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## Abstract

This article discusses the concept of mathematics discourses by analysing two main questions. The first question is about the plurality of mathematics and the possibility of the simultaneous existence of culturally different mathematics. The second question is about the respective value of the different mathematics and its means of power in terms of 'disciplining' discourse. In order to investigate these questions we will use a theoretical toolkit that borrows the concepts of 'language games' and of 'family resemblance' from Wittgenstein, the concepts of 'discourses' and of 'disciplining' from Foucault and the concept of vertical and horizontal discourses, and recontextualisation from Bernstein.

One of the most challenging tasks in present-day philosophy of mathematics is to defend the thesis that "real" mathematics is a long distance away from the idealized core of its practices, called the "skeleton" in this paper. Nevertheless, this skeleton serves to identify what is mathematics proper, i.e. mathematics performed in the academic area. All other elements in the mathematics discourse are ignored, shifted to the background to increase its skeleton's visibility. Such a strategy must lead to the rejection as being mathematical of a huge set of cultural practices that, according to many, do include mathematical aspects. If instead of a skeleton idea, family resemblances are called into play, an interesting multiplication and diversification of mathematics discourses and practices occurs, and it will include "street mathematics", as well as ethnomathematical or other educational and pedagogical discourses, strongly or weakly related to academic mathematics.

The necessity of the plural of mathematics discourses will force us to abandon a Foucauldian view that stresses the control and power of a unique discours in favour of a more layered perspective. Because mathematical practices happen in diverse local, temporal and spatial contexts, multiple recontextualizations of what the flesh around the skeleton might be will occur. These will prevent one unique fixity and allow for multiple versions of the game.

One of the most challenging tasks in present-day philosophy of mathematics is to defend the thesis that "real" mathematics is a long distance away from the idealized core of its practices, called the "skeleton" in this paper. Nevertheless, this skeleton serves to identify what is mathematics proper, i.e. mathematics performed in the academic area. All other elements in the mathematics discourse are ignored, shifted to the background to increase its skeleton's visibility. Such a strategy must lead to the rejection as being mathematical of a huge set of cultural practices that, according to many, do include mathematical aspects. If instead of a skeleton idea, family resemblances are called into play, an interesting multiplication and diversification of mathematics discourses and practices occurs, and it will include "street mathematics", as well as ethnomathematical or other educational and pedagogical discourses, strongly or weakly related to academic mathematics.

The necessity of the plural of mathematics discourses will force us to abandon a Foucauldian view that stresses the control and power of a unique discours in favour of a more layered perspective. Because mathematical practices happen in diverse local, temporal and spatial contexts, multiple recontextualizations of what the flesh around the skeleton might be will occur. These will prevent one unique fixity and allow for multiple versions of the game.

Original language | English |
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Title of host publication | Discourses of Change and Changes of Discours |

Editors | P. Smeyers |

Pages | 72-83 |

Number of pages | 12 |

Publication status | Published - 2014 |

Event | Discourses of Change and Changes of Discours - Leuven, Belgium Duration: 13 Nov 2014 → 15 Nov 2014 |

### Conference

Conference | Discourses of Change and Changes of Discours |
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Country | Belgium |

City | Leuven |

Period | 13/11/14 → 15/11/14 |

### Bibliographical note

P. Smeyers, & M. Depaepe (eds.). Discourses of Change and Changes of Discours. Conference Leuven, 13-15 November.## Keywords

- Mathematics education
- Wittgenstein
- prime numbers
- Foucault
- mathematical practices

## Fingerprint

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