Exemplifying definitions: A case of a square

Rina Zazkis; Roza Leikin

doi:10.1007/s10649-008-9131-7

Exemplifying definitions: A case of a square

Rina Zazkis, Roza Leikin

Department of Mathematics Education

Research output: Contribution to journal › Article › peer-review

Abstract

In this study we utilize the notion of learner-generated examples, suggesting that examples generated by students mirror their understanding of particular mathematical concepts. In particular, we explore examples generated by a group of prospective secondary school teachers for a definition of a square. Our framework for analysis includes the categories of accessibility and correctness, richness, and generality. Results shed light on participants' understanding of what a mathematical definition should entail and, moreover, contrast their pedagogical preferences with mathematical considerations.

Original language	English
Pages (from-to)	131-148
Number of pages	18
Journal	Educational Studies in Mathematics
Volume	69
Issue number	2
DOIs	https://doi.org/10.1007/s10649-008-9131-7
State	Published - Oct 2008

Keywords

Definitions
Example spaces
Examples
Learner-generated examples
Necessary and Sufficient conditions
Prospective teachers
Secondary mathematics teachers

ASJC Scopus subject areas

Education
General Mathematics

Access to Document

10.1007/s10649-008-9131-7

Cite this

@article{8a9b9fd33c57406eb03130c05412ec38,

title = "Exemplifying definitions: A case of a square",

abstract = "In this study we utilize the notion of learner-generated examples, suggesting that examples generated by students mirror their understanding of particular mathematical concepts. In particular, we explore examples generated by a group of prospective secondary school teachers for a definition of a square. Our framework for analysis includes the categories of accessibility and correctness, richness, and generality. Results shed light on participants' understanding of what a mathematical definition should entail and, moreover, contrast their pedagogical preferences with mathematical considerations.",

keywords = "Definitions, Example spaces, Examples, Learner-generated examples, Necessary and Sufficient conditions, Prospective teachers, Secondary mathematics teachers",

author = "Rina Zazkis and Roza Leikin",

year = "2008",

month = oct,

doi = "10.1007/s10649-008-9131-7",

language = "English",

volume = "69",

pages = "131--148",

journal = "Educational Studies in Mathematics",

issn = "0013-1954",

publisher = "Springer",

number = "2",

}

TY - JOUR

T1 - Exemplifying definitions

T2 - A case of a square

AU - Zazkis, Rina

AU - Leikin, Roza

PY - 2008/10

Y1 - 2008/10

N2 - In this study we utilize the notion of learner-generated examples, suggesting that examples generated by students mirror their understanding of particular mathematical concepts. In particular, we explore examples generated by a group of prospective secondary school teachers for a definition of a square. Our framework for analysis includes the categories of accessibility and correctness, richness, and generality. Results shed light on participants' understanding of what a mathematical definition should entail and, moreover, contrast their pedagogical preferences with mathematical considerations.

AB - In this study we utilize the notion of learner-generated examples, suggesting that examples generated by students mirror their understanding of particular mathematical concepts. In particular, we explore examples generated by a group of prospective secondary school teachers for a definition of a square. Our framework for analysis includes the categories of accessibility and correctness, richness, and generality. Results shed light on participants' understanding of what a mathematical definition should entail and, moreover, contrast their pedagogical preferences with mathematical considerations.

KW - Definitions

KW - Example spaces

KW - Examples

KW - Learner-generated examples

KW - Necessary and Sufficient conditions

KW - Prospective teachers

KW - Secondary mathematics teachers

UR - https://www.scopus.com/pages/publications/51549113561

U2 - 10.1007/s10649-008-9131-7

DO - 10.1007/s10649-008-9131-7

M3 - Article

AN - SCOPUS:51549113561

SN - 0013-1954

VL - 69

SP - 131

EP - 148

JO - Educational Studies in Mathematics

JF - Educational Studies in Mathematics

IS - 2

ER -

Exemplifying definitions: A case of a square

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this