Measures of Problem-Solving Performance and of Problem-Solving Instruction.

This chapter discusses three paper-and-pencil measures of problem-solving performance. These measures were characterized as Measure 1, Measure 2, and Measure 3. All three measures include matched pretests and post-tests that focus on what the student does while trying to solve problems, rather than on the final solution he or she produces. The two versions of Measure 1 contain five problems, each of which can be solved in two or three, sometimes four or five different ways. Problems on the two examinations are matched not by form or by subject matter but by solution methods; the same problem-solving approaches yield solutions to corresponding pretest and post-test problems. Measure 1 explored performance on problems related to those studied in the course. Measure 2 asked for students' qualitative reactions to their work on the problems in Measure 1. It determines how familiar they perceived each problem to be, whether or not they planned their solution to the problem, whether their work on the problem was organized or disorganized, and how difficult they thought the problem was. The two versions of Measure 3 each containing nine problems that, similar to those in Measure 1, were paired by solution type. All these three measures were used to evaluate the before and after performance of students in a course in mathematical problem solving.