Gerald A. Goldin
There is increasing recognition that the methods currently used most widely by schools for assessing student mathematics achievement are having a substantial negative impact on meaningful learning. Often it is assumed that the situation can be improved by replacing tests that measure low-level skills, computational algorithms, and routine problem-solving with new instruments containing more sophisticated, nonroutine problems. Ideally, with an appropriate pool of test items, it is suggested that "teaching toward the test" would no longer compromise the goals of the assessment and that a student's successful performance would unquestionably reflect a deep mathematical understanding.
This chapter argues against this approach and stresses the need for a sound cognitive model as the basis of a framework for assessing meaningful mathematics learning and understanding in schools. Exploring in detail a few mathematical assessment items illustrates how the outcomes of any assessment--traditional or non traditional--depend on the teacher's prior understanding of what is being assessed. Particular cognitive processes cannot be identified with a mathematics problem that elicits them, nor can they be assumed to be necessary to solve the problem. It follows that reform of assessment involves much more than the creation of new instruments. What is needed is not only an appropriate cognitive model, but also an understanding among teachers, school administrators, students, and the general