In this article we share a study on a professional development training program for math teachers. It is presented as innovative as it focuses on the reflection on the practice of teaching through the raising and solution of professional problems. We define professional problems, such as those teaching situations to which the teacher seeks solutions. We demonstrate with excerpts from working sessions that these solutions are nourished by the reflection on the practice they are trying to modify. They are, as a whole, indicators of specialized knowledge that characterize a professional of teaching mathematics.