## Abstract

This chapter analyzes three different types of problem posing associated with geometry investigations in school mathematics, namely (a) problem posing through proving; (b) problem posing for investigation; and (c) problem posing through investigation. Mathematical investigations and problem posing which are central for activities of professional mathematicians, when integrated in school mathematics, allow teachers and students to experience meaningful mathematical activities, including the discovery of new mathematical facts when posing mathematical problems. A dynamic geometry environment (DGE) plays a special role in mathematical problem posing. I describe different types of problem posing associated with geometry investigations by using examples from a course with prospective mathematics teachers. Starting from one simple problem I invite the readers to track one particular mathematical activity in which participants arrive at least at 25 new problems through investigation in a DGE and through proving.

Original language | English |
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Title of host publication | Mathematical Problem Posing |

Subtitle of host publication | From Research to Effective Practice |

Place of Publication | Dordrecht, the Netherlands |

Publisher | Springer Netherlands |

Pages | 373-391 |

Number of pages | 19 |

ISBN (Electronic) | 9781461462583 |

ISBN (Print) | 9781461462576 |

DOIs | |

State | Published - 1 Jan 2015 |

### Bibliographical note

Publisher Copyright:© Springer Science+Business Media New York 2015.

## Keywords

- Investigations in a dynamic geometry environment
- Multiple proof tasks
- Problem posing for investigation
- Problem posing through investigation
- Problem posing through proving
- Teacher knowledge and skills

## ASJC Scopus subject areas

- General Social Sciences