26: Assessment of Students’ Knowledge of Mathematics: Steps Toward A Theory

Assessment has begun to assume an increasingly important role in education. More than ever before, state and district assessments are exerting pressure on teachers and students to achieve high levels of performance. National and international assessment results have drawn the attention of policymakers, who use them as leverage for mandating change in education in hopes of bettering the nation’s competitive edge. The Nation at Risk report (National Commission on Excellence in Education, 1983) delineated the problem by comparing American students’ relatively low test scores with those of students from other industrialized nations, as well as noting the decline from 1963 to 1980 in average mathematics scores on the College Board’s Scholastic Aptitude Tests (SAT). Recent developments in cognitive psychology (Brown, 1988; Carpenter & Fennema, 1988; Glaser, 1986) have resulted in the creation of new instructional programs that integrate assessment with instruction and minimize paper-and-pencil drill and exercises. These programs have influenced and are supported by recommendations included in the National Council of Teachers of Mathematics’ Curriculum and Evaluation Standards for School Mathematics (1989).