Proofs as bearers of mathematical knowledge |
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Authors: | Gila Hanna Ed Barbeau |
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Institution: | 1. Department of Curriculum, Teaching and Learning, Ontario Institute for Studies in Education of the University of Toronto, Toronto, ON, Canada, M5S 1V6 2. Department of Mathematics, University of Toronto, Toronto, ON, Canada, M5S 2E4
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Abstract: | Yehuda Rav’s inspiring paper “Why do we prove theorems?” published in Philosophia Mathematica (1999, 7, pp. 5–41) has interesting implications for mathematics education. We examine Rav’s central ideas on proof—that proofs convey important elements of mathematics such as strategies and methods, that it is “proofs rather than theorems that are the bearers of mathematical knowledge”and thus that proofs should be the primary focus of mathematical interest—and then discuss their significance for mathematics education in general and for the teaching of proof in particular. |
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