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Students' Conceptions of a Mathematical Definition

Orit Zaslavsky, Karni Shir 

July 2005, Volume 36, Issue 4, Page 317

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.

Keywords:
Grade 12
Article
Conceptual Development
Math Coordinator / Coach
Geometry & Measurement
Teacher
Survey Studies
Skill and Fluency
Professional Development / Teacher Education
Reasoning and Proof
Representation
Theory