Journal
EDUCATIONAL STUDIES IN MATHEMATICS
Volume 103, Issue 2, Pages 173-189Publisher
SPRINGER
DOI: 10.1007/s10649-020-09933-8
Keywords
Proof; Proofs that explain and convince; Combinatorics; Binomial identities
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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.
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