Students' Conceptions of a Mathematical Definition

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.