Percurso de estudo e pesquisa no conceito de função : analisando o processo de ensino e aprendizagem e as influências na formação do professor de matemática

Abstract

The purpose of this thesis was to analyze the application of the Study and Research Path (SRP), a didactic device that can be used as a methodology for the teaching and learning of mathematical concepts in undergraduate mathematics, such as can also work in the initial and continuing education of the Math teacher. The (SRP) has its bases in the French Mathematics Didactics and its theoretical basis in Anthropological Theory of Didactics (ATD), with Yves Chevallard as its main representative. We also use the notion of Didactic Contract (CD) of Guy Brousseau, which brings important elements of the analysis of the SRP directions, highlighting the established contracts, the renegotiations, the effects and disruptions of the didactic contract in the process. To complement our analysis and verify a possible learning provided by SRP, we use the Cycle of Solutions of Problems (CSP) approached by the Cognitive Psychology, identifying the steps of the evolution and the possible insights. The proposed implementation of the SRP was by the function content, an important content of the Basic Education and College Education. Our research presents some points of connection between the DC and the SRP, and, consequently, with the CSP, which may identify some advances and difficulties in the implementation of the didactic device, especially in the change from the didactic contract already established to a new didactic. Therefore, with the ATD and the DC checking the questions related to the teaching supported by the CSP, which can give us clues of the learning about the concept of function in the application of SRP, noting also its influence on the formation of the Mathematics teacher. As results, we observed that the CSP promotes a change in the praxeology of the students and teachers, while influencing the teaching practices used by the teacher, promoting their professional training.