Performance tasks provide an opportunity to assess students’ higher-order thinking and reasoning, which is sometimes difficult to evaluate using multiple-choice or other content-driven assessment items. As indicated in the name, this type of assessment is truly a “performance,” where students demonstrate their knowledge and understanding of designated mathematical standards. On next-generation assessments in particular, these tasks are usually composed of several technology-enhanced items and at least one item requiring a short or extended constructed response. Here are three strategies for developing rigorous a math performance task:
1) Assess Content Through Processes
A well-written performance task demands that students demonstrate comprehension of mathematical content standards through problem solving, communication, and conceptual understanding—all of which are covered in the Common Core’s Standards for Mathematical Practice. For example, in a task addressing 3D figures, rather than merely asking students to calculate the surface area of a rectangular prism given its dimensions, you could ask students to explain why there is more than one rectangular prism with a surface area of 100 square centimeters and justify their response with examples. Not only does this question assess whether or not a student can calculate the surface area of a 3D object (CCSS.Math.Content.7.G.B.6), but it demands that a student construct an argument of their own in order to demonstrate their understanding of this concept (CCSS.Math.Practice.MP3). When deciding upon the context and format of a performance task, math course writers should not only ask themselves what content the task will assess, but also what learning the task will demonstrate.
2) Integrate Authentic Contexts
Real-world scenarios of mathematical content make math meaningful for students by establishing authentic contexts in which the content can be applied. A student’s mathematical proficiency is better assessed when they must demonstrate their learning through application to an unfamiliar context. Since a performance task is expected to be non-routine and more cognitively demanding than a single problem, this is an excellent opportunity for math item writers to incorporate real-world data and connections. Another way this authenticity can be accomplished is through the use of technology-enhanced assessment items (TEIs). An appropriately selected TEI, such as equation builder or line plot, might allow students to demonstrate their learning in a way similar to what they would be asked to do in the classroom while simultaneously incorporating 21st century skills such as critical thinking, creativity, and technological literacy.
3) Balance Ambiguity with Structure
When developing performance tasks, it is important to include items that yield multiple approaches or solutions. However, it is also important that an item not be so open-ended that students’ responses do not address the standards the task was intended to assess. Think about how you can word the directions and question stems in performance tasks to ensure that students understand the parameters of the task and what mathematical content is expected in their response. At the same time, be sure to avoid fragmenting the instructions into steps that lead students to a singular approach. In order to find the appropriate amount of scaffolding to include in a clear and coherent task, ask yourself what you had to know mathematically to find the solution.
For ideas on developing your own performance tasks, download this free handout.
