Instrument-to-think-mathematics-with: intertwining mathematical concepts and schemes of use in the instrumental genesis of the Mathematics teacher

This article discusses the integration of digital technologies in the Mathematics classroom and the process of appropriation of these technologies by teachers and students. Based on theoretical studies and reflections on the actions of teacher-researchers, it is analyzed how the activities proposed by the Mathematics teacher reveal levels in a continuous process of appropriation of the artifact and impact the constitution of didactic instruments that enhance the learning of Mathematics. The research is anchored in the theoretical framework of instrumental genesis, especially for the role of usage schemes that are established in the development of the execution of the activity. The results of the study propose categories for different activities in a dynamic mathematics environment. In addition, they indicate that artifacts evolve into instruments as an instrument-for-thinking-mathematics-with as mathematical concepts and the constitution of usage schemes of the artifact intertwine in a coordinated whole.