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Social Construction of Mathematical Knowledge: Presented Problems in Mathematics Classrooms

Abstract

This study examined how mathematical problems are articulated, i.e., identified and defined, in the context of a fiflh-grade lesson on equivalent fractions. Opportunities to participate in mathematical discourse and reasoning activities were closely related to the structure, organization, and content of classroom presented problems. In this lesson, the presented problem took the form of a concatenation of tasks. Each task in the series became the mathematical context that animated students' talk about solution methods. Classroom discourse limited to serial tasks constrained students' opportunities to develop relational knowledge about the properties and principles of equivalent fractions. "Does a child learn only to talk, or also to think? Does it learn the sense of multiplication before or after it learns multiplication?" -- Wittgenstein, Zettel, p. 324

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