Students' conceptions of a mathematical definition

Orit Zaslavsky, Karni Shir

Research output: Contribution to journalReview article

Abstract

This article deals with 12th-grade students' conceptions of a mathematical definition. Their conceptions of a definition were revealed through individual and group activities in which they were asked to consider a number of possible definitions of four mathematical concepts: two geometric and two analytic. Data consisted of written responses to questionnaires and transcriptions of videotaped group discussions. The findings point to three types of students' arguments: mathematical, communicative, and figurative. In addition, two types of reasoning were identified surrounding the contemplation of alternative definitions: for the geometric concepts, the dominant type of reasoning was a definition-based reasoning; for the analytic concepts, the dominant type was an example-based reasoning. Students' conceptions of a definition are described in terms of the features and roles they attribute to a mathematical definition.

Original languageEnglish (US)
Pages (from-to)317-346
Number of pages30
JournalJournal for Research in Mathematics Education
Volume36
Issue number4
StatePublished - Jul 2005

Keywords

  • Beliefs
  • Calculus/analysis
  • Conceptual knowledge
  • Geometry
  • Higher order thinking
  • Reasoning
  • Secondary mathematics

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Education

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