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 language | English (US) |
|---|---|
| Pages (from-to) | 317-346 |
| Number of pages | 30 |
| Journal | Journal for Research in Mathematics Education |
| Volume | 36 |
| Issue number | 4 |
| State | Published - Jul 2005 |
Keywords
- Beliefs
- Calculus/analysis
- Conceptual knowledge
- Geometry
- Higher order thinking
- Reasoning
- Secondary mathematics
ASJC Scopus subject areas
- Mathematics (miscellaneous)
- Education