(Federal University of Pará, Brazil)

Abstract: This theoretical article aims to weave reflections, briefly, on a fragment of the theoretical contribution of the didactics of mathematics to the understanding of the teaching and learning processes of mathematical concepts. I will focus essentially on the theory of didactical situations (TDS) and the anthropological theory of the didactic (ATD), whose scope goes beyond the study of the phenomena related to the students’ construction of mathematical concepts. My reflections will focus on the contributions of those theories to the education of teachers who teach mathematics. I will also reflect on the study and research path (SRP, PEP in the Portuguese acronym) and study and research path for teacher education (SRP-TE, in Portuguese acronym), developed as methodologies within the anthropological theory of the didactic. The study shows a part of the potential of TDS and ATD in investigative and formative processes. It also shows that the SPR and the SRP-TE, as a methodological reference for research and teacher education articulated to the ATD, are configured as theoretical and methodological devices that allow integrating the teaching and learning processes in the paradigm of questioning the world, more specifically, the world of school mathematics.