Using task-based interviews to generate hypotheses about mathematical practice: mathematics education research on mathematicians’ use of examples in proof-related activities

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Abstract

Mathematics education researchers frequently use task-based interviews to gain insight into mathematicians’ practice. However, there are a number of factors that should prevent mathematics educators from extrapolating how individual mathematicians respond to researcher-generated tasks in laboratory conditions, to how mathematicians practice their craft in authentic settings. In this paper we critically analyze the rationality of using task-based interviews to investigate mathematical practice, focusing on how task-based interview studies have been used to inform our understanding of mathematicians’ use of examples in mathematical practice. We discuss four specific generalizations about mathematical practice drawn from these studies, and suggest other types of studies that can be used to corroborate or challenge those generalizations.

Original languageEnglish (US)
JournalZDM - Mathematics Education
DOIs
StateAccepted/In press - Jan 1 2020

All Science Journal Classification (ASJC) codes

  • Education
  • Mathematics(all)

Keywords

  • Conjecturing
  • Examples
  • Mathematical practice
  • Proof
  • Task-based interviews

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