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Measuring What Counts: A Conceptual Guide for Mathematics Assessment
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), 125-146; 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), 195-221]. 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.
Lorrie A. Shepard, "Why We Need Better Assessments," Educational Leadership, 46:7 (1989), 7.
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), 211-230); Thomas L. Good, Catherine Mulryan, and Mary McCaslin "Grouping for Instruction in Mathematics: A Call for Programmatic Research on Small-Group 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), 241-271; 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), 179-187.
Linda D. Wilson, "Assessment in a Secondary Mathematics Classroom" (Ph.D. diss., University of Wisconsin-Madison, 1993).
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), 93-114.
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), 38-40.
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), 184-222.
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).