## Abstract

The relationship between mathematical creativity, knowledge and expertise is a phenomenon which can be seen as a “creativity-knowledge dilemma”: Having

knowledge is a necessary condition for a person to be creative; on the other hand, creativity is an important condition for knowledge construction. In this paper, we analyze mathematical activity that is directed at both the development of problem solving expertise and creativity in geometry. Creativity in this study is connected to the discovery of new properties of the given geometrical

objects through investigation in DGE. We introduce a framework for the analysis of the complexity of a discovered property. Based on the analysis performed, we

hypothesize that (1) discovery skills can be developed in people with different levels of problem solving expertise while the range of this development depends on the expertise; (2) the discovery process is rooted in the problem-solving expertise of a person.

knowledge is a necessary condition for a person to be creative; on the other hand, creativity is an important condition for knowledge construction. In this paper, we analyze mathematical activity that is directed at both the development of problem solving expertise and creativity in geometry. Creativity in this study is connected to the discovery of new properties of the given geometrical

objects through investigation in DGE. We introduce a framework for the analysis of the complexity of a discovered property. Based on the analysis performed, we

hypothesize that (1) discovery skills can be developed in people with different levels of problem solving expertise while the range of this development depends on the expertise; (2) the discovery process is rooted in the problem-solving expertise of a person.

Original language | English |
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Title of host publication | CERME 9 - Ninth Congress of the European Society for Research in Mathematics Education |

Editors | Konrad Krainer, Naďa Vondrová |

Place of Publication | Prague, Czech Republic |

Pages | 1024-1031 |

Number of pages | 8 |

State | Published - 1 Feb 2015 |

### Publication series

Name | Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education |
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## Keywords

- Mathematical creativity
- problem-solving expertise
- geometry investigations
- complexity of discovery