Mathematics Professional Series Alternative Assessment — Algebra   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 ow 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 algebra students. Write a problem that has x < 13 as the solution. Describe how you would solve a problem by using the strategy of working backward. Give an example to support your answer to the following question: When choosing values for x in an equation with two variables, are some numbers better choices than others? A coin is flipped, a die is rolled, and a card is drawn from a standard deck of 52 playing cards. Explain what the probability is of getting a head, a six, and a queen. Research and write a report on a famous French or African mathematician. Work in groups of two to four to discuss the following problem: A 3-digit base-ten numeral can be represented as a polynomial in x with x = 10 as shown. 45610 = 4 · 102 + 5 · 101 + 6 · 100, or 456x = 4x2 + 5x + 6x0; If the base is changed from 10 to 2, the number 15 would be represented as: 1 · 23 + 1 · 22 + 1 · 21 + 1 · 20, or x3 + x2 + x1 + x0; Look for a pattern and represent the number 28 in base 2, using polynomials. 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.