Contribuições da Sequência Fedathi para o desenvolvimento do Pensamento Matemático Avançado: uma análise da mediação docente em aulas de álgebra Linear

Abstract

This paper discusses the relationship between the Fedathi Sequence (SF) teaching methodology and the Advanced Mathematical Thinking (PMA) theory, aiming to understand how the teaching action favors the development of student mathematical thinking, as it enables reflection-action in the classroom. class. In this context, the main objective was to understand how the teacher mediation supported in SF, influences the development of the PMA of undergraduate students in classes of Linear Algebra. It was characterized as a qualitative study whose research questions referred to the case study. The field investigation was divided into three stages: (a) observation of a Linear Algebra discipline; (b) completion of an extension course; and (c) study group, with participants from the previous stage. The first two steps addressed the teaching in Linear Algebra using the SF and the third dealt with its study as teaching methodology. In the results it was identified, in the teacher mediation, the incentive to the mobilization of different mental processes, triggered by the use of questions, that facilitated the dialogical mediation, as well as the use of Geogebra software and the way mathematical representations were explored. In addition, the processing and conversion of representation records were explored. The processes of generalization and abstraction were noted with more emphasis on teacher action / mediation, especially when students were encouraged to observe the mathematical structure underlying the content. In addition, evidence has been found that SF can contribute not only to students 'cognitive development but also to social, affective and metacognitive development, which significantly contribute to students' willingness to acquire new knowledge and put into practice the research reasoning. We conclude that SF can provide a favorable environment for the development of PMA processes for undergraduate students in Mathematics in Linear Algebra classes, since it favors student action and guides the teacher as to how to interact and mediate content in classroom, so as to respect the student's maturation time, their cognitive development, leading him to understand concepts in a meaningful way, without limiting himself to rote memorization and algorithmic manipulation.