Proof as a cluster category

Jennifer A. Czocher, Keith Weber

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)50-74
Number of pages25
JournalJournal for Research in Mathematics Education
Volume51
Issue number1
DOIs
StatePublished - Jan 2020

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)
  • Education

Keywords

  • Definitions
  • Mathematical practice
  • Proof

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