This work of mathematics education based on the framework of the theory of didactic situations, focuses on the joint action of teachers and students in a digital environment. We give an important place to the theoretical framework of documentary genesis, which complements and extends the scope of the instrumental genesis and considers artifacts as well as elements of the digital library system for teachers and students.
In the general context of the use of technology in the regular classroom of mathematics, we seek to understand how the incidents are indicative of perturbations that change the dynamic of the class. In developing this notion of didactical incident, we build a framework to highlight the phenomena of documentational genesis of teachers and students and to monitor the short or long term effects on mathematics teaching and learning.
We show that the didactical incidents, under certain conditions, offer opportunities for restructuring local and global knowledge for the teacher as part of his teaching or the student's learning of mathematics.
Keywords: theory of didactical situations, joint action, incident, dynamics, ordinary classrooms, instrumental genesis, documentational genesis.