An essay on proof, conviction, and explanation: multiple representation systems in combinatorics

Autor:	Keith Weber, Elise Lockwood, John S. Caughman
Rok vydání:	2020
Předmět:	Mathematical logic Computer science General Mathematics media_common.quotation_subject 05 social sciences 050301 education Combinatorial proof Context (language use) Representation (arts) Mathematical proof Education Combinatorics Proof theory 0501 psychology and cognitive sciences Conversation 0503 education Binomial coefficient 050104 developmental & child psychology media_common
Zdroj:	Educational Studies in Mathematics. 103:173-189
ISSN:	1573-0816 0013-1954
DOI:	10.1007/s10649-020-09933-8
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::f59956d4b4c7d25f2f66646e9af5988e https://doi.org/10.1007/s10649-020-09933-8 Zobrazit plný text záznamu Plný text ve formátu PDF Plný text ve formátu HTML
Nepřihlášeným uživatelům se plný text nezobrazuje	K zobrazení výsledku je třeba se přihlásit.