期刊
EDUCATIONAL STUDIES IN MATHEMATICS
卷 103, 期 2, 页码 173-189出版社
SPRINGER
DOI: 10.1007/s10649-020-09933-8
关键词
Proof; Proofs that explain and convince; Combinatorics; Binomial identities
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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