The use of the ICT to teach mathematics remains weak and lacks of diversity as shown by recent statistical studies that we synthesized in a first part of this PhD thesis. Our hypothesis is that there is a qualitative deficit in teachers’ education courses, which contributes to explain why it is so difficult for teachers to integrate ICT in their teaching. Our goal is to specify the existence and the nature of this deficit. For that purpose we built a theoretical framework of analysis starting from two theoretical frameworks: the twofold approach and the instrumental approach. The first framework allows a recombining of teacher’s educator activity and helps to build a grid for analysing classrooms’ situations on which teacher’s education courses are based. The second framework allows analyzing the relationship between technological artefacts and human being involved at three levels: the student, the teacher and the teachers’ educator. We used our framework to analyze a panel of three teachers’ education courses and the representations of fourteen teachers’ educators. This analysis helped to bring to light a professional type defined by invariants in practices and a gap between two professional identifies: the teacher’s and the teacher’s educator’s. It also highlights the limits of practices observed, mainly based on a strategy of « homology ». The introduction of a reflexive component into teacher educators’ practices seems a relevant idea to go beyond these limits. This new hypothesis is tested twice by means of a didactic engineering. This method shows the interest of introducing of a reflexive component this idea as well as questions for further investigation.