Exemplifying definitions: A case of a square

Rina Zazkis, Roza Leikin

Research output: Contribution to journalArticlepeer-review

Abstract

In this study we utilize the notion of learner-generated examples, suggesting that examples generated by students mirror their understanding of particular mathematical concepts. In particular, we explore examples generated by a group of prospective secondary school teachers for a definition of a square. Our framework for analysis includes the categories of accessibility and correctness, richness, and generality. Results shed light on participants' understanding of what a mathematical definition should entail and, moreover, contrast their pedagogical preferences with mathematical considerations.

Original languageEnglish
Pages (from-to)131-148
Number of pages18
JournalEducational Studies in Mathematics
Volume69
Issue number2
DOIs
StatePublished - Oct 2008

Keywords

  • Definitions
  • Example spaces
  • Examples
  • Learner-generated examples
  • Necessary and Sufficient conditions
  • Prospective teachers
  • Secondary mathematics teachers

ASJC Scopus subject areas

  • General Mathematics
  • Education

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