### 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 |

### Fingerprint

### Keywords

- Beliefs
- Calculus/analysis
- Conceptual knowledge
- Geometry
- Higher order thinking
- Reasoning
- Secondary mathematics

### ASJC Scopus subject areas

- Education

### Cite this

*Journal for Research in Mathematics Education*,

*36*(4), 317-346.

**Students' conceptions of a mathematical definition.** / Zaslavsky, Orit; Shir, Karni.

Research output: Contribution to journal › Review article

*Journal for Research in Mathematics Education*, vol. 36, no. 4, pp. 317-346.

}

TY - JOUR

T1 - Students' conceptions of a mathematical definition

AU - Zaslavsky, Orit

AU - Shir, Karni

PY - 2005/7

Y1 - 2005/7

N2 - 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.

AB - 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.

KW - Beliefs

KW - Calculus/analysis

KW - Conceptual knowledge

KW - Geometry

KW - Higher order thinking

KW - Reasoning

KW - Secondary mathematics

UR - http://www.scopus.com/inward/record.url?scp=22544445858&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=22544445858&partnerID=8YFLogxK

M3 - Review article

VL - 36

SP - 317

EP - 346

JO - Journal for Research in Mathematics Education

JF - Journal for Research in Mathematics Education

SN - 0021-8251

IS - 4

ER -