Students' Conceptions of a Mathematical Definition
Orit Zaslavsky, Karni Shir
July 2005, Volume 36, Issue 4, Page 317
Abstract:
This article deals with 12thgrade 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 definitionbased reasoning; for the analytic concepts, the dominant type was an examplebased 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
