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


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D. Roeber, "Association of State Assessment Programs: Annual Survey of America's Large-Scale Assessment Programs" (Unpublished document, Fall 1991).


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), 21-38; Thomas A. Romberg, "Evaluation: A Coat of Many Colors" (A paper presented at the Sixth International Congress on Mathematical Education, Budapest, Hungary, July 27-August 3, 1988), Division of Science, Technical and Environmental Education, UNESCO.


Linda M. McNeil, "Contradictions of Control: Part 3, Contradictions of Reform," Phi Delta Kappan 69 (1998): 478-485.


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).


Patricia Ann Kenney and Edward A. Silver, "Student Self-Assessment 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.


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.


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.


Education and Learning to Think, 12.


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).


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): 396-406; and Y. Anzai and Herbert A. Simon, "The Theory of Learning by Doing" Psychological Review 86 (1979): 124-40). Classroom-based studies such as the ones cited earlier (Paul Cobb, Terry Wood, and Erna Yackel "Class

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