### Abstract

The purpose of this paper is to further the notion of defining as a mathematical activity by elaborating a framework that structures the role of defining in student progress from informal to more formal ways of reasoning. The framework is the result of a retrospective account of a significant learning experience that occurred in an undergraduate geometry course. The framework integrates the instructional design theory of Realistic Mathematics Education (RME) and distinctions between concept image and concept definition and offers other researchers and instructional designers a structured way to analyze or plan for the role of defining in students' mathematical progress.

Original language | English (US) |
---|---|

Pages (from-to) | 57-75 |

Number of pages | 19 |

Journal | Journal of Mathematical Behavior |

Volume | 29 |

Issue number | 2 |

DOIs | |

State | Published - Jun 2010 |

### Fingerprint

### Keywords

- Concept definition
- Concept image
- Defining
- Definition
- Realistic Mathematics Education
- Undergraduate mathematics education

### ASJC Scopus subject areas

- Applied Mathematics
- Applied Psychology
- Education

### Cite this

**Defining as a mathematical activity : A framework for characterizing progress from informal to more formal ways of reasoning.** / Zandieh, Michelle; Rasmussen, Chris.

Research output: Contribution to journal › Article

*Journal of Mathematical Behavior*, vol. 29, no. 2, pp. 57-75. https://doi.org/10.1016/j.jmathb.2010.01.001

}

TY - JOUR

T1 - Defining as a mathematical activity

T2 - A framework for characterizing progress from informal to more formal ways of reasoning

AU - Zandieh, Michelle

AU - Rasmussen, Chris

PY - 2010/6

Y1 - 2010/6

N2 - The purpose of this paper is to further the notion of defining as a mathematical activity by elaborating a framework that structures the role of defining in student progress from informal to more formal ways of reasoning. The framework is the result of a retrospective account of a significant learning experience that occurred in an undergraduate geometry course. The framework integrates the instructional design theory of Realistic Mathematics Education (RME) and distinctions between concept image and concept definition and offers other researchers and instructional designers a structured way to analyze or plan for the role of defining in students' mathematical progress.

AB - The purpose of this paper is to further the notion of defining as a mathematical activity by elaborating a framework that structures the role of defining in student progress from informal to more formal ways of reasoning. The framework is the result of a retrospective account of a significant learning experience that occurred in an undergraduate geometry course. The framework integrates the instructional design theory of Realistic Mathematics Education (RME) and distinctions between concept image and concept definition and offers other researchers and instructional designers a structured way to analyze or plan for the role of defining in students' mathematical progress.

KW - Concept definition

KW - Concept image

KW - Defining

KW - Definition

KW - Realistic Mathematics Education

KW - Undergraduate mathematics education

UR - http://www.scopus.com/inward/record.url?scp=77953914099&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77953914099&partnerID=8YFLogxK

U2 - 10.1016/j.jmathb.2010.01.001

DO - 10.1016/j.jmathb.2010.01.001

M3 - Article

VL - 29

SP - 57

EP - 75

JO - Journal of Mathematical Behavior

JF - Journal of Mathematical Behavior

SN - 0732-3123

IS - 2

ER -