### Abstract

This paper was triggered by an authentic conversation between two mathematics teacher educators who debated whether a constant function is a periodic function, within the framework of a professional development program for secondary mathematics teachers. Their initial conversation led to deep mathematical and pedagogical musing surrounding mathematical definitions. In this paper, we present various aspects of a mathematical definition, including the role and nature of definitions in school mathematics, critical versus preferable features of a definition, and the arbitrariness underlying the choice of definition. We discuss the interplay between logical and pedagogical considerations with respect to definitions, drawing on the definition of a periodic function as an example.

Original language | English (US) |
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Pages (from-to) | 91-106 |

Number of pages | 16 |

Journal | Journal of Mathematical Behavior |

Volume | 22 |

Issue number | 1 |

DOIs | |

State | Published - 2003 |

### Keywords

- Logic
- Mathematical definition
- Pedagogy
- Periodicity
- Secondary school mathematics
- Teacher education

### ASJC Scopus subject areas

- Education
- Applied Psychology
- Applied Mathematics

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## Cite this

*Journal of Mathematical Behavior*,

*22*(1), 91-106. https://doi.org/10.1016/S0732-3123(03)00006-3