Mathematics Professional Series Alternative Assessment — Middle School   Performance Assessment Description Performance assessment techniques show how students actually perform tasks. For students to be good problem solvers, tests of problem-solving competency must logically assess performance on problem-solving tasks. Paper-and-pencil tests that grade an answer right or wrong cannot evaluate performance adequately. For example, think about a musician, artist, basketball player, or writer. Their work may be judged by a performance in a concert, by a work of art, a game, or a book. These people do not take paper-and-pencil tests to demonstrate what they know. They perform! The same standards need to apply to students studying mathematics. If they are to become problem solvers, students must be taught how to analyze, formulate, and solve difficult and non-routine problems, and their performance as solvers of problems needs to be determined. What Does a Performance Assessment Task Attempt to Do? The purpose of a performance assessment task is to determine what students know and what they can do. The task should be meaningful, authentic, and worth mastering. The following criteria help to define a performance task. It should: Be aligned with the goals, objectives, and content of the curriculum. Allow students to display their thinking and understanding of a mathematical situation and not just provide a single answer. Provide an opportunity for an evaluation of the processes involved in the task. Be realistic, interesting, and thought-provoking. Be representative of the goal being evaluated so generalizations can be made about a student's performance. Stress depth more than breadth and mastery more than speed. Be more open-ended than tightly structured. Be nonalgorithmic, that is, not have one clear path of action specified at the beginning of the task. Raise other questions or lead to other problems. Sample Performance Assessment Tasks The following activities are representative of performance assessment tasks for middle school students. Write a paragraph explaining the four-step plan for problem solving. Tell why you can use an estimate to place the decimal point in the quotient of 15.6 ÷ 13. Give an argument or a counterexample to support your answer to these questions: Are all numbers that are divisible by 9 also divisible by 3? Are all numbers that are divisible by 3 also divisible by 9? Suppose that in a poster, all parallelograms are colored red or green, all triangles are blue, all rectangles are green, and all trapezoids are purple. What color would the squares and rhombuses be? Write a quiz for classmates consisting of five problems to solve by finding the percent of a number. Use actual information from a newspaper, magazine, or catalog to formulate the problems. Work in groups. Choose a place you would like to visit. Determine how much it would cost to get there by different means of transportation, such as by car, plane, train, bus, or boat. Make a poster of your information that includes the advantages and disadvantages of each type of transportation and the one you would be most likely to choose. Write a description of a project you would like to work on during the next month. The project should involve a research investigation and be related to the content of this course. Evaluating Results of a Performance Assessment Task The first step in evaluating a performance task is to establish a system for documenting students' performances. A scoring rubric is often used to assess performance tasks. A rubric should stress assessment of the process goals of instruction, which are difficult to assess by conventional testing. Students should know what constitutes each level of performance. When students have completed the performance task, their work is compared to the specific rubric and scored holistically according to the level that best describes the work. More Information For more information on performance assessment and other types of alternative assessment, see "Alternative Assessment in the Mathematics Classroom," one of the booklets in the Glencoe Mathematics Professional Series.