In his evaluation of the CPS movement, Sternberg (1995) compared (young) European approaches to CPS with (older) American research on expertise. His analysis of the differences between the European and American traditions shows advantages but also potential drawbacks for each side. He states (p. 301): “I believe that although there are problems with the European approach, it deals with some fundamental questions that American research scarcely addresses.” So, even though the echo of the European approach did not enjoy strong resonance in the US at that time, it was valued by scholars like Sternberg and others. Before attending to validity issues, we will first present a short review of different streams.

Different Approaches to CPS

In the short history of CPS research, different approaches can be identified ( Buchner, 1995 ; Fischer et al., 2017 ). To systematize, we differentiate between the following five lines of research:

  • simple (a) The search for individual differences comprises studies identifying interindividual differences that affect the ability to solve complex problems. This line of research is reflected, for example, in the early work by Dörner et al. (1983) and their “Lohhausen” study. Here, naïve student participants took over the role of the mayor of a small simulated town named Lohhausen for a simulation period of ten years. According to the results of the authors, it is not intelligence (as measured by conventional IQ tests) that predicts performance, but it is the ability to stay calm in the face of a challenging situation and the ability to switch easily between an analytic mode of processing and a more holistic one.
  • simple (b) The search for cognitive processes deals with the processes behind understanding complex dynamic systems. Representative of this line of research is, for example, Berry and Broadbent’s (1984) work on implicit and explicit learning processes when people interact with a dynamic system called “Sugar Production”. They found that those who perform best in controlling a dynamic system can do so implicitly, without explicit knowledge of details regarding the systems’ relations.
  • simple (c) The search for system factors seeks to identify the aspects of dynamic systems that determine the difficulty of complex problems and make some problems harder than others. Representative of this line of research is, for example, work by Funke (1985) , who systematically varied the number of causal effects within a dynamic system or the presence/absence of eigendynamics. He found, for example, that solution quality decreases as the number of systems relations increases.
  • simple (d) The psychometric approach develops measurement instruments that can be used as an alternative to classical IQ tests, as something that goes “beyond IQ”. The MicroDYN approach ( Wüstenberg et al., 2012 ) is representative for this line of research that presents an alternative to reasoning tests (like Raven matrices). These authors demonstrated that a small improvement in predicting school grade point average beyond reasoning is possible with MicroDYN tests.
  • simple (e) The experimental approach explores CPS under different experimental conditions. This approach uses CPS assessment instruments to test hypotheses derived from psychological theories and is sometimes used in research about cognitive processes (see above). Exemplary for this line of research is the work by Rohe et al. (2016) , who test the usefulness of “motto goals” in the context of complex problems compared to more traditional learning and performance goals. Motto goals differ from pure performance goals by activating positive affect and should lead to better goal attainment especially in complex situations (the mentioned study found no effect).

To be clear: these five approaches are not mutually exclusive and do overlap. But the differentiation helps to identify different research communities and different traditions. These communities had different opinions about scaling complexity.

The Race for Complexity: Use of More and More Complex Systems

In the early years of CPS research, microworlds started with systems containing about 20 variables (“Tailorshop”), soon reached 60 variables (“Moro”), and culminated in systems with about 2000 variables (“Lohhausen”). This race for complexity ended with the introduction of the concept of “minimal complex systems” (MCS; Greiff and Funke, 2009 ; Funke and Greiff, 2017 ), which ushered in a search for the lower bound of complexity instead of the higher bound, which could not be defined as easily. The idea behind this concept was that whereas the upper limits of complexity are unbound, the lower limits might be identifiable. Imagine starting with a simple system containing two variables with a simple linear connection between them; then, step by step, increase the number of variables and/or the type of connections. One soon reaches a point where the system can no longer be considered simple and has become a “complex system”. This point represents a minimal complex system. Despite some research having been conducted in this direction, the point of transition from simple to complex has not been identified clearly as of yet.

Some years later, the original “minimal complex systems” approach ( Greiff and Funke, 2009 ) shifted to the “multiple complex systems” approach ( Greiff et al., 2013a ). This shift is more than a slight change in wording: it is important because it taps into the issue of validity directly. Minimal complex systems have been introduced in the context of challenges from large-scale assessments like PISA 2012 that measure new aspects of problem solving, namely interactive problems besides static problem solving ( Greiff and Funke, 2017 ). PISA 2012 required test developers to remain within testing time constraints (given by the school class schedule). Also, test developers needed a large item pool for the construction of a broad class of problem solving items. It was clear from the beginning that MCS deal with simple dynamic situations that require controlled interaction: the exploration and control of simple ticket machines, simple mobile phones, or simple MP3 players (all of these example domains were developed within PISA 2012) – rather than really complex situations like managerial or political decision making.

As a consequence of this subtle but important shift in interpreting the letters MCS, the definition of CPS became a subject of debate recently ( Funke, 2014a ; Greiff and Martin, 2014 ; Funke et al., 2017 ). In the words of Funke (2014b , p. 495):

  • simple  It is funny that problems that nowadays come under the term ‘CPS’, are less complex (in terms of the previously described attributes of complex situations) than at the beginning of this new research tradition. The emphasis on psychometric qualities has led to a loss of variety. Systems thinking requires more than analyzing models with two or three linear equations – nonlinearity, cyclicity, rebound effects, etc. are inherent features of complex problems and should show up at least in some of the problems used for research and assessment purposes. Minimal complex systems run the danger of becoming minimal valid systems.

Searching for minimal complex systems is not the same as gaining insight into the way how humans deal with complexity and uncertainty. For psychometric purposes, it is appropriate to reduce complexity to a minimum; for understanding problem solving under conditions of overload, intransparency, and dynamics, it is necessary to realize those attributes with reasonable strength. This aspect is illustrated in the next section.

Importance of the Validity Issue

The most important reason for discussing the question of what complex problem solving is and what it is not stems from its phenomenology: if we lose sight of our phenomena, we are no longer doing good psychology. The relevant phenomena in the context of complex problems encompass many important aspects. In this section, we discuss four phenomena that are specific to complex problems. We consider these phenomena as critical for theory development and for the construction of assessment instruments (i.e., microworlds). These phenomena require theories for explaining them and they require assessment instruments eliciting them in a reliable way.

The first phenomenon is the emergency reaction of the intellectual system ( Dörner, 1980 ): When dealing with complex systems, actors tend to (a) reduce their intellectual level by decreasing self-reflections, by decreasing their intentions, by stereotyping, and by reducing their realization of intentions, (b) they show a tendency for fast action with increased readiness for risk, with increased violations of rules, and with increased tendency to escape the situation, and (c) they degenerate their hypotheses formation by construction of more global hypotheses and reduced tests of hypotheses, by increasing entrenchment, and by decontextualizing their goals. This phenomenon illustrates the strong connection between cognition, emotion, and motivation that has been emphasized by Dörner (see, e.g., Dörner and Güss, 2013 ) from the beginning of his research tradition; the emergency reaction reveals a shift in the mode of information processing under the pressure of complexity.

The second phenomenon comprises cross-cultural differences with respect to strategy use ( Strohschneider and Güss, 1999 ; Güss and Wiley, 2007 ; Güss et al., 2015 ). Results from complex task environments illustrate the strong influence of context and background knowledge to an extent that cannot be found for knowledge-poor problems. For example, in a comparison between Brazilian and German participants, it turned out that Brazilians accept the given problem descriptions and are more optimistic about the results of their efforts, whereas Germans tend to inquire more about the background of the problems and take a more active approach but are less optimistic (according to Strohschneider and Güss, 1998 , p. 695).

The third phenomenon relates to failures that occur during the planning and acting stages ( Jansson, 1994 ; Ramnarayan et al., 1997 ), illustrating that rational procedures seem to be unlikely to be used in complex situations. The potential for failures ( Dörner, 1996 ) rises with the complexity of the problem. Jansson (1994) presents seven major areas for failures with complex situations: acting directly on current feedback; insufficient systematization; insufficient control of hypotheses and strategies; lack of self-reflection; selective information gathering; selective decision making; and thematic vagabonding.

The fourth phenomenon describes (a lack of) training and transfer effects ( Kretzschmar and Süß, 2015 ), which again illustrates the context dependency of strategies and knowledge (i.e., there is no strategy that is so universal that it can be used in many different problem situations). In their own experiment, the authors could show training effects only for knowledge acquisition, not for knowledge application. Only with specific feedback, performance in complex environments can be increased ( Engelhart et al., 2017 ).

These four phenomena illustrate why the type of complexity (or degree of simplicity) used in research really matters. Furthermore, they demonstrate effects that are specific for complex problems, but not for toy problems. These phenomena direct the attention to the important question: does the stimulus material used (i.e., the computer-simulated microworld) tap and elicit the manifold of phenomena described above?

Dealing with partly unknown complex systems requires courage, wisdom, knowledge, grit, and creativity. In creativity research, “little c” and “BIG C” are used to differentiate between everyday creativity and eminent creativity ( Beghetto and Kaufman, 2007 ; Kaufman and Beghetto, 2009 ). Everyday creativity is important for solving everyday problems (e.g., finding a clever fix for a broken spoke on my bicycle), eminent creativity changes the world (e.g., inventing solar cells for energy production). Maybe problem solving research should use a similar differentiation between “little p” and “BIG P” to mark toy problems on the one side and big societal challenges on the other. The question then remains: what can we learn about BIG P by studying little p? What phenomena are present in both types, and what phenomena are unique to each of the two extremes?

Discussing research on CPS requires reflecting on the field’s research methods. Even if the experimental approach has been successful for testing hypotheses (for an overview of older work, see Funke, 1995 ), other methods might provide additional and novel insights. Complex phenomena require complex approaches to understand them. The complex nature of complex systems imposes limitations on psychological experiments: The more complex the environments, the more difficult is it to keep conditions under experimental control. And if experiments have to be run in labs one should bring enough complexity into the lab to establish the phenomena mentioned, at least in part.

There are interesting options to be explored (again): think-aloud protocols , which have been discredited for many years ( Nisbett and Wilson, 1977 ) and yet are a valuable source for theory testing ( Ericsson and Simon, 1983 ); introspection ( Jäkel and Schreiber, 2013 ), which seems to be banned from psychological methods but nevertheless offers insights into thought processes; the use of life-streaming ( Wendt, 2017 ), a medium in which streamers generate a video stream of think-aloud data in computer-gaming; political decision-making ( Dhami et al., 2015 ) that demonstrates error-proneness in groups; historical case studies ( Dörner and Güss, 2011 ) that give insights into the thinking styles of political leaders; the use of the critical incident technique ( Reuschenbach, 2008 ) to construct complex scenarios; and simulations with different degrees of fidelity ( Gray, 2002 ).

The methods tool box is full of instruments that have to be explored more carefully before any individual instrument receives a ban or research narrows its focus to only one paradigm for data collection. Brehmer and Dörner (1993) discussed the tensions between “research in the laboratory and research in the field”, optimistically concluding “that the new methodology of computer-simulated microworlds will provide us with the means to bridge the gap between the laboratory and the field” (p. 183). The idea behind this optimism was that computer-simulated scenarios would bring more complexity from the outside world into the controlled lab environment. But this is not true for all simulated scenarios. In his paper on simulated environments, Gray (2002) differentiated computer-simulated environments with respect to three dimensions: (1) tractability (“the more training subjects require before they can use a simulated task environment, the less tractable it is”, p. 211), correspondence (“High correspondence simulated task environments simulate many aspects of one task environment. Low correspondence simulated task environments simulate one aspect of many task environments”, p. 214), and engagement (“A simulated task environment is engaging to the degree to which it involves and occupies the participants; that is, the degree to which they agree to take it seriously”, p. 217). But the mere fact that a task is called a “computer-simulated task environment” does not mean anything specific in terms of these three dimensions. This is one of several reasons why we should differentiate between those studies that do not address the core features of CPS and those that do.

What is not CPS?

Even though a growing number of references claiming to deal with complex problems exist (e.g., Greiff and Wüstenberg, 2015 ; Greiff et al., 2016 ), it would be better to label the requirements within these tasks “dynamic problem solving,” as it has been done adequately in earlier work ( Greiff et al., 2012 ). The dynamics behind on-off-switches ( Thimbleby, 2007 ) are remarkable but not really complex. Small nonlinear systems that exhibit stunningly complex and unstable behavior do exist – but they are not used in psychometric assessments of so-called CPS. There are other small systems (like MicroDYN scenarios: Greiff and Wüstenberg, 2014 ) that exhibit simple forms of system behavior that are completely predictable and stable. This type of simple systems is used frequently. It is even offered commercially as a complex problem-solving test called COMPRO ( Greiff and Wüstenberg, 2015 ) for business applications. But a closer look reveals that the label is not used correctly; within COMPRO, the used linear equations are far from being complex and the system can be handled properly by using only one strategy (see for more details Funke et al., 2017 ).

Why do simple linear systems not fall within CPS? At the surface, nonlinear and linear systems might appear similar because both only include 3–5 variables. But the difference is in terms of systems behavior as well as strategies and learning. If the behavior is simple (as in linear systems where more input is related to more output and vice versa), the system can be easily understood (participants in the MicroDYN world have 3 minutes to explore a complex system). If the behavior is complex (as in systems that contain strange attractors or negative feedback loops), things become more complicated and much more observation is needed to identify the hidden structure of the unknown system ( Berry and Broadbent, 1984 ; Hundertmark et al., 2015 ).

Another issue is learning. If tasks can be solved using a single (and not so complicated) strategy, steep learning curves are to be expected. The shift from problem solving to learned routine behavior occurs rapidly, as was demonstrated by Luchins (1942) . In his water jar experiments, participants quickly acquired a specific strategy (a mental set) for solving certain measurement problems that they later continued applying to problems that would have allowed for easier approaches. In the case of complex systems, learning can occur only on very general, abstract levels because it is difficult for human observers to make specific predictions. Routines dealing with complex systems are quite different from routines relating to linear systems.

What should not be studied under the label of CPS are pure learning effects, multiple-cue probability learning, or tasks that can be solved using a single strategy. This last issue is a problem for MicroDYN tasks that rely strongly on the VOTAT strategy (“vary one thing at a time”; see Tschirgi, 1980 ). In real-life, it is hard to imagine a business manager trying to solve her or his problems by means of VOTAT.

What is CPS?

In the early days of CPS research, planet Earth’s dynamics and complexities gained attention through such books as “The limits to growth” ( Meadows et al., 1972 ) and “Beyond the limits” ( Meadows et al., 1992 ). In the current decade, for example, the World Economic Forum (2016) attempts to identify the complexities and risks of our modern world. In order to understand the meaning of complexity and uncertainty, taking a look at the worlds’ most pressing issues is helpful. Searching for strategies to cope with these problems is a difficult task: surely there is no place for the simple principle of “vary-one-thing-at-a-time” (VOTAT) when it comes to global problems. The VOTAT strategy is helpful in the context of simple problems ( Wüstenberg et al., 2014 ); therefore, whether or not VOTAT is helpful in a given problem situation helps us distinguish simple from complex problems.

Because there exist no clear-cut strategies for complex problems, typical failures occur when dealing with uncertainty ( Dörner, 1996 ; Güss et al., 2015 ). Ramnarayan et al. (1997) put together a list of generic errors (e.g., not developing adequate action plans; lack of background control; learning from experience blocked by stereotype knowledge; reactive instead of proactive action) that are typical of knowledge-rich complex systems but cannot be found in simple problems.

Complex problem solving is not a one-dimensional, low-level construct. On the contrary, CPS is a multi-dimensional bundle of competencies existing at a high level of abstraction, similar to intelligence (but going beyond IQ). As Funke et al. (2018) state: “Assessment of transversal (in educational contexts: cross-curricular) competencies cannot be done with one or two types of assessment. The plurality of skills and competencies requires a plurality of assessment instruments.”

There are at least three different aspects of complex systems that are part of our understanding of a complex system: (1) a complex system can be described at different levels of abstraction; (2) a complex system develops over time, has a history, a current state, and a (potentially unpredictable) future; (3) a complex system is knowledge-rich and activates a large semantic network, together with a broad list of potential strategies (domain-specific as well as domain-general).

Complex problem solving is not only a cognitive process but is also an emotional one ( Spering et al., 2005 ; Barth and Funke, 2010 ) and strongly dependent on motivation (low-stakes versus high-stakes testing; see Hermes and Stelling, 2016 ).

Furthermore, CPS is a dynamic process unfolding over time, with different phases and with more differentiation than simply knowledge acquisition and knowledge application. Ideally, the process should entail identifying problems (see Dillon, 1982 ; Lee and Cho, 2007 ), even if in experimental settings, problems are provided to participants a priori . The more complex and open a given situation, the more options can be generated (T. S. Schweizer et al., 2016 ). In closed problems, these processes do not occur in the same way.

In analogy to the difference between formative (process-oriented) and summative (result-oriented) assessment ( Wiliam and Black, 1996 ; Bennett, 2011 ), CPS should not be reduced to the mere outcome of a solution process. The process leading up to the solution, including detours and errors made along the way, might provide a more differentiated impression of a person’s problem-solving abilities and competencies than the final result of such a process. This is one of the reasons why CPS environments are not, in fact, complex intelligence tests: research on CPS is not only about the outcome of the decision process, but it is also about the problem-solving process itself.

Complex problem solving is part of our daily life: finding the right person to share one’s life with, choosing a career that not only makes money, but that also makes us happy. Of course, CPS is not restricted to personal problems – life on Earth gives us many hard nuts to crack: climate change, population growth, the threat of war, the use and distribution of natural resources. In sum, many societal challenges can be seen as complex problems. To reduce that complexity to a one-hour lab activity on a random Friday afternoon puts it out of context and does not address CPS issues.

Theories about CPS should specify which populations they apply to. Across populations, one thing to consider is prior knowledge. CPS research with experts (e.g., Dew et al., 2009 ) is quite different from problem solving research using tasks that intentionally do not require any specific prior knowledge (see, e.g., Beckmann and Goode, 2014 ).

More than 20 years ago, Frensch and Funke (1995b) defined CPS as follows:

  • simple  CPS occurs to overcome barriers between a given state and a desired goal state by means of behavioral and/or cognitive, multi-step activities. The given state, goal state, and barriers between given state and goal state are complex, change dynamically during problem solving, and are intransparent. The exact properties of the given state, goal state, and barriers are unknown to the solver at the outset. CPS implies the efficient interaction between a solver and the situational requirements of the task, and involves a solver’s cognitive, emotional, personal, and social abilities and knowledge. (p. 18)

The above definition is rather formal and does not account for content or relations between the simulation and the real world. In a sense, we need a new definition of CPS that addresses these issues. Based on our previous arguments, we propose the following working definition:

  • simple  Complex problem solving is a collection of self-regulated psychological processes and activities necessary in dynamic environments to achieve ill-defined goals that cannot be reached by routine actions. Creative combinations of knowledge and a broad set of strategies are needed. Solutions are often more bricolage than perfect or optimal. The problem-solving process combines cognitive, emotional, and motivational aspects, particularly in high-stakes situations. Complex problems usually involve knowledge-rich requirements and collaboration among different persons.

The main differences to the older definition lie in the emphasis on (a) the self-regulation of processes, (b) creativity (as opposed to routine behavior), (c) the bricolage type of solution, and (d) the role of high-stakes challenges. Our new definition incorporates some aspects that have been discussed in this review but were not reflected in the 1995 definition, which focused on attributes of complex problems like dynamics or intransparency.

This leads us to the final reflection about the role of CPS for dealing with uncertainty and complexity in real life. We will distinguish thinking from reasoning and introduce the sense of possibility as an important aspect of validity.

CPS as Combining Reasoning and Thinking in an Uncertain Reality

Leading up to the Battle of Borodino in Leo Tolstoy’s novel “War and Peace”, Prince Andrei Bolkonsky explains the concept of war to his friend Pierre. Pierre expects war to resemble a game of chess: You position the troops and attempt to defeat your opponent by moving them in different directions.

“Far from it!”, Andrei responds. “In chess, you know the knight and his moves, you know the pawn and his combat strength. While in war, a battalion is sometimes stronger than a division and sometimes weaker than a company; it all depends on circumstances that can never be known. In war, you do not know the position of your enemy; some things you might be able to observe, some things you have to divine (but that depends on your ability to do so!) and many things cannot even be guessed at. In chess, you can see all of your opponent’s possible moves. In war, that is impossible. If you decide to attack, you cannot know whether the necessary conditions are met for you to succeed. Many a time, you cannot even know whether your troops will follow your orders…”

In essence, war is characterized by a high degree of uncertainty. A good commander (or politician) can add to that what he or she sees, tentatively fill in the blanks – and not just by means of logical deduction but also by intelligently bridging missing links. A bad commander extrapolates from what he sees and thus arrives at improper conclusions.

Many languages differentiate between two modes of mentalizing; for instance, the English language distinguishes between ‘thinking’ and ‘reasoning’. Reasoning denotes acute and exact mentalizing involving logical deductions. Such deductions are usually based on evidence and counterevidence. Thinking, however, is what is required to write novels. It is the construction of an initially unknown reality. But it is not a pipe dream, an unfounded process of fabrication. Rather, thinking asks us to imagine reality (“Wirklichkeitsfantasie”). In other words, a novelist has to possess a “sense of possibility” (“Möglichkeitssinn”, Robert Musil; in German, sense of possibility is often used synonymously with imagination even though imagination is not the same as sense of possibility, for imagination also encapsulates the impossible). This sense of possibility entails knowing the whole (or several wholes) or being able to construe an unknown whole that could accommodate a known part. The whole has to align with sociological and geographical givens, with the mentality of certain peoples or groups, and with the laws of physics and chemistry. Otherwise, the entire venture is ill-founded. A sense of possibility does not aim for the moon but imagines something that might be possible but has not been considered possible or even potentially possible so far.

Thinking is a means to eliminate uncertainty. This process requires both of the modes of thinking we have discussed thus far. Economic, political, or ecological decisions require us to first consider the situation at hand. Though certain situational aspects can be known, but many cannot. In fact, von Clausewitz (1832) posits that only about 25% of the necessary information is available when a military decision needs to be made. Even then, there is no way to guarantee that whatever information is available is also correct: Even if a piece of information was completely accurate yesterday, it might no longer apply today.

Once our sense of possibility has helped grasping a situation, problem solvers need to call on their reasoning skills. Not every situation requires the same action, and we may want to act this way or another to reach this or that goal. This appears logical, but it is a logic based on constantly shifting grounds: We cannot know whether necessary conditions are met, sometimes the assumptions we have made later turn out to be incorrect, and sometimes we have to revise our assumptions or make completely new ones. It is necessary to constantly switch between our sense of possibility and our sense of reality, that is, to switch between thinking and reasoning. It is an arduous process, and some people handle it well, while others do not.

If we are to believe Tuchman’s (1984) book, “The March of Folly”, most politicians and commanders are fools. According to Tuchman, not much has changed in the 3300 years that have elapsed since the misguided Trojans decided to welcome the left-behind wooden horse into their city that would end up dismantling Troy’s defensive walls. The Trojans, too, had been warned, but decided not to heed the warning. Although Laocoön had revealed the horse’s true nature to them by attacking it with a spear, making the weapons inside the horse ring, the Trojans refused to see the forest for the trees. They did not want to listen, they wanted the war to be over, and this desire ended up shaping their perception.

The objective of psychology is to predict and explain human actions and behavior as accurately as possible. However, thinking cannot be investigated by limiting its study to neatly confined fractions of reality such as the realms of propositional logic, chess, Go tasks, the Tower of Hanoi, and so forth. Within these systems, there is little need for a sense of possibility. But a sense of possibility – the ability to divine and construe an unknown reality – is at least as important as logical reasoning skills. Not researching the sense of possibility limits the validity of psychological research. All economic and political decision making draws upon this sense of possibility. By not exploring it, psychological research dedicated to the study of thinking cannot further the understanding of politicians’ competence and the reasons that underlie political mistakes. Christopher Clark identifies European diplomats’, politicians’, and commanders’ inability to form an accurate representation of reality as a reason for the outbreak of World War I. According to Clark’s (2012) book, “The Sleepwalkers”, the politicians of the time lived in their own make-believe world, wrongfully assuming that it was the same world everyone else inhabited. If CPS research wants to make significant contributions to the world, it has to acknowledge complexity and uncertainty as important aspects of it.

For more than 40 years, CPS has been a new subject of psychological research. During this time period, the initial emphasis on analyzing how humans deal with complex, dynamic, and uncertain situations has been lost. What is subsumed under the heading of CPS in modern research has lost the original complexities of real-life problems. From our point of view, the challenges of the 21st century require a return to the origins of this research tradition. We would encourage researchers in the field of problem solving to come back to the original ideas. There is enough complexity and uncertainty in the world to be studied. Improving our understanding of how humans deal with these global and pressing problems would be a worthwhile enterprise.

Author Contributions

JF drafted a first version of the manuscript, DD added further text and commented on the draft. JF finalized the manuscript.

Authors Note

After more than 40 years of controversial discussions between both authors, this is the first joint paper. We are happy to have done this now! We have found common ground!

Conflict of Interest Statement

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Acknowledgments

The authors thank the Deutsche Forschungsgemeinschaft (DFG) for the continuous support of their research over many years. Thanks to Daniel Holt for his comments on validity issues, thanks to Julia Nolte who helped us by translating German text excerpts into readable English and helped us, together with Keri Hartman, to improve our style and grammar – thanks for that! We also thank the two reviewers for their helpful critical comments on earlier versions of this manuscript. Finally, we acknowledge financial support by Deutsche Forschungsgemeinschaft and Ruprecht-Karls-Universität Heidelberg within their funding programme Open Access Publishing .

1 The fMRI-paper from Anderson (2012) uses the term “complex problem solving” for tasks that do not fall in our understanding of CPS and is therefore excluded from this list.

  • Alison L., van den Heuvel C., Waring S., Power N., Long A., O’Hara T., et al. (2013). Immersive simulated learning environments for researching critical incidents: a knowledge synthesis of the literature and experiences of studying high-risk strategic decision making. J. Cogn. Eng. Deci. Mak. 7 255–272. 10.1177/1555343412468113 [ CrossRef ] [ Google Scholar ]
  • Anderson J. R. (2012). Tracking problem solving by multivariate pattern analysis and hidden markov model algorithms. Neuropsychologia 50 487–498. 10.1016/j.neuropsychologia.2011.07.025 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Barth C. M., Funke J. (2010). Negative affective environments improve complex solving performance. Cogn. Emot. 24 1259–1268. 10.1080/02699930903223766 [ CrossRef ] [ Google Scholar ]
  • Beckmann J. F., Goode N. (2014). The benefit of being naïve and knowing it: the unfavourable impact of perceived context familiarity on learning in complex problem solving tasks. Instruct. Sci. 42 271–290. 10.1007/s11251-013-9280-7 [ CrossRef ] [ Google Scholar ]
  • Beghetto R. A., Kaufman J. C. (2007). Toward a broader conception of creativity: a case for “mini-c” creativity. Psychol. Aesthetics Creat. Arts 1 73–79. 10.1037/1931-3896.1.2.73 [ CrossRef ] [ Google Scholar ]
  • Bennett R. E. (2011). Formative assessment: a critical review. Assess. Educ. Princ. Policy Pract. 18 5–25. 10.1080/0969594X.2010.513678 [ CrossRef ] [ Google Scholar ]
  • Berry D. C., Broadbent D. E. (1984). On the relationship between task performance and associated verbalizable knowledge. Q. J. Exp. Psychol. 36 209–231. 10.1080/14640748408402156 [ CrossRef ] [ Google Scholar ]
  • Blech C., Funke J. (2010). You cannot have your cake and eat it, too: how induced goal conflicts affect complex problem solving. Open Psychol. J. 3 42–53. 10.2174/1874350101003010042 [ CrossRef ] [ Google Scholar ]
  • Brehmer B., Dörner D. (1993). Experiments with computer-simulated microworlds: escaping both the narrow straits of the laboratory and the deep blue sea of the field study. Comput. Hum. Behav. 9 171–184. 10.1016/0747-5632(93)90005-D [ CrossRef ] [ Google Scholar ]
  • Buchner A. (1995). “Basic topics and approaches to the study of complex problem solving,” in Complex Problem Solving: The European Perspective , eds Frensch P. A., Funke J. (Hillsdale, NJ: Erlbaum; ), 27–63. [ Google Scholar ]
  • Buchner A., Funke J. (1993). Finite state automata: dynamic task environments in problem solving research. Q. J. Exp. Psychol. 46A , 83–118. 10.1080/14640749308401068 [ CrossRef ] [ Google Scholar ]
  • Clark C. (2012). The Sleepwalkers: How Europe Went to War in 1914 . London: Allen Lane. [ Google Scholar ]
  • Csapó B., Funke J. (2017a). “The development and assessment of problem solving in 21st-century schools,” in The Nature of Problem Solving: Using Research to Inspire 21st Century Learning , eds Csapó B., Funke J. (Paris: OECD Publishing; ), 19–31. [ Google Scholar ]
  • Csapó B., Funke J. (eds) (2017b). The Nature of Problem Solving. Using Research to Inspire 21st Century Learning. Paris: OECD Publishing. [ Google Scholar ]
  • Danner D., Hagemann D., Holt D. V., Hager M., Schankin A., Wüstenberg S., et al. (2011a). Measuring performance in dynamic decision making. Reliability and validity of the Tailorshop simulation. J. Ind. Differ. 32 225–233. 10.1027/1614-0001/a000055 [ CrossRef ] [ Google Scholar ]
  • Danner D., Hagemann D., Schankin A., Hager M., Funke J. (2011b). Beyond IQ: a latent state-trait analysis of general intelligence, dynamic decision making, and implicit learning. Intelligence 39 323–334. 10.1016/j.intell.2011.06.004 [ CrossRef ] [ Google Scholar ]
  • Dew N., Read S., Sarasvathy S. D., Wiltbank R. (2009). Effectual versus predictive logics in entrepreneurial decision-making: differences between experts and novices. J. Bus. Ventur. 24 287–309. 10.1016/j.jbusvent.2008.02.002 [ CrossRef ] [ Google Scholar ]
  • Dhami M. K., Mandel D. R., Mellers B. A., Tetlock P. E. (2015). Improving intelligence analysis with decision science. Perspect. Psychol. Sci. 10 753–757. 10.1177/1745691615598511 [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Dillon J. T. (1982). Problem finding and solving. J. Creat. Behav. 16 97–111. 10.1002/j.2162-6057.1982.tb00326.x [ CrossRef ] [ Google Scholar ]
  • Dörner D. (1975). Wie Menschen eine Welt verbessern wollten [How people wanted to improve a world]. Bild Der Wissenschaft 12 48–53. [ Google Scholar ]
  • Dörner D. (1980). On the difficulties people have in dealing with complexity. Simulat. Gam. 11 87–106. 10.1177/104687818001100108 [ CrossRef ] [ Google Scholar ]
  • Dörner D. (1996). The Logic of Failure: Recognizing and Avoiding Error in Complex Situations. New York, NY: Basic Books. [ Google Scholar ]
  • Dörner D., Drewes U., Reither F. (1975). “Über das Problemlösen in sehr komplexen Realitätsbereichen,” in Bericht über den 29. Kongreß der DGfPs in Salzburg 1974 Band 1 , ed. Tack W. H. (Göttingen: Hogrefe; ), 339–340. [ Google Scholar ]
  • Dörner D., Güss C. D. (2011). A psychological analysis of Adolf Hitler’s decision making as commander in chief: summa confidentia et nimius metus. Rev. Gen. Psychol. 15 37–49. 10.1037/a0022375 [ CrossRef ] [ Google Scholar ]
  • Dörner D., Güss C. D. (2013). PSI: a computational architecture of cognition, motivation, and emotion. Rev. Gen. Psychol. 17 297–317. 10.1037/a0032947 [ CrossRef ] [ Google Scholar ]
  • Dörner D., Kreuzig H. W., Reither F., Stäudel T. (1983). Lohhausen. Vom Umgang mit Unbestimmtheit und Komplexität. Bern: Huber. [ Google Scholar ]
  • Ederer P., Patt A., Greiff S. (2016). Complex problem-solving skills and innovativeness – evidence from occupational testing and regional data. Eur. J. Educ. 51 244–256. 10.1111/ejed.12176 [ CrossRef ] [ Google Scholar ]
  • Edwards W. (1962). Dynamic decision theory and probabiIistic information processing. Hum. Factors 4 59–73. 10.1177/001872086200400201 [ CrossRef ] [ Google Scholar ]
  • Engelhart M., Funke J., Sager S. (2017). A web-based feedback study on optimization-based training and analysis of human decision making. J. Dynamic Dec. Mak. 3 1–23. [ Google Scholar ]
  • Ericsson K. A., Simon H. A. (1983). Protocol Analysis: Verbal Reports As Data. Cambridge, MA: Bradford. [ Google Scholar ]
  • Fischer A., Greiff S., Funke J. (2017). “The history of complex problem solving,” in The Nature of Problem Solving: Using Research to Inspire 21st Century Learning , eds Csapó B., Funke J. (Paris: OECD Publishing; ), 107–121. [ Google Scholar ]
  • Fischer A., Holt D. V., Funke J. (2015). Promoting the growing field of dynamic decision making. J. Dynamic Decis. Mak. 1 1–3. 10.11588/jddm.2015.1.23807 [ CrossRef ] [ Google Scholar ]
  • Fischer A., Holt D. V., Funke J. (2016). The first year of the “journal of dynamic decision making.” J. Dynamic Decis. Mak. 2 1–2. 10.11588/jddm.2016.1.28995 [ CrossRef ] [ Google Scholar ]
  • Fischer A., Neubert J. C. (2015). The multiple faces of complex problems: a model of problem solving competency and its implications for training and assessment. J. Dynamic Decis. Mak. 1 1–14. 10.11588/jddm.2015.1.23945 [ CrossRef ] [ Google Scholar ]
  • Frensch P. A., Funke J. (eds) (1995a). Complex Problem Solving: The European Perspective. Hillsdale, NJ: Erlbaum. [ Google Scholar ]
  • Frensch P. A., Funke J. (1995b). “Definitions, traditions, and a general framework for understanding complex problem solving,” in Complex Problem Solving: The European Perspective , eds Frensch P. A., Funke J. (Hillsdale, NJ: Lawrence Erlbaum; ), 3–25. [ Google Scholar ]
  • Frischkorn G. T., Greiff S., Wüstenberg S. (2014). The development of complex problem solving in adolescence: a latent growth curve analysis. J. Educ. Psychol. 106 1004–1020. 10.1037/a0037114 [ CrossRef ] [ Google Scholar ]
  • Funke J. (1985). Steuerung dynamischer Systeme durch Aufbau und Anwendung subjektiver Kausalmodelle. Z. Psychol. 193 435–457. [ Google Scholar ]
  • Funke J. (1986). Komplexes Problemlösen - Bestandsaufnahme und Perspektiven [Complex Problem Solving: Survey and Perspectives]. Heidelberg: Springer. [ Google Scholar ]
  • Funke J. (1993). “Microworlds based on linear equation systems: a new approach to complex problem solving and experimental results,” in The Cognitive Psychology of Knowledge , eds Strube G., Wender K.-F. (Amsterdam: Elsevier Science Publishers; ), 313–330. [ Google Scholar ]
  • Funke J. (1995). “Experimental research on complex problem solving,” in Complex Problem Solving: The European Perspective , eds Frensch P. A., Funke J. (Hillsdale, NJ: Erlbaum; ), 243–268. [ Google Scholar ]
  • Funke J. (2010). Complex problem solving: a case for complex cognition? Cogn. Process. 11 133–142. 10.1007/s10339-009-0345-0 [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Funke J. (2012). “Complex problem solving,” in Encyclopedia of the Sciences of Learning Vol. 38 ed. Seel N. M. (Heidelberg: Springer; ), 682–685. [ Google Scholar ]
  • Funke J. (2014a). Analysis of minimal complex systems and complex problem solving require different forms of causal cognition. Front. Psychol. 5 : 739 10.3389/fpsyg.2014.00739 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Funke J. (2014b). “Problem solving: what are the important questions?,” in Proceedings of the 36th Annual Conference of the Cognitive Science Society , eds Bello P., Guarini M., McShane M., Scassellati B. (Austin, TX: Cognitive Science Society; ), 493–498. [ Google Scholar ]
  • Funke J., Fischer A., Holt D. V. (2017). When less is less: solving multiple simple problems is not complex problem solving—A comment on Greiff et al. (2015). J. Intell. 5 : 5 10.3390/jintelligence5010005 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Funke J., Fischer A., Holt D. V. (2018). “Competencies for complexity: problem solving in the 21st century,” in Assessment and Teaching of 21st Century Skills , eds Care E., Griffin P., Wilson M. (Dordrecht: Springer; ), 3. [ Google Scholar ]
  • Funke J., Greiff S. (2017). “Dynamic problem solving: multiple-item testing based on minimally complex systems,” in Competence Assessment in Education. Research, Models and Instruments , eds Leutner D., Fleischer J., Grünkorn J., Klieme E. (Heidelberg: Springer; ), 427–443. [ Google Scholar ]
  • Gobert J. D., Kim Y. J., Pedro M. A. S., Kennedy M., Betts C. G. (2015). Using educational data mining to assess students’ skills at designing and conducting experiments within a complex systems microworld. Think. Skills Creat. 18 81–90. 10.1016/j.tsc.2015.04.008 [ CrossRef ] [ Google Scholar ]
  • Goode N., Beckmann J. F. (2010). You need to know: there is a causal relationship between structural knowledge and control performance in complex problem solving tasks. Intelligence 38 345–352. 10.1016/j.intell.2010.01.001 [ CrossRef ] [ Google Scholar ]
  • Gray W. D. (2002). Simulated task environments: the role of high-fidelity simulations, scaled worlds, synthetic environments, and laboratory tasks in basic and applied cognitive research. Cogn. Sci. Q. 2 205–227. [ Google Scholar ]
  • Greiff S., Fischer A. (2013). Measuring complex problem solving: an educational application of psychological theories. J. Educ. Res. 5 38–58. [ Google Scholar ]
  • Greiff S., Fischer A., Stadler M., Wüstenberg S. (2015a). Assessing complex problem-solving skills with multiple complex systems. Think. Reason. 21 356–382. 10.1080/13546783.2014.989263 [ CrossRef ] [ Google Scholar ]
  • Greiff S., Stadler M., Sonnleitner P., Wolff C., Martin R. (2015b). Sometimes less is more: comparing the validity of complex problem solving measures. Intelligence 50 100–113. 10.1016/j.intell.2015.02.007 [ CrossRef ] [ Google Scholar ]
  • Greiff S., Fischer A., Wüstenberg S., Sonnleitner P., Brunner M., Martin R. (2013a). A multitrait–multimethod study of assessment instruments for complex problem solving. Intelligence 41 579–596. 10.1016/j.intell.2013.07.012 [ CrossRef ] [ Google Scholar ]
  • Greiff S., Holt D. V., Funke J. (2013b). Perspectives on problem solving in educational assessment: analytical, interactive, and collaborative problem solving. J. Problem Solv. 5 71–91. 10.7771/1932-6246.1153 [ CrossRef ] [ Google Scholar ]
  • Greiff S., Wüstenberg S., Molnár G., Fischer A., Funke J., Csapó B. (2013c). Complex problem solving in educational contexts—something beyond g: concept, assessment, measurement invariance, and construct validity. J. Educ. Psychol. 105 364–379. 10.1037/a0031856 [ CrossRef ] [ Google Scholar ]
  • Greiff S., Funke J. (2009). “Measuring complex problem solving: the MicroDYN approach,” in The Transition to Computer-Based Assessment. New Approaches to Skills Assessment and Implications for Large-Scale Testing , eds Scheuermann F., Björnsson J. (Luxembourg: Office for Official Publications of the European Communities; ), 157–163. [ Google Scholar ]
  • Greiff S., Funke J. (2017). “Interactive problem solving: exploring the potential of minimal complex systems,” in The Nature of Problem Solving: Using Research to Inspire 21st Century Learning , eds Csapó B., Funke J. (Paris: OECD Publishing; ), 93–105. [ Google Scholar ]
  • Greiff S., Martin R. (2014). What you see is what you (don’t) get: a comment on Funke’s (2014) opinion paper. Front. Psychol. 5 : 1120 10.3389/fpsyg.2014.01120 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Greiff S., Neubert J. C. (2014). On the relation of complex problem solving, personality, fluid intelligence, and academic achievement. Learn. Ind. Diff. 36 37–48. 10.1016/j.lindif.2014.08.003 [ CrossRef ] [ Google Scholar ]
  • Greiff S., Niepel C., Scherer R., Martin R. (2016). Understanding students’ performance in a computer-based assessment of complex problem solving: an analysis of behavioral data from computer-generated log files. Comput. Hum. Behav. 61 36–46. 10.1016/j.chb.2016.02.095 [ CrossRef ] [ Google Scholar ]
  • Greiff S., Stadler M., Sonnleitner P., Wolff C., Martin R. (2017). Sometimes more is too much: a rejoinder to the commentaries on Greif et al. (2015). J. Intell. 5 : 6 10.3390/jintelligence5010006 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Greiff S., Wüstenberg S. (2014). Assessment with microworlds using MicroDYN: measurement invariance and latent mean comparisons. Eur. J. Psychol. Assess. 1 1–11. 10.1027/1015-5759/a000194 [ CrossRef ] [ Google Scholar ]
  • Greiff S., Wüstenberg S. (2015). Komplexer Problemlösetest COMPRO [Complex Problem-Solving Test COMPRO]. Mödling: Schuhfried. [ Google Scholar ]
  • Greiff S., Wüstenberg S., Funke J. (2012). Dynamic problem solving: a new assessment perspective. Appl. Psychol. Measure. 36 189–213. 10.1177/0146621612439620 [ CrossRef ] [ Google Scholar ]
  • Griffin P., Care E. (2015). “The ATC21S method,” in Assessment and Taching of 21st Century Skills , eds Griffin P., Care E. (Dordrecht, NL: Springer; ), 3–33. [ Google Scholar ]
  • Güss C. D., Dörner D. (2011). Cultural differences in dynamic decision-making strategies in a non-linear, time-delayed task. Cogn. Syst. Res. 12 365–376. 10.1016/j.cogsys.2010.12.003 [ CrossRef ] [ Google Scholar ]
  • Güss C. D., Tuason M. T., Orduña L. V. (2015). Strategies, tactics, and errors in dynamic decision making in an Asian sample. J. Dynamic Deci. Mak. 1 1–14. 10.11588/jddm.2015.1.13131 [ CrossRef ] [ Google Scholar ]
  • Güss C. D., Wiley B. (2007). Metacognition of problem-solving strategies in Brazil, India, and the United States. J. Cogn. Cult. 7 1–25. 10.1163/156853707X171793 [ CrossRef ] [ Google Scholar ]
  • Herde C. N., Wüstenberg S., Greiff S. (2016). Assessment of complex problem solving: what we know and what we don’t know. Appl. Meas. Educ. 29 265–277. 10.1080/08957347.2016.1209208 [ CrossRef ] [ Google Scholar ]
  • Hermes M., Stelling D. (2016). Context matters, but how much? Latent state – trait analysis of cognitive ability assessments. Int. J. Sel. Assess. 24 285–295. 10.1111/ijsa.12147 [ CrossRef ] [ Google Scholar ]
  • Hotaling J. M., Fakhari P., Busemeyer J. R. (2015). “Dynamic decision making,” in International Encyclopedia of the Social & Behavioral Sciences , 2nd Edn, eds Smelser N. J., Batles P. B. (New York, NY: Elsevier; ), 709–714. [ Google Scholar ]
  • Hundertmark J., Holt D. V., Fischer A., Said N., Fischer H. (2015). System structure and cognitive ability as predictors of performance in dynamic system control tasks. J. Dynamic Deci. Mak. 1 1–10. 10.11588/jddm.2015.1.26416 [ CrossRef ] [ Google Scholar ]
  • Jäkel F., Schreiber C. (2013). Introspection in problem solving. J. Problem Solv. 6 20–33. 10.7771/1932-6246.1131 [ CrossRef ] [ Google Scholar ]
  • Jansson A. (1994). Pathologies in dynamic decision making: consequences or precursors of failure? Sprache Kogn. 13 160–173. [ Google Scholar ]
  • Kaufman J. C., Beghetto R. A. (2009). Beyond big and little: the four c model of creativity. Rev. Gen. Psychol. 13 1–12. 10.1037/a0013688 [ CrossRef ] [ Google Scholar ]
  • Knauff M., Wolf A. G. (2010). Complex cognition: the science of human reasoning, problem-solving, and decision-making. Cogn. Process. 11 99–102. 10.1007/s10339-010-0362-z [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Kretzschmar A. (2017). Sometimes less is not enough: a commentary on Greiff et al. (2015). J. Intell. 5 : 4 10.3390/jintelligence5010004 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Kretzschmar A., Neubert J. C., Wüstenberg S., Greiff S. (2016). Construct validity of complex problem solving: a comprehensive view on different facets of intelligence and school grades. Intelligence 54 55–69. 10.1016/j.intell.2015.11.004 [ CrossRef ] [ Google Scholar ]
  • Kretzschmar A., Süß H.-M. (2015). A study on the training of complex problem solving competence. J. Dynamic Deci. Mak. 1 1–14. 10.11588/jddm.2015.1.15455 [ CrossRef ] [ Google Scholar ]
  • Lee H., Cho Y. (2007). Factors affecting problem finding depending on degree of structure of problem situation. J. Educ. Res. 101 113–123. 10.3200/JOER.101.2.113-125 [ CrossRef ] [ Google Scholar ]
  • Leutner D., Fleischer J., Wirth J., Greiff S., Funke J. (2012). Analytische und dynamische Problemlösekompetenz im Lichte internationaler Schulleistungsvergleichsstudien: Untersuchungen zur Dimensionalität. Psychol. Rundschau 63 34–42. 10.1026/0033-3042/a000108 [ CrossRef ] [ Google Scholar ]
  • Luchins A. S. (1942). Mechanization in problem solving: the effect of einstellung. Psychol. Monogr. 54 1–95. 10.1037/h0093502 [ CrossRef ] [ Google Scholar ]
  • Mack O., Khare A., Krämer A., Burgartz T. (eds) (2016). Managing in a VUCA world. Heidelberg: Springer. [ Google Scholar ]
  • Mainert J., Kretzschmar A., Neubert J. C., Greiff S. (2015). Linking complex problem solving and general mental ability to career advancement: does a transversal skill reveal incremental predictive validity? Int. J. Lifelong Educ. 34 393–411. 10.1080/02601370.2015.1060024 [ CrossRef ] [ Google Scholar ]
  • Mainzer K. (2009). Challenges of complexity in the 21st century. An interdisciplinary introduction. Eur. Rev. 17 219–236. 10.1017/S1062798709000714 [ CrossRef ] [ Google Scholar ]
  • Meadows D. H., Meadows D. L., Randers J. (1992). Beyond the Limits. Vermont, VA: Chelsea Green Publishing. [ Google Scholar ]
  • Meadows D. H., Meadows D. L., Randers J., Behrens W. W. (1972). The Limits to Growth. New York, NY: Universe Books. [ Google Scholar ]
  • Meißner A., Greiff S., Frischkorn G. T., Steinmayr R. (2016). Predicting complex problem solving and school grades with working memory and ability self-concept. Learn. Ind. Differ. 49 323–331. 10.1016/j.lindif.2016.04.006 [ CrossRef ] [ Google Scholar ]
  • Molnàr G., Greiff S., Wüstenberg S., Fischer A. (2017). “Empirical study of computer-based assessment of domain-general complex problem-solving skills,” in The Nature of Problem Solving: Using research to Inspire 21st Century Learning , eds Csapó B., Funke J. (Paris: OECD Publishing; ), 125–141. [ Google Scholar ]
  • National Research Council (2011). Assessing 21st Century Skills: Summary of a Workshop. Washington, DC: The National Academies Press. [ PubMed ] [ Google Scholar ]
  • Newell A., Shaw J. C., Simon H. A. (1959). A general problem-solving program for a computer. Comput. Automat. 8 10–16. [ Google Scholar ]
  • Nisbett R. E., Wilson T. D. (1977). Telling more than we can know: verbal reports on mental processes. Psychol. Rev. 84 231–259. 10.1037/0033-295X.84.3.231 [ CrossRef ] [ Google Scholar ]
  • OECD (2014). “PISA 2012 results,” in Creative Problem Solving: Students’ Skills in Tackling Real-Life problems , Vol. 5 (Paris: OECD Publishing; ). [ Google Scholar ]
  • Osman M. (2010). Controlling uncertainty: a review of human behavior in complex dynamic environments. Psychol. Bull. 136 65–86. 10.1037/a0017815 [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Osman M. (2012). The role of reward in dynamic decision making. Front. Neurosci. 6 : 35 10.3389/fnins.2012.00035 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Qudrat-Ullah H. (2015). Better Decision Making in Complex, Dynamic Tasks. Training with Human-Facilitated Interactive Learning Environments. Heidelberg: Springer. [ Google Scholar ]
  • Ramnarayan S., Strohschneider S., Schaub H. (1997). Trappings of expertise and the pursuit of failure. Simulat. Gam. 28 28–43. 10.1177/1046878197281004 [ CrossRef ] [ Google Scholar ]
  • Reuschenbach B. (2008). Planen und Problemlösen im Komplexen Handlungsfeld Pflege. Berlin: Logos. [ Google Scholar ]
  • Rohe M., Funke J., Storch M., Weber J. (2016). Can motto goals outperform learning and performance goals? Influence of goal setting on performance, intrinsic motivation, processing style, and affect in a complex problem solving task. J. Dynamic Deci. Mak. 2 1–15. 10.11588/jddm.2016.1.28510 [ CrossRef ] [ Google Scholar ]
  • Scherer R., Greiff S., Hautamäki J. (2015). Exploring the relation between time on task and ability in complex problem solving. Intelligence 48 37–50. 10.1016/j.intell.2014.10.003 [ CrossRef ] [ Google Scholar ]
  • Schoppek W., Fischer A. (2015). Complex problem solving – single ability or complex phenomenon? Front. Psychol. 6 : 1669 10.3389/fpsyg.2015.01669 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Schraw G., Dunkle M., Bendixen L. D. (1995). Cognitive processes in well-defined and ill-defined problem solving. Appl. Cogn. Psychol. 9 523–538. 10.1002/acp.2350090605 [ CrossRef ] [ Google Scholar ]
  • Schweizer F., Wüstenberg S., Greiff S. (2013). Validity of the MicroDYN approach: complex problem solving predicts school grades beyond working memory capacity. Learn. Ind. Differ. 24 42–52. 10.1016/j.lindif.2012.12.011 [ CrossRef ] [ Google Scholar ]
  • Schweizer T. S., Schmalenberger K. M., Eisenlohr-Moul T. A., Mojzisch A., Kaiser S., Funke J. (2016). Cognitive and affective aspects of creative option generation in everyday life situations. Front. Psychol. 7 : 1132 10.3389/fpsyg.2016.01132 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Selten R., Pittnauer S., Hohnisch M. (2012). Dealing with dynamic decision problems when knowledge of the environment is limited: an approach based on goal systems. J. Behav. Deci. Mak. 25 443–457. 10.1002/bdm.738 [ CrossRef ] [ Google Scholar ]
  • Simon H. A. (1957). Administrative Behavior: A Study of Decision-Making Processes in Administrative Organizations , 2nd Edn New York, NY: Macmillan. [ Google Scholar ]
  • Sonnleitner P., Brunner M., Keller U., Martin R. (2014). Differential relations between facets of complex problem solving and students’ immigration background. J. Educ. Psychol. 106 681–695. 10.1037/a0035506 [ CrossRef ] [ Google Scholar ]
  • Spering M., Wagener D., Funke J. (2005). The role of emotions in complex problem solving. Cogn. Emot. 19 1252–1261. 10.1080/02699930500304886 [ CrossRef ] [ Google Scholar ]
  • Stadler M., Becker N., Gödker M., Leutner D., Greiff S. (2015). Complex problem solving and intelligence: a meta-analysis. Intelligence 53 92–101. 10.1016/j.intell.2015.09.005 [ CrossRef ] [ Google Scholar ]
  • Stadler M., Niepel C., Greiff S. (2016). Easily too difficult: estimating item difficulty in computer simulated microworlds. Comput. Hum. Behav. 65 100–106. 10.1016/j.chb.2016.08.025 [ CrossRef ] [ Google Scholar ]
  • Sternberg R. J. (1995). “Expertise in complex problem solving: a comparison of alternative conceptions,” in Complex Problem Solving: The European Perspective , eds Frensch P. A., Funke J. (Hillsdale, NJ: Erlbaum; ), 295–321. [ Google Scholar ]
  • Sternberg R. J., Frensch P. A. (1991). Complex Problem Solving: Principles and Mechanisms. (eds) Sternberg R. J., Frensch P. A. Hillsdale, NJ: Erlbaum. [ Google Scholar ]
  • Strohschneider S., Güss C. D. (1998). Planning and problem solving: differences between brazilian and german students. J. Cross-Cult. Psychol. 29 695–716. 10.1177/0022022198296002 [ CrossRef ] [ Google Scholar ]
  • Strohschneider S., Güss C. D. (1999). The fate of the Moros: a cross-cultural exploration of strategies in complex and dynamic decision making. Int. J. Psychol. 34 235–252. 10.1080/002075999399873 [ CrossRef ] [ Google Scholar ]
  • Thimbleby H. (2007). Press On. Principles of Interaction. Cambridge, MA: MIT Press. [ Google Scholar ]
  • Tobinski D. A., Fritz A. (2017). “EcoSphere: a new paradigm for problem solving in complex systems,” in The Nature of Problem Solving: Using Research to Inspire 21st Century Learning , eds Csapó B., Funke J. (Paris: OECD Publishing; ), 211–222. [ Google Scholar ]
  • Tremblay S., Gagnon J.-F., Lafond D., Hodgetts H. M., Doiron M., Jeuniaux P. P. J. M. H. (2017). A cognitive prosthesis for complex decision-making. Appl. Ergon. 58 349–360. 10.1016/j.apergo.2016.07.009 [ PubMed ] [ CrossRef ] [ Google Scholar ]
  • Tschirgi J. E. (1980). Sensible reasoning: a hypothesis about hypotheses. Child Dev. 51 1–10. 10.2307/1129583 [ CrossRef ] [ Google Scholar ]
  • Tuchman B. W. (1984). The March of Folly. From Troy to Vietnam. New York, NY: Ballantine Books. [ Google Scholar ]
  • Verweij M., Thompson M. (eds) (2006). Clumsy Solutions for A Complex World. Governance, Politics and Plural Perceptions. New York, NY: Palgrave Macmillan; 10.1057/9780230624887 [ CrossRef ] [ Google Scholar ]
  • Viehrig K., Siegmund A., Funke J., Wüstenberg S., Greiff S. (2017). “The heidelberg inventory of geographic system competency model,” in Competence Assessment in Education. Research, Models and Instruments , eds Leutner D., Fleischer J., Grünkorn J., Klieme E. (Heidelberg: Springer; ), 31–53. [ Google Scholar ]
  • von Clausewitz C. (1832). Vom Kriege [On war]. Berlin: Dämmler. [ Google Scholar ]
  • Wendt A. N. (2017). The empirical potential of live streaming beyond cognitive psychology. J. Dynamic Deci. Mak. 3 1–9. 10.11588/jddm.2017.1.33724 [ CrossRef ] [ Google Scholar ]
  • Wiliam D., Black P. (1996). Meanings and consequences: a basis for distinguishing formative and summative functions of assessment? Br. Educ. Res. J. 22 537–548. 10.1080/0141192960220502 [ CrossRef ] [ Google Scholar ]
  • World Economic Forum (2015). New Vsion for Education Unlocking the Potential of Technology. Geneva: World Economic Forum. [ Google Scholar ]
  • World Economic Forum (2016). Global Risks 2016: Insight Report , 11th Edn Geneva: World Economic Forum. [ Google Scholar ]
  • Wüstenberg S., Greiff S., Funke J. (2012). Complex problem solving — more than reasoning? Intelligence 40 1–14. 10.1016/j.intell.2011.11.003 [ CrossRef ] [ Google Scholar ]
  • Wüstenberg S., Greiff S., Vainikainen M.-P., Murphy K. (2016). Individual differences in students’ complex problem solving skills: how they evolve and what they imply. J. Educ. Psychol. 108 1028–1044. 10.1037/edu0000101 [ CrossRef ] [ Google Scholar ]
  • Wüstenberg S., Stadler M., Hautamäki J., Greiff S. (2014). The role of strategy knowledge for the application of strategies in complex problem solving tasks. Technol. Knowl. Learn. 19 127–146. 10.1007/s10758-014-9222-8 [ CrossRef ] [ Google Scholar ]

Netflix's hit sci-fi series '3 Body Problem' is based on a real math problem that is so complex it's impossible to solve

  • The three-body problem is a centuries-old physics question that puzzled Isaac Newton .
  • It describes the orbits of three bodies, like planets or stars, trapped in each other's gravity.
  • The problem is unsolvable and led to the development of chaos theory.

Insider Today

While Netflix's "3 Body Problem" is a science-fiction show, its name comes from a real math problem that's puzzled scientists since the late 1600s.

In physics, the three-body problem refers to the motion of three bodies trapped in each other's gravitational grip — like a three-star system.

It might sound simple enough, but once you dig into the mathematics, the orbital paths of each object get complicated very quickly.

Two-body vs. three- and multi-body systems

A simpler version is a two-body system like binary stars. Two-body systems have periodic orbits, meaning they are mathematically predictable because they follow the same trajectory over and over. So, if you have the stars' initial positions and velocities, you can calculate where they've been or will be in space far into the past and future.

However, "throwing in a third body that's close enough to interact leads to chaos," Shane Ross, an aerospace and ocean engineering professor at Virginia Tech, told Business Insider. In fact, it's nearly impossible to precisely predict the orbital paths of any system with three bodies or more.

While two orbiting planets might look like a ven diagram with ovular paths overlapping, the paths of three bodies interacting often resemble tangled spaghetti. Their trajectories usually aren't as stable as systems with only two bodies.

All that uncertainty makes what's known as the three-body problem largely unsolvable, Ross said. But there are certain exceptions.

The three-body problem is over 300 years old

The three-body problem dates back to Isaac Newton , who published his "Principia" in 1687.

In the book, the mathematician noted that the planets move in elliptical orbits around the sun. Yet the gravitational pull from Jupiter seemed to affect Saturn's orbital path.

Related stories

The three-body problem didn't just affect distant planets. Trying to understand the variations in the moon's movements caused Newton literal headaches, he complained.

But Newton never fully figured out the three-body problem. And it remained a mathematical mystery for nearly 200 years.

In 1889, a Swedish journal awarded mathematician Henri Poincaré a gold medal and 2,500 Swedish crowns, roughly half a year's salary for a professor at the time, for his essay about the three-body problem that outlined the basis for an entirely new mathematical theory called chaos theory .

According to chaos theory, when there is uncertainty about a system's initial conditions, like an object's mass or velocity, that uncertainty ripples out, making the future more and more unpredictable.

Think of it like taking a wrong turn on a trip. If you make a left instead of a right at the end of your journey, you're probably closer to your destination than if you made the mistake at the very beginning.

Can you solve the three-body problem?

Cracking the three-body problem would help scientists chart the movements of meteors and planets, including Earth, into the extremely far future. Even comparatively small movements of our planet could have large impacts on our climate, Ross said.

Though the three-body problem is considered mathematically unsolvable, there are solutions to specific scenarios. In fact, there are a few that mathematicians have found.

For example, three bodies could stably orbit in a figure eight or equally spaced around a ring. Both are possible depending on the initial positions and velocities of the bodies.

One way researchers look for solutions is with " restricted " three-body problems, where two main bodies (like the sun and Earth) interact and a third object with much smaller mass (like the moon) offers less gravitational interference. In this case, the three-body problem looks a lot like a two-body problem since the sun and Earth comprise the majority of mass in the system.

However, if you're looking at a three-star system, like the one in Netflix's show "3 Body Problem," that's a lot more complicated.

Computers can also run simulations far more efficiently than humans, though due to the inherent uncertainties, the results are typically approximate orbits instead of exact.

Finding solutions to three-body problems is also essential to space travel, Ross said. For his work, he inputs data about the Earth, moon, and spacecraft into a computer. "We can build up a whole library of possible trajectories," he said, "and that gives us an idea of the types of motion that are possible."

what is a complex problem solver

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Title: self-improved learning for scalable neural combinatorial optimization.

Abstract: The end-to-end neural combinatorial optimization (NCO) method shows promising performance in solving complex combinatorial optimization problems without the need for expert design. However, existing methods struggle with large-scale problems, hindering their practical applicability. To overcome this limitation, this work proposes a novel Self-Improved Learning (SIL) method for better scalability of neural combinatorial optimization. Specifically, we develop an efficient self-improved mechanism that enables direct model training on large-scale problem instances without any labeled data. Powered by an innovative local reconstruction approach, this method can iteratively generate better solutions by itself as pseudo-labels to guide efficient model training. In addition, we design a linear complexity attention mechanism for the model to efficiently handle large-scale combinatorial problem instances with low computation overhead. Comprehensive experiments on the Travelling Salesman Problem (TSP) and the Capacitated Vehicle Routing Problem (CVRP) with up to 100K nodes in both uniform and real-world distributions demonstrate the superior scalability of our method.

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COMMENTS

  1. Complex Problem-Solving: Definition and Steps

    Complex problem solving is a series of observations and informed decisions used to find and implement a solution to a problem. Beyond finding and implementing a solution, complex problem solving also involves considering future changes to circumstance, resources and capabilities that may affect the trajectory of the process and success of the ...

  2. The 7 Timeless Steps to Guide You Through Complex Problem Solving

    Solving complex problems is a crucial skill for success, whether it's a business challenge, a personal dilemma, or a societal issue. This guide will explore the fundamentals of complex problem-solving and provide practical tips and strategies for mastering this critical skill.

  3. Complex Problem Solving: What It Is and What It Is Not

    Complex problem solving is a collection of self-regulated psychological processes and activities necessary in dynamic environments to achieve ill-defined goals that cannot be reached by routine actions. Creative combinations of knowledge and a broad set of strategies are needed. Solutions are often more bricolage than perfect or optimal.

  4. How To Solve Complex Problems

    "Complex problem solving" is the term for how to address a complex problem or messes that have the characteristics listed above. Since a complex problem is a different phenomenon than a simple or complicated problem, solving them requires a different approach.

  5. What It Takes to Think Deeply About Complex Problems

    The problems we're facing often seem as intractable as they do complex. But as Albert Einstein famously observed, "We cannot solve our problems with the same level of thinking that created ...

  6. Overlap

    Complex problem solving involves gathering observations and asking questions to make informed decisions, considering how future developments could affect a potential solution's continued success, and understanding how the solution will affect both the people involved and the surrounding environment. As you can tell, it's called complex ...

  7. The Right Way to Solve Complex Business Problems

    All episodes. Details. Transcript. December 04, 2018. Corey Phelps, a strategy professor at McGill University, says great problem solvers are hard to find. Even seasoned professionals at the ...

  8. Complex Problem Solving

    Problems within complex problem-solving research deal with the following issues: Identifying the quality of solution. A decision about the quality of simple problem solving is easily possible, because the criteria for success are transparent. For complex problems the situation is different, because mostly there are no obvious goal conditions.

  9. An Introduction to Complex Problem Solving

    Complex problem solving is a skill you can continue to improve with each new complex problem. The more you test your assumptions, open your mind, put feedback into practice, and test new ideas ...

  10. Complex Problem Solving

    Complex Problem Solving is the skill of applying a method to a problem, often not seen before, to obtain a satisfactory solution. It requires a creative combination of knowledge and strategies to arrive at an answer. Rapid technological change, the increasingly global exchange of ideas, and the proliferation of easy-to-access information ...

  11. 35 problem-solving techniques and methods for solving complex problems

    Part of the liberating structures toolkit, 15% solutions is a problem-solving technique that focuses on finding and implementing solutions quickly. A process of iterating and making small changes quickly can help generate momentum and an appetite for solving complex problems. Problem-solving strategies can live and die on whether people are ...

  12. How to master the seven-step problem-solving process

    Simon London: Problem solving is a really interesting piece of terminology. It could mean so many different things. I have a son who's a teenage climber. They talk about solving problems. Climbing is problem solving. Charles, when you talk about problem solving, what are you talking about?

  13. Intelligence, Creativity, and Wisdom: A Case for Complex Problem Solving?

    If the problem is a complex problem (e.g., intransparent), the problem solver is confronted with uncertainty and needs to acquire further knowledge about the problem, including its variables, their connections, and the possible goals and barriers involved in the problem (e.g., Osman, 2010). This knowledge is gathered through an active ...

  14. How to solve complex problems

    The best way to solve it is to consider a 1x2 bar first, then a 1x3, a 2x3, etc. The lesson behind this, is that if you have to solve a complex problem, you will want to cut it in the smallest pieces as possible, until reaching the most elementary ones, and then expand them little by little to understand the overall problem.

  15. Complex Problem Solving Through Systems Thinking

    This complex problem-solving course introduces participants to MIT's unique, powerful, and integrative System Dynamics approach to assess problems that will not go away and to produce the results they want. Through exercises and simulation models, participants experience the long-term side effects and impacts of decisions and understand the ...

  16. How to Solve Complex Problems: 6 Essential Skills

    1 Define the problem. The first skill you need is to define the problem clearly and precisely. This means identifying the root cause, the scope, the stakeholders, and the desired outcome. A well ...

  17. What is Problem Solving? An Introduction

    Problem solving, in the simplest terms, is the process of identifying a problem, analyzing it, and finding the most effective solution to overcome it. For software engineers, this process is deeply embedded in their daily workflow. It could be something as simple as figuring out why a piece of code isn't working as expected, or something as ...

  18. Complex Problem Solving: What It Is and What It Is Not

    Computer-simulated scenarios have been part of psychological research on problem solving for more than 40 years. The shift in emphasis from simple toy problems to complex, more real-life oriented problems has been accompanied by discussions about the best ways to assess the process of solving complex problems.

  19. 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 ...

  20. Solving Complex Problems Specialization

    To solve complex problems, whether it is the challenge of developing a new product, or Einstein's task of trying to explain how gravity worked - and literally everything else in between - it is not enough to take the problem and apply already existing skills. The skill that has always led to big breakthroughs in any field or industry is the ...

  21. What is Problem Solving? Steps, Process & Techniques

    1. Define the problem. Diagnose the situation so that your focus is on the problem, not just its symptoms. Helpful problem-solving techniques include using flowcharts to identify the expected steps of a process and cause-and-effect diagrams to define and analyze root causes.. The sections below help explain key problem-solving steps.

  22. Solving Complex Problems: Team Building Strategies

    Remember, complex problems are not roadblocks; they're puzzles waiting to be solved by a unified team. Find expert answers in this collaborative article

  23. The Simplest Math Problem Could Be Unsolvable

    It's really fun to go through the iterative calculation rule for different numbers and look at the resulting sequences. If you start with 6: 6 → 3 → 10 → 5 → 16 → 8 → 4 → 2 → 1.

  24. Complex Problem Solving: What It Is and What It Is Not

    Go to: Computer-simulated scenarios have been part of psychological research on problem solving for more than 40 years. The shift in emphasis from simple toy problems to complex, more real-life oriented problems has been accompanied by discussions about the best ways to assess the process of solving complex problems.

  25. Why the Three-Body Problem in Physics Is Unsolvable

    The three-body problem is a question in physics that deals with planets and stars. ... Netflix's hit sci-fi series '3 Body Problem' is based on a real math problem that is so complex it's ...

  26. Self-Improved Learning for Scalable Neural Combinatorial Optimization

    The end-to-end neural combinatorial optimization (NCO) method shows promising performance in solving complex combinatorial optimization problems without the need for expert design. However, existing methods struggle with large-scale problems, hindering their practical applicability. To overcome this limitation, this work proposes a novel Self-Improved Learning (SIL) method for better ...