Tarefas de aprendizagem profissional para o desenvolvimento do raciocínio matemático em futuros professores

Abstract

The present work is inserted in the theme of Mathematical Reasoning (MR) and teacher education, recognizing the importance of MR development in the classroom, as recommended by the Brazilian National Common Curricular Base (BNCC). The research starts from the premise that, for prospective teachers to promote MR in their students, it is fundamental that they themselves develop both the capacity to reason and the knowledge about reasoning. The central motivation lies in the scarcity of research in Brazil on initial teacher education focused on MR, and the need to fill this formative gap. The general objective of this dissertation is to analyze the understandings about the processes of mathematical reasoning evidenced by mathematics undergraduates when discussing Professional Learning Tasks (PLT). To this end, two guiding questions were proposed: (1) How to elaborate a formative process for the initial education of mathematics teachers, concerning the understanding of Mathematical Reasoning? and (2) What are the contributions of the three domains of the PLOT (Professional Learning Opportunities for Teachers) model, with the purpose of analyzing the understanding of mathematical reasoning processes in prospective teachers? The methodology involved the structuring and development of a formative process in two classes of the Teaching Practice discipline at a public university in Paraná. This process was directed towards the initial education of mathematics teachers, aiming at reflection on MR and the ways of its implementation in the classroom. The theoretical framework is grounded in research that discusses mathematical reasoning and its forms of implementation, as well as studies on mathematics teacher education. The results and conclusions indicate the effectiveness of PLT for the development of undergraduates' knowledge about MR processes. The analysis reveals that the formative process contributed to the expansion of prospective teachers' awareness of the structure and processes of MR, allowing them to go beyond the mere application of procedures and advance in the understanding of the conceptual foundations that support each reasoning category, reaching the maximum level of understanding about MR processes. The research contributes to the area of Mathematics Education by proposing and analyzing a model of initial education focused on MR, offering subsidies for the elaboration of more effective curricular and pedagogical practices.