Instrumentalization of school problems of mathematics teachers in service

The research is carried out in a university context of continuous training of mathematics teachers. The use schemes of 39 teachers when employing, in different situations, "school problems" as resources are described. To this aim, the operational invariants of such schemes are identified in the framework of the theory of conceptual fields and the instrumental approach. The results show a lack of operational invariants that facilitate didactic gestures typical of questioning. A possible pivotal element of the teachers' instrument system is emerging, which may generate new research to bring teachers' teaching patterns towards of questioning the knowledge.