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

International audienceAt 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