Published In
Educational Studies in Mathematics
Document Type
Post-Print
Publication Date
2-1-2020
Subjects
Proof theory, Combinatorial analysis, Binomial equations
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.
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DOI
10.1007/s10649-020-09933-8
Persistent Identifier
https://archives.pdx.edu/ds/psu/32537
Citation Details
Lockwood, E., Caughman, J. S., & Weber, K. (2020). An essay on proof, conviction, and explanation: multiple representation systems in combinatorics. Educational Studies in Mathematics, 103(2), 173-189.
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
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