The Tension Between Theories of Learning and Instruction in Mathematics Education

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Abstract
This article addresses the contradiction between the assumption that the goal of mathematics instruction is to transmit knowledge to students and the view that students construct mathematical knowledge by reorganizing their cognitive structures. Transmission and constructivist analyses of communication are contrasted. It is concluded that the task of accounting for successful instruction is not one of explaining how students take in and process information transmitted by the teacher. Instead, it is to explain how students actively construct knowledge in ways that satisfy constraints inherent in instruction. A brief case study is presented to support this contention, and general implications that take account of both cognitive and noncognitive instructional goals are discussed.

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