### 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) |
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Pages (from-to) | 57-75 |

Number of pages | 19 |

Journal | Journal of Mathematical Behavior |

Volume | 29 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1 2010 |

### Keywords

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

### ASJC Scopus subject areas

- Education
- Applied Psychology
- Applied Mathematics