^{1}

National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematics (Reston, VA: Author, 1989), 196.

^{2}

This statistic was compiled by using information from Edward D. Roeber, "Association of State Assessment Programs: Annual Survey of America's LargeScale Assessment Programs" (Unpublished document, Fall 1991).

^{3}

Edward A. Silver and Patricia A. Kenney, "Sources of Assessment Information for Instructional Guidance in Mathematics" in Thomas A. Romberg, ed., Reform in School Mathematics and Authentic Assessment, in press; Edward A. Silver, Jeremy Kilpatrick, and S. Schlesinger, Thinking Through Mathematics (New York, NY: College Entrance Examination Board, 1990); Thomas A. Romberg, E. Anne Zarinnia, and Kevin F. Collis, "A New World View of Assessment in Mathematics," in Gerald Kulm, ed., Assessing Higher Order Thinking in Mathematics (Washington, D.C.: American Association for the Advancement of Science, 1990), 2138; Thomas A. Romberg, "Evaluation: A Coat of Many Colors" (A paper presented at the Sixth International Congress on Mathematical Education, Budapest, Hungary, July 27August 3, 1988), Division of Science, Technical and Environmental Education, UNESCO.

^{4}

Linda M. McNeil, "Contradictions of Control: Part 3, Contradictions of Reform," Phi Delta Kappan 69 (1998): 478485.

^{5}

Lauren B. Resnick, National Research Council, Committee on Mathematics, Science, and Technology Education, Education and Learning to Think (Washington, D.C.: National Academy Press, 1987).

^{6}

Patricia Ann Kenney and Edward A. Silver, "Student SelfAssessment in Mathematics," in Norman L. Webb and Arthur Coxford, eds., Assessment in the Mathematics Classroom, 1993 NCTM Yearbook (Reston, VA: National Council of Teachers of Mathematics, 1993), 230.

^{7}

Thomas A. Romberg, "How One Comes to Know: Models and Theories of the Learning of Mathematics," in Mogens Niss, ed., Investigations into Assessment in Mathematics Education: An ICMI Study (Dordrecht, The Netherlands: Kluwer Academic Publishers, 1993), 109.

^{8}

Thomas A. Romberg and Thomas P. Carpenter, "Research on Teaching and Learning Mathematics: Two Disciplines of Scientific Inquiry," in Merlin C. Wittrock, ed., Handbook of Research on Teaching, 3rd ed. (New York, NY: Macmillan, 1986), 851.

^{9}

Education and Learning to Think, 12.

^{10}

Nancy S. Cole, "Changing Assessment Practice in Mathematics Education: Reclaiming Assessment for Teaching and Learning" (Paper presented at the Conference on Partnerships for Systemic Change in Mathematics, Science, and Technology Education, Washington, D.C., 7 December 1992).

^{11}

This constructivist view of learning is becoming increasingly prevalent. Analyses of learning from a cognitive perspective point to the centrality of the learner's activity in acquiring understanding [see, for example, John R. Anderson, "Acquisition of Cognitive Skill, Psychological Review, 89 (1982): 396406; and Y. Anzai and Herbert A. Simon, "The Theory of Learning by Doing" Psychological Review 86 (1979): 12440). Classroombased studies such as the ones cited earlier (Paul Cobb, Terry Wood, and Erna Yackel "Class
