The aim of this research is to analyze the pedagogical management system of students in Science and Technology of Physical and Sports Activities in initial training at the National Institute of Youth, Physical Education and Sports (INJEPS ) during their internships in secondary schools. From a reading grid composed of the systemic model of the intervention process of Dunkin and Biddle (1974) and that of Chevallard (1992), this study problematizes on the one hand the didactic fact based on the variables of context, program, process and product and on the other hand the concept of praxeology. It also seeks to understand the key variables in the pedagogical supervision process and how the INJEPS manages the feedback produced by the supervisors of the INJEPS and the Pedagogical Inspectorate. From the analysis of the results of the investigations, it emerges that the supervisors of the two institutions focus mainly on the context, process and product variables during the pedagogical supervision of the trainees of the 3rd, 4th and 5th year, while the program variables are also taken into account in the first and second year. At the end of the supervisions, only the internship notes produced by the supervisors' teaching reports are taken into account by the administration during the partial and final evaluations of the students. No didactic treatment of the content of the feedbacks is done with a view to improving the pedagogical training of future teachers.