INTEGRATION OF TEACHING NOTIONS IN MATHEMATIC PRAXEOLOGIES IN THE STUDY OF QUADRATIC FUNCTION
Quadratic Function, Parable, Praxeological Reconstruction, Anthropological Theory of Didactics, Study Path and Research.
In the field of anthropology of didactics, the didactic knowledge (professionals) can be used to question the curricular contents and the strategies for their teaching. In this research, it is proposed that the integration of didactic notions in mathematical theories is a way to promote such questioning. This is closely watched on the diffusion of the mathematical quadratic function object in a mathematics teacher training course. This implies that the restrictions on the practices that constitute the mathematical activity of teachers and students constitute the object this investigation. Thus, the objective is to analyze the conditions and / or institutional constraints of a proposal to construct an alternative praxeological model for the study of quadratic function, to work out situations that lead us to the quadratic function as a parable in teacher training course. It is also a discussion of the status of the parable, as well as the interrelationships between mathematical domains. This investigation is based on the paradigm of questioning of the world, supported theoretically in the framework of the Anthropological Theory of Didactics, from which some notions necessary for the interpretation of the data built in its development are taken. It is part of a second generation Didactic Engineering, called Engineering of the Study and Research Path - SRP, which constitutes the methodological path of this investigation. The results indicate that the proposition of situations that take the quadratic function to the parable through the experimentation of a SRP potentiated the integration of didactic notions in the mathematical praxeologies of the research participants and, consequently, the questioning of the contents to be taught. This also characterized a kind of reconstruction of didactic-mathematical praxeologies in this formative context.