### 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) |
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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

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## Cite this

*Journal for Research in Mathematics Education*,

*36*(4), 317-346.