1 A pedagogy-embedded Computer Algebra System

The constraints of a Computer Algebra System are generally classified as internal constraints, command constraints and organization constraints. In fact, a fourth kind of constraints exists, namely motivating constraints. These constraints consist in features or commands of the CAS whose understanding demands sometimes from the user to acquire more mathematical knowledge than what has been taught in a standard course. Theorems can appear which necessitate learning beyond the syllabus framework. Such "new " theorems appear generally in two situations, namely when using a pedagogy-embedded feature of the CAS (either a posteriori help, or a priori hints), or when using certain commands and trying to analyze the results. We describe a research frame in the first year Foundation Courses in Mathematics, in our Engineering College. With this research, we wish to understand more deeply the instrumentation processes at work with the students and to check motivations for a change in the institution's culture. I. Levels of intervention of a Computer Algebra System. As an assistant to mathematical learning, a Computer Algebra System (a CAS) offers three levels of help: 1) a technical tool performing technical tasks; 2) a tool whose performances help to develop more conceptual understanding; 3) a technological help to bypass a lack of conceptual knowledge, where such knowledge is out of reach, at least in ”the next future”. The first level is the blackbox level and has no great pedagogical value. Maybe it allows the teacher to save time for reflexion and theoretical understanding, but a perverse effect is the loss of manual computatio