Abstract

Developing the teachers’ capacities to manage the mathematical tasks that he proposes in the classroom is an objective of teacher education that has had great relevance in recent years. Located on this theme, this reflection article proposes a way to understand how mathematics teachers mo-bilize knowledge about the resolution, analysis, and elaboration of investigative tasks of dynamic geometry (ITDG) for teaching, during the development of continuing education process. To achieve this goal, it becomes by assuming and theorizing the concepts of knowledge and joint work pro-vided by the theory of objectification, highlighting its main defining characteristics. Subsequently, these concepts are adapted to the context of ITDG resolution, analysis, and elaboration activities in the continuing education of mathematics teachers, to conceptualize next three types of joint work (resolution, analysis, and elaboration) and three professional knowledge capable of mobilization in this formative context. For each knowledge, the specific actions and reflections that can characterize each type of joint work developed by teachers during formative process are described. Finally, it is concluded that the theoretical approach exposed is not a finished product, but a critical reflection at the beginning that can be refined eventually when analyzing specific formative processes in geometry, oriented to the resolution, analysis, and elaboration of ITDG for teaching mathematics in middle and high school.