Proofs and refutations in the undergraduate mathematics classroom

Sean Larsen, Michelle Zandieh

Research output: Contribution to journalArticle

41 Scopus citations

Abstract

In his 1976 book, Proofs and Refutations, Lakatos presents a collection of case studies to illustrate methods of mathematical discovery in the history of mathematics. In this paper, we reframe these methods in ways that we have found make them more amenable for use as a framework for research on learning and teaching mathematics. We present an episode from an undergraduate abstract algebra classroom to illustrate the guided reinvention of mathematics through processes that strongly parallel those described by Lakatos. Our analysis suggests that the constructs described by Lakatos can provide a useful framework for making sense of the mathematical activity in classrooms where students are actively engaged in the development of mathematical ideas and provide design heuristics for instructional approaches that support the learning of mathematics through the process of guided reinvention.

Original languageEnglish (US)
Pages (from-to)205-216
Number of pages12
JournalEducational Studies in Mathematics
Volume67
Issue number3
DOIs
StatePublished - Mar 1 2008

Keywords

  • Abstract algebra
  • Counterexamples
  • Defining refutations
  • Exception barring
  • Guided reinvention
  • Lakatos
  • Monster barring
  • Proof
  • Proof-analysis
  • Proving
  • Realistic mathematics education

ASJC Scopus subject areas

  • Mathematics(all)
  • Education

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