**ERIC Number:**EJ764983

**Record Type:**Journal

**Publication Date:**2005-Jul

**Pages:**30

**Abstractor:**Author

**ISBN:**N/A

**ISSN:**ISSN-0021-8251

Students' Conceptions of a Mathematical Definition

Zaslavsky, Orit; Shir, Karni

Journal for Research in Mathematics Education, v36 n4 p317-346 Jul 2005

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. (Contains 3 figures, 6 tables and 4 footnotes.)

Descriptors: Group Activities, Geometric Concepts, Definitions, Grade 12, High School Students, Independent Study, Mathematical Concepts, Questionnaires, Group Discussion, Mathematical Logic, Thinking Skills, Concept Formation, Mathematics Instruction, Secondary School Mathematics, Calculus, Foreign Countries

National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191-1502. Tel: 800-235-7566; Tel: 703-620-3702; Fax: 703-476-2970; e-mail: orders@nctm.org; Web site: http://www.nctm.org/publications/

**Publication Type:**Journal Articles; Reports - Research

**Education Level:**Grade 12

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A

**Identifiers - Location:**Israel