The many facets of a definition: The case of periodicity

Joop Van Dormolen, Orit Zaslavsky

Research output: Contribution to journalArticle

Abstract

This paper was triggered by an authentic conversation between two mathematics teacher educators who debated whether a constant function is a periodic function, within the framework of a professional development program for secondary mathematics teachers. Their initial conversation led to deep mathematical and pedagogical musing surrounding mathematical definitions. In this paper, we present various aspects of a mathematical definition, including the role and nature of definitions in school mathematics, critical versus preferable features of a definition, and the arbitrariness underlying the choice of definition. We discuss the interplay between logical and pedagogical considerations with respect to definitions, drawing on the definition of a periodic function as an example.

Original languageEnglish (US)
Pages (from-to)91-106
Number of pages16
JournalJournal of Mathematical Behavior
Volume22
Issue number1
DOIs
StatePublished - 2003

Keywords

  • Logic
  • Mathematical definition
  • Pedagogy
  • Periodicity
  • Secondary school mathematics
  • Teacher education

ASJC Scopus subject areas

  • Education
  • Applied Psychology
  • Applied Mathematics

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