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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.

June 23, 2015
A student is working on a peper for his geography class.


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
  • Missions
  • Worksheets
  • Rubrics to assess the project

Prep Work

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:

You are working for the American Red Cross. It is the responsibility of the air traffic controller to redirect the pilots to avoid storms, other planes, and more. It is the responsibility of the pilots to complete the missions they are given.
Mission 3: A cruise liner left port and traveled 25 miles on a bearing of N 42 degrees W off the coast of Key West, Florida, when it started to experience engine difficulties. A second cruise liner was at port in Cape Coral, 150 miles due north of the port of the first liner. What bearing should the second cruise liner travel in order to rescue the people from the troubled liner, and how far does it need to travel?

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.

Evaluation/Utilizing Rubrics

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.


School Snapshot

Hampton High School

Grades 9-12 | Allison Park, PA
1112 | Public, Suburban
Per Pupil Expenditures
$13,864 District
Free / Reduced Lunch
96% White
2% Asian/Pacific Islander
1% Black
1% Hispanic
Data is from the 2013-14 academic year.

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