Functional representations produced and used by students during their introduction to the concept of derivative: a window on their understanding processes

International audience; This article is about student understanding processes during their introduction to the concept of derivative that were constructed as part of a doctoral dissertation. The observation of these understanding processes is made from the standpoint of representations in the sense of Duval (1993) and Hitt (2006). More specifically, two aspects of the models of the comprehension process are underlined. First, the fact that students can sometimes work well in different registers, but that they can not necessarily do a proper coordination of these representations is put forward. In addition, the particular role played by the verbal register is also discussed.