Proving in number theory at the transition from the secondary level to the tertiary level : between organizing and operative dimensions

Véronique Battie (1)

1 LEPS-LIRDHIST - Laboratoire Interdisciplainaire de Didactique et d'Histoire des Sciences et Techniques

At the beginning of French University, the failure rate in proving in mathematics is important. In this paper, we explore this phenomenon in the case of number theory. In the proving process, we distinguish two complementary dimensions, namely the organizing one and the operative one. This distinction permits to situate the autonomy devolved to learners in proving tasks. We focus on the transfer of this autonomy in the secondary-tertiary transition from examples out of examinations given in 2006 in Grade 12 and in first year at University concerning congruences. According to us, this captures one of the sources of difficulties to prove in number theory faced by students arriving at University.

Mots clés: University; Grade 12; Number theory; congruences; organizing dimension; operative dimension; didactic of mathematics

Domaines: Sciences de l'Homme et Société

Véronique Battie. Proving in number theory at the transition from the secondary level to the tertiary level : between organizing and operative dimensions. ICMI Study 19 conference: Proof and Proving in Mathematics Education, 2009, Taipei, Taiwan. pp.71-76. ⟨hal-01129054⟩