Annotated Bibliography of Resources for Educational Reform, Coherent Teaching Practice, and Improved Student Learning

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• Confrey, J. (1992). What constructivism implies for teaching. In R. B. Davis, C. A. Maher, & N. Noddings (Eds.), Constructivist views on the teaching and learning of mathematics (pp. 107-122). Journal for Research in Mathematics Education Monograph No. 4.

Direct instruction in mathematics follows a familiar patternÑintroductory review, a development portion, a controlled transition to seatwork, and a period of seatwork. The assumptions underlying direct instruction, however, are subject to challenge from a constructivist perspective. In this book chapter, Confrey relates two major aspects of constructivismÑconstruction and reflectionÑto mathematical learning. Reflection, she says, functions as the "bootstrap" for the construction of mathematical ideas. Students receiving direct instruction tend to memorize and imitate examples so as to produce the "right" answer. Confrey's premise is that instruction compatible with constructivist ideas will help students learn how to create "powerful" constructions that are internally consistent and can be applied to a range of problems. Confrey presents results of a case study of a teacher committed to constructivist beliefs. The focus of the study was on teacher-student interactions. From the study, a model of practice is generated which has six components: promotion of student autonomy; development of reflective processes; construction of case histories; identification and negotiation of a tentative solution path; retracing and group discussion of the paths; and adherence to the intent of the materials. Examples are provided of each component of this alternative to direct instruction.

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