An Essay on Proof, Conviction, and Explanation: Multiple Representation Systems in Combinatorics

Autor/inn/en	Lockwood, Elise; Caughman, John S.; Weber, Keith
Titel	An Essay on Proof, Conviction, and Explanation: Multiple Representation Systems in Combinatorics
Quelle	In: Educational Studies in Mathematics, 103 (2020) 2, S.173-189 (17 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Lockwood, Elise)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0013-1954
DOI	10.1007/s10649-020-09933-8
Schlagwörter	Mathematical Logic; Mathematics Education; Theories; Mathematical Concepts + Suchen Sie Ihr Suchwort? Mathematical logics; Mathematische Logik; Mathematische Bildung; Theory; Theorie
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. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2022/1/01