Proofs as Bearers of Mathematical Knowledge
Yehuda Rav’s inspiring paper “Why do we prove theorems?” published in Philosophia Mathematica (1999; 7: 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.
KeywordsQuadratic Equation Mathematical Knowledge Mathematics Curriculum Isosceles Triangle Central Thesis
Preparation of this paper was supported in part by the Social Sciences and Humanities Research Council of Canada. We are grateful to Ella Kaye and Ysbrand DeBruyn for their assistance. We wish to thank the anonymous reviewers for their helpful comments.
A previous version appeared in ZDM, The International Journal on Mathematics Education 2008;40(3):345–353. It is reproduced by permission from Springer.
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