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Reflections on Proof as Explanation

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Advances in Mathematics Education Research on Proof and Proving

Part of the book series: ICME-13 Monographs ((ICME13Mo))

Abstract

This chapter explores the connection between two distinct ways of defining mathematical explanation and thus of identifying explanatory proofs . The first is the one discussed in the philosophy of mathematics, in which a proof is considered explanatory when it helps account for a mathematical fact, clarifying why it follows from others. It is concerned with intra-mathematical factors, not with pedagogical considerations. The second definition is the one current among mathematics educators, who consider a proof to be explanatory when it helps convey mathematical insights to an audience in a manner that is pedagogically appropriate. This latter view brings cognitive factors very much into play. The two views of explanation are quite different. The chapter shows, however, citing examples, that insights from what are considered by philosophers of mathematics to be explanatory proofs can sometimes form a basis for explanatory proofs in the pedagogical sense and thus add value to the curriculum .

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Acknowledgements

Preparation of this chapter was supported in part by the Social Sciences and Humanities Research Council of Canada.

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Authors and Affiliations

  1. Ontario Institute for Studies in Education, University of Toronto, Toronto, Canada

    Gila Hanna

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  1. Gila Hanna
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Correspondence to Gila Hanna .

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Editors and Affiliations

  1. Faculty of Education, University of Cambridge, Cambridge, United Kingdom

    Andreas J. Stylianides

  2. Department of Mathematics, University of California San Diego, La Jolla, California, USA

    Guershon Harel

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Hanna, G. (2018). Reflections on Proof as Explanation. In: Stylianides, A., Harel, G. (eds) Advances in Mathematics Education Research on Proof and Proving. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-70996-3_1

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  • DOI: https://doi.org/10.1007/978-3-319-70996-3_1

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  • Publisher Name: Springer, Cham

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