some strong evidence supporting the constructivist approach: The first is the "Second Grade Classroom Teaching Project" that has been reported extensively by Paul Cobb, Terry Wood, Erna Yackel and their colleagues [see, for example, Cobb, Wood, and Yackel "Classrooms as Learning Environments for Teachers and Researchers," in Robert Davis, Carolyn Maher and Nel Noddings, eds., Constructivist Views on the Teaching and Learning of Mathematics, monograph, no. 4 (Reston, VA: National Curriculum of Teachers of Mathematics, 1990), 125-146]. The second is the Cognitively Guided Instruction project, which has been described by Elizabeth Fennema, Thomas Carpenter, and Penelope Peterson [see, for example, Fennema, Carpenter, and Peterson, "Learning Mathematics with Understanding: Cognitively Guided Instruction," in J. Brophy, ed., Advances in Research in Teaching (Greenwich, CT: JAI Press, 1989), 195-221]. For a more general discussion, see Lauren B. Resnick, Education and Learning to Think, National Research Council, Committee on Mathematics, Science, and Technology Education, Commission on Behavioral and Social Sciences and Education (Washington, D.C.: National Academy Press, 1987); and Everybody Counts, 58-59.

16  

Yvette Solomon, The Practice of Mathematics (London, England: Routledge, 1989), 179-187.

17  

Thomas L. Good, Catherine Mulryan, and Mary McCaslin, "Grouping for Instruction in Mathematics: A Call for Programmatic Research on Small Group Processes," in Douglas A. Grouws, ed., Handbook of Research on Mathematics Teaching and Learning (New York, NY: Macmillan, 1992), 165-196. Neil Davidson and Toni Worshem, "Enhancing Thinking Through Cooperative Learning" (New York, NY: Teachers College, 1992).

18  

Vinetta Jones, "Responses to Three Questions" (Paper prepared for The State of American Public Education: Views on the State of Public Schools, Washington, D.C., 4-5 February 1993).

19  

Jeannie Oakes, Keeping Track: How Schools Structure Inequality (New Haven, CT: Yale University Press, 1985); Jeannie Oakes, Multiplying Inequalities: The Effect of Race, Social Class, and Tracking on Opportunities to Learn Mathematics (Santa Monica, CA: Rand Corporation, 1990); Leigh Burstein, ed., Student Growth and Classroom Processes, vol. 3, IEA Study of Mathematics (Oxford, England: Pergamon Press, 1992).

20  

Harold W., Stevenson and James W. Stigler, The Learning Gap: Why Our Schools Are Failing and What We Can Learn from Japanese and Chinese Education (New York, NY: Summit Books, 1992), 113-129.

21  

S. Stodolsky, S. Salk, and B. Glaessner, "Student Views About Learning Math and Social Studies," American Educational Research Journal 28:1 (1991), 89-116.

22  

Heibert Ginsburg, Children's Arithmetic: The Learning Process (New York, NY: D. Van Nostrand Co., 1977); Lauren B. Resnick and Wendy W. Ford, The Psychology of Mathematics for Instruction (Hillsdale, NJ: Lawrence Erlbaum Associates, 1981).

23  

Michael Cole and Peg Griffin, eds., Contextual Factors in Education: Improving



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