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Performance-Based Assessment in Math
Instead of doing math problems with no context, students at this school role-play real jobs.
Performance-Based Assessment: Math
Through performance-based assessment, students demonstrate the knowledge, skills, and material that they have learned. This practice measures how well a student can apply or use what he or she knows, often in real-world situations. Research has shown that performance-based assessment provides a means to assess higher-order thinking skills and helps teachers and principals support students in developing a deeper understanding of content.
How It's Done
Performance-based assessment can work with the curriculum, instruction, or unit that you're teaching right now. How would you design a performance-based assessment for this content? Because PBA requires students to demonstrate their knowledge and skills with the concepts that they've learned, this assessment requires them to create a product or response, or to perform a specific set of tasks.
At Hampton High School, teachers calibrate their assessments against a rigor scale with the goal of high performance. They use the common Rigor, Relevance, and Relationships framework to demonstrate that the higher levels of rigor and relevance embody higher-level cognition and application. "What's the level of performance?" teachers will ask when designing assessments. "Is the performance that we want from kids short-term memory and fragmented applications, or should they demonstrate comprehensive understanding of big ideas?" This shifts the focus from content measures to student performance measures.
For example, a performance task in history would require students to produce a piece of writing rather than answering a series of multiple-choice questions about dates or events. The value of performance assessment is that it mimics the kind of work done in real-world contexts. So an authentic performance task in environmental science might require a student to investigate the impact of fertilizer on local groundwater and then report the results through a public service campaign (like a video, a radio announcement, or a presentation to a group).
Performance assessment draws on students’ higher-order thinking skills -- evaluating the reliability of information, synthesizing data to draw conclusions, or solving a problem with deductive or inductive reasoning. Performance tasks may require students to present supporting evidence in an argument, conduct a controlled experiment, solve a complex problem, or build a model. A performance task often has more than one acceptable solution, and teachers use rubrics as a key part of assessing student work.
Math: Disaster Relief Mission
Hampton High School's pre-calculus teachers aimed to create a performance-based assessment that asked students to demonstrate their knowledge of concepts, and apply it to circumstances unfamiliar to them. They came up with Disaster Relief Mission, a simulation where students play the role of air traffic controllers and pilots responding to crisis situations around the country. In these situations, students have to figure out what math to use in order to rescue those in need.
In the Resources tab, you'll find all the math materials that Hampton teachers created for the Disaster Relief Mission project. These materials include:
- Project directions
- Rubrics to assess the project
Disaster Relief Mission is a sophisticated example of performance assessment, developed and refined over the past three years by Hampton's teachers. The prep work involved in such a project does require some time, including coming up with the missions, setting up the gymnasium with the correct coordinates, and configuring all the technology (iPods, FaceTime, and a Compass App) used in this exam. Teachers also spend some time training students on how to use the technology so that it won't be an issue during the actual work. Students are also trained for the roles of both pilot and air traffic controller, in case teams need to be reconfigured on the day of the exam.
Disaster Relief Mission PBA
Students are split into teams of three (one air traffic controller and two pilots) and given four disaster missions to solve. Each team is distributed across two locations (air traffic controllers in one room, pilots in the gymnasium), and all communicate via FaceTime.
The teachers set up ten missions in the gymnasium, each with different coordinates. However, students have only four problems to solve, allowing multiple groups teams work in the gym at the same time but not on the same problem.
A sample disaster relief mission looked like this:
Air traffic controllers are responsible for determining the angle and distance that the pilots need to move to get them from one mission to another. They calculate these numbers and relay them to the pilots via FaceTime. If correct, the pilots in the gym reach the mission site and then have to figure out what math will help them complete the mission. For example, will their calculations require the Law of Sines, Law of Cosines, right triangle trigonometry, or bearings?
After students complete one mission, they restart the whole process for the next mission, until they complete all four. The whole PBA takes one class period to complete.
Teachers design a rubric to measure the performance of students. The rubric is given to students ahead of time, so that they're clear about what they will be assessed on. For Disaster Relief Mission, the rubric is designed so that each team member -- whether pilot or air traffic controller -- receives the same number of points on the exam. For a perfect score, a team receives 45 points for completing and solving all four missions. The rubric assesses the accuracy of how well students solve each mission, including:
- Looking at the accuracy of how polar coordinates were calculated
- Looking at the accuracy of math used in each mission, including all calculations (not just final answers)
- Supporting work, including maps that showed how the air traffic controllers determined the angles at which the plane would travel
- Neatness of the work
- How students collaborated and communicated as a team
If a team doesn't submit its calculations, for example, but has the correct answer, less points are given. If a team has a correct answer but the units of measure are missing, they're also given fewer points. The rubric allows teachers to grade across a spectrum, taking into consideration how accurate and complete the students' work is.
- What Is Performance-Based Assessment?
- What Is Performance-Based Learning and Assessment, and Why Is It Important?
- What Is a Performance Task?
- Performance Tasks for Math
- Performance-Based Assessment for Hampton H.S. Disaster Relief Mission
Hampton High School
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Performance Assessment Tasks
These tasks are grade-level formative performance assessment tasks with accompanying scoring rubrics and discussion of student work samples. They are aligned to the Common Core State Standards for Mathematics. You may download and use these tasks for professional development purposes without modifying the tasks.
The tasks for 3rd Grade through High School were developed by the Mathematics Assessment Resource Service (MARS) of the Shell Centre for Mathematical Education, University of Nottingham, England. The tasks for 2nd Grade were developed by the Silicon Valley Mathematics Initiative’s Mathematics Assessment Collaborative (MAC).
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Delivered online for educators, this supplemental resource for K–5 offers educators a powerful collection of planning, instruction, and assessment tools that help students learn to think critically, solve problems creatively, communicate, collaborate, and succeed.
Material is based on 21st century math concepts and skills, organized by rich Units of Study inspired by the NCTM Focal Points and leading state standards. 350+ problem-solving performance tasks are provided.
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Rich, problem-solving supplements are organized by Units of Study inspired by the NCTM Focal points and leading state standards.
Each Unit offers 5 (or more) open-ended performance tasks that address the big mathematical ideas. These may be used for classroom instruction, exploration, formative assessment, and summative assessment.
Our DOK 3 problems naturally elicit the NCTM Process Standards and are designed to engage students and develop their abilities to reason and communicate mathematically. Spanish translations are available.
Material supports the Concrete Representational Abstract (CRA) instructional approach for teaching mathematics.
Launch images are also included to pique student curiosity.
Exemplars instructional tasks are differentiated at 3 entry points, allowing easy integration in mixed-ability classrooms. These problems may also be used for formative assessment. There are 4 or more instructional tasks provided for each Unit of Study.
Preliminary Planning Sheets serve as a teacher's guide for every task.
They outline the math concepts and skills students will need to know as well as alternative strategies for solving each problem.
This resource assists with lesson preparation and assessing student work.
The Exemplars Standards-Based Math Rubric allows teachers to examine student work against a set of analytic criteria to determine student performance. Our rubric criteria reflect the NCTM Process Standards. There are 4 performance levels – Novice, Apprentice, Practitioner (meets the standard), and Expert.
This assessment tool is designed to identify what is important, define what meets the standard, and distinguish between different levels of performance. It also provides teachers with guidelines for giving meaningful feedback to their students.
Student rubrics , written in kid-friendly language, are also included. These may be used to develop a child's ability to self- and peer-assess.
Student anchor papers and scoring rationales are provided at the 4 performance levels of the Exemplars assessment rubric and accompany each Summative Assessment.
These tools demonstrate for teachers and students what work meets (and does not meet) the standard in accordance with the assessment rubric and explain why.
They are also a valuable staff development resource and may be used with students as a basis for self- and peer-assessment.
One (or more) summative assessment task is provided for each Unit of Study.
To assist schools and districts new to problem solving performance-based assessment and instruction, Exemplars offers a complimentary Implementation Planning Webinar. During this session, your leadership team will gain a deeper understanding of Exemplars materials and resources as well as tips for getting started successfully. We'll also put together a schedule of periodic check-ins that make the most sense for your needs and goals.
Exemplars also offers professional development workshops designed to generate immediate and sustained results.
- 350+ engaging performance tasks to develop and assess students’ critical thinking and reasoning skills for grades K–5.
- Differentiated tasks at 3 points of entry for instruction, exploration, and formative assessment.
- Launch images to pique student curiosity.
- Spanish task translations.
- Student anchor papers and scoring rationales that demonstrate for teachers and students what work meets and does not meet the standard.
- Assessment rubrics that provide teachers with clear guidelines for evaluating their student’s understanding and providing meaningful feedback.
- Student rubrics that provide tool for self- and peer-assessment.
- Alignments to state, national, and Common Core standards.
- Online delivery for teachers.
- Google Classroom and ClassLink integration.
Access to the Exemplars Library requires a computer with one of the following Internet browsers: Internet Explorer 8+, Chrome, Safari, or Firefox.
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The links below contain a variety of free resources provided to our many users and to those of you just learning about Exemplars. We hope you find these resources useful.
Assessment & Student Rubrics
Formative assessment, related products.
An extensive library of math performance tasks and assessment tools built to align with the Common Core standards. 500+ problem-solving tasks are organized by domain and standard. An interactive scoring tutorial is included to help teachers hone assessment skills.
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Expressly created for Texas classrooms to align with the Math TEKS and build proficiency in problem-solving math skills. This collection includes 380+ performance tasks and assessment tools for teachers and students.
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Understanding Students with Additional Needs as Learners pp 101–114 Cite as
The Development of Problem-Solving Rubrics to Define Learning Progressions for Students with Additional Needs
- Toshiko Kamei 3 &
- Kerry Woods 3
- First Online: 01 December 2020
In a changing society with evolving needs and occupations, problem-solving is increasingly seen as an essential skill for success in many contexts, including school and the workplace. However, students with additional learning needs often lack the necessary support to be successful in this skill domain. The aim of the study described in this chapter was to design rubrics for problem-solving that define progressive levels of learning to support the instruction of this cohort of students. A working definition of problem- solving was used to draft observation statements in the form of rubrics that teachers could use to describe their students’ skill development. Workshops were conducted with specialist teachers (n = 13) who critiqued and extended these draft rubrics and mapped them to a learning progression. These materials were then trialed with experienced special education teachers, who reviewed them and generated intervention strategies for students at different skill levels on the derived progression. The outcome of the study was a set of assessment rubrics and level descriptions that teachers could use to support the learning of students with additional needs in a skill domain often dismissed as too demanding to be included in their personal programs.
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This chapter was originally published on the Australian Association for Research in Education’s (AARE) website as a refereed conference paper from the 2016 AARE Annual Conference.
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Kamei, T., Woods, K. (2020). The Development of Problem-Solving Rubrics to Define Learning Progressions for Students with Additional Needs. In: Griffin, P., Woods, K. (eds) Understanding Students with Additional Needs as Learners. Springer, Cham. https://doi.org/10.1007/978-3-030-56596-1_8
DOI : https://doi.org/10.1007/978-3-030-56596-1_8
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iRubric: Problem Solving- Performance Task rubric
5 Reasons to Use Rubrics for Performance Tasks
Rubrics for performance tasks are an excellent tool for educators to utilize throughout the school year for ongoing assessment of a student’s skills. A rubric is a scoring guide to judge performance on a specific task. A skill is broken down into different components and a numerical value is given to each component. The performance is then scored by totaling the sum of the numerical values.
5 Reasons to Use Rubrics For Performance Tasks
Here are 5 reasons why educators should use rubrics:
Provides the Steps Necessary to Complete the Task
A rubric informs the individual of what is expected of a task. It clarifies step by step what is required for proficiency. The student will know all the steps that are needed to complete a task.
Establishes a Standard or Goal
A rubric can provide a standard to assess the quality of how a task is completed.
The score on a rubric can determine if changes (improvements or regression) have occurred over time. It is a great tool to use after a long weekend, absences or school vacation to determine if regression has occurred to justify summer services.
Use a rubric to compare the abilities of a student with a peer to determine if the student’s skills are functional.
Helps with Objective Scoring
It can help increase the consistency of scoring. Instead of documenting minimal, moderate or significant progress, you can document an actual score to have a more quantitative measure.
Need some examples?
If you need some examples of rubrics for performance tasks, you can download some free rubrics below:
- Dressing Rubric – Putting On and Taking Off Socks
- Overall Personal Hygiene Rubric
- Meal Time Rubric – Using a Spoon
- Mobility Rubric – Walking in a Line
- Overall Handwriting Rubric
- Proper Positioning for Keyboarding Rubric
Your Therapy Source
Email: email@example.com Phone: (800) 507-4958 Fax: (518) 308-0290
Rubrics for Performance Tasks, Essay, Problem Solving, Poster Making, etc.
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Ready Made Rubric Assessment Tools for Performance Task
What is a rubric.
Analytic rubrics, here are examples of ready made rubric assessment tools that you can use in assessing the performance task you give to your learners..
- Rubric Assessment Tool for Research Report
- Rubric Assessment Tool for Story Writing
- Rubric Assessment Tool for Cooking Presentation
- Rubric Assessment Tool for Letter Writing
- Rubric Assessment Tool for Building a Structure
- Rubric Assessment Tool for Group Presentation
- Rubric Assessment Tool for Problem Solving in Math
- Rubric Assessment Tool for Class Debate
- Rubric Assessment Tool for Math Graphing
- Rubric Assessment Tool for Creating a Painting
- Rubric Assessment Tool for Independent Reading
- Rubric Assessment Tool for Poem Recitation
- Rubric Assessment Tool for Poster Making
- Rubric Assessment Tool for Interview
- Rubric Assessment Tool for Music
- Rubric Assessment Tool for Reading Comprehension
- Rubric Assessment Tool for Folk Dance
- Rubric Assessment Tool for Essay Writing
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- Rubric Assessment Tool for Skit/Role Playing
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