Proof as a Cluster Category

Author:
Jennifer A. Czocher Texas State University

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Keith Weber Rutgers University

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Volume/Issue:
Volume 51: Issue 1
Page(s):
50–74
DOI:
https://doi.org/10.5951/jresematheduc.2019.0007
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Keywords:
Definitions; Mathematical practice; Proof

To design and improve instruction in mathematical proof, mathematics educators require an adequate definition of proof that is faithful to mathematical practice and relevant to pedagogical situations. In both mathematics education and the philosophy of mathematics, mathematical proof is typically defined as a type of justification that satisfies a collection of necessary and sufficient conditions. We argue that defining the proof category in this way renders the definition incapable of accurately capturing how category membership is determined. We propose an alternative account—proof as a cluster category—and demonstrate its potential for addressing many of the intractable challenges inherent in previous accounts. We will also show that adopting the cluster account has utility for how proof is researched and taught.

Footnotes

We would like to thank Kristen Bieda, Paul Dawkins, Matthew Inglis, and the anonymous reviewers for their very helpful comments on earlier drafts of this manuscript.

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Copyright:
The National Council of Teachers of Mathematics, Inc. All rights reserved. 2020
Page Count:
25
Article Category:
Research Article
Received:
12 Apr 2018
Accepted:
28 Aug 2018
Print Publication Date:
01 Jan 2020
Online Publication Date:
Jan 2020
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