Number theory in the national compulsory examination at the end of the French secondary level: between organizing and operative dimensions

International audienceIn our researches in didactic of number theory, we are especially interested in proving in the secondary-tertiary transition. In this paper, we focus on the "baccalauréat", the national examination that pupils have to take at the end of French secondary level. In reasoning in number theory, we distinguish two complementary dimensions, namely the organising one and the operative one, and this distinction permits to situate the autonomy devolved to learners in number theory problems such as baccalauréat's exercises. We have analysed 38 exercises, from 1999 to 2008, and we present the results obtained giving emblematic examples