
rooms as Learning Environments for Teachers and Researchers," in Robert Davis, Carolyn Maher, and Nel Noddings, ads., Consructivist Views on the Teaching and Learning of Mathematics, monograph, no. 4 (Reston, VA: National Council of Teachers of Mathematics, 1990), 125146; and Elizabeth Fennema, Thomas Carpenter, and Penelope Paterson "Learning Mathematics with Understanding: Cognitively Guided Instruction," in J. Brophy, ed., Advances in Research in Teaching (Greenwich, CT: JAI Press, 1989), 195221]. Purely epistemological analyses [e.g., Ernst van Glasersfeld, "Learning as a Constructive Activity", in Claude Janvier, ed., Problems of Representation in the Teaching and Learning of Mathematics (Hillsdale, NJ: Lawrence Erlbaum Associates, 1987)], also lend credence to the conception of learners as constructors of their own knowledge.

^{12}

Lorrie A. Shepard, "Why We Need Better Assessments," Educational Leadership, 46:7 (1989), 7.

^{13}

There have been several reviews of the literature in this area, including Nail Davidson, "Small Group Learning and Teaching in Mathematics: A Selective Review of the Literature, in R. Slavin et al., ads., Learning to Cooperate, Cooperating to Learn (New York, NY: Plenum, 1985), 211230); Thomas L. Good, Catherine Mulryan, and Mary McCaslin "Grouping for Instruction in Mathematics: A Call for Programmatic Research on SmallGroup Processes" in Douglas Grouws, ed., Handbook of Research on Mathematics Teaching and Learning (New York, NY: Macmillan, 1992); S. Sharan, "Cooperative Learning in Small Groups: Recent Methods and Effects on Achievement, Attitudes, and Ethinic Relations," Review of Educational Research 50 (1980), 241271; R. Slavin, ed., School and Classroom Organization (Hillsdale, NJ: Lawrence Erlbaum Associates, 1989). See also Yvette Solomon, The Practice of Mathematics (London, England: Routledge, 1989), 179187.

^{14}

Linda D. Wilson, "Assessment in a Secondary Mathematics Classroom" (Ph.D. diss., University of WisconsinMadison, 1993).

^{15}

Dedre Gentner and Albert L. Stevens, eds., Mental Models (Hillsdale, NJ: Lawrence Erlbaum Associates, 1981); Lauren Resnick and Wendy Ford, The Psychology of Mathematics for Instruction (Hillsdale, NJ: Lawrence Erlbaum Associates, 1981); Joseph C. Campione, Ann L. Brown, and Michael L. Connell, "Metacognition: On the Importance of Understanding What You Are Doing," in Randall I. Charles and Edward A. Silver, eds., The Teaching and Assessing of Mathematical Problem Solving (Reston, VA: Lawrence Erlbaum and National Council of Teachers of Mathematics, 1988), 93114.

^{16}

Robert Glaser, "Cognitive and Environmental Perspectives on Assessing Achievement," in Assessment in the Service of Learning: Proceedings of the 1987 ETS Invitational Conference (Princeton, NJ: Educational Testing Service, 1988), 3840.

^{17}

Jan de Lange, Mathematics, Insight and Meaning: Teaching, Learning and Testing of Mathematics for the Life and Social Sciences (Utrecht, The Netherlands: Rijksuniversiteit Utrecht, Vakgroep Onderzoek Wiskundeonderwijs en Onterwijscomputercentrum, 1987), 184222.

^{18}

Vermont Department of Education, Looking Beyond 'the Answer': The Report of Vermont's Mathematics Portfolio Assessment Program (Montpelier, VA: Author, 1991); Jean Kerr Stenmark, Assessment Alternatives in Mathematics: An Overview of Assessment Techniques that Promote Learning (Berkeley, CA: University of California, EQUALS, 1989).
