Grenier D. (2000)
Learning proof and modeling. Inventory of Teaching Practice and New Problems.

Contribution to: Paolo Boero, G. Harel, C. Maher, M. Miyazaki (organisers) Proof and Proving in Mathematics Education. ICME9 TSG 12. Tokyo/Makuhari, Japan.

Abstract
First, we study the status and role of proof in 11-16 years pupils'curricula and schoolbooks. We then develop our thesis on possibilities offered by others mathematics fields for the learning of proof. In order to support our thesis, we investigate some specificities of proof practice in Discrete Mathematics, especially from the viewpoint of truth checking and validation.
© Denise Grenier

  

First, we study the status and role of proof in 11-16 years pupils'curricula and schoolbooks. We then develop our thesis on possibilities offered by others mathematics fields for the learning of proof. In order to support our thesis, we investigate some specificities of proof practice in Discrete Mathematics, especially from the viewpoint of truth checking and validation.

 I. Elements of ecology of proof practice

 II. A new mathematics field for proof and news problems

Conclusion

In this article, we have tried to analyse the status for proof in French secondary School and to show the lack of the question of Truth and Falsehood and the predominant position of the activity of writting proof. We show also that, in the usual mathematics activity in class, there are no links between proof and modeling. Then, we present a few " basic " situations for proof and modeling, in which meaning and truth become central in the cognitive and teaching process.

References

Balacheff N. (1987) Processus de preuve et situations de validation, Educational Studies for Mathematics, vol.18, n°2, 147-176.
Grenier D. (1999), Discrete mathematics in relation to learning and teaching proof and modelization, proceedings of the first Conference of European Society for Research in Mathematics Education, ed. Inge Schwank, Osnabrueck University (Germany).
Grenier D., Payan Ch. (1998) Spécificités de la preuve et de la modélisation en Mathématiques Discrètes, Revue de Didactique des Mathématiques, vol. 18.1, pp. 59-100, ed. La Pensée Sauvage, Grenoble.