Abstract
Our research into the didactics of geometry and algebra in secondary schools has led us to identify student difficulties that could be explained by the transparency of certain knowledge in classrooms. The continuation of this research in the context of ongoing work on a collaborative arrangement between teachers and researchers leads us to raise a certain number of questions at the crossroads of three strongly intertwined poles. The first is that of the transparency of knowledge, the second is that of the professional development of teachers within collaborative arrangements with researchers, and the third concerns the role of language in the teaching-learning of mathematics. This text aims to give an account of the questions that emerge in the light of initial analyses of the secondarising process of discourse based on a corpus made up of videos of sessions implemented in classes of 6e and 3e, as well as tests proposed to the pupils of these classes.