Published In

Educational Studies in Mathematics

Document Type

Post-Print

Publication Date

2-1-2020

Abstract

There is a longstanding conversation in the mathematics education literature about proofs that explain versus proofs that only convince. In this essay, we offer a characterization of explanatory proofs with three goals in mind. We first propose a theory of explanatory proofs for mathematics education in terms of representation systems. Then, we illustrate these ideas in terms of combinatorial proofs, focusing on binomial identities. Finally, we leverage our theory to explain audience-dependent and audience-invariant aspects of explanatory proof. Throughout, we use the context of combinatorics to emphasize points and to offer examples of proofs that can be explanatory or only convincing, depending on how one understands the claim being made.

Description

This is a post-peer-review, pre-copyedit version of an article published in Educational Studies in Mathematics. The final authenticated version is available online at: http://doi.org/10.1007/s10649-020-09933-8

© 2020 Springer Nature Switzerland AG

DOI

10.1007/s10649-020-09933-8

Persistent Identifier

https://archives.pdx.edu/ds/psu/32537

Available for download on Monday, February 01, 2021

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