Um estudo acerca da Matriz Repunidade e suas Características Voltadas ao Ensino da Matemática

Abstract

This study essentially aims to design and present teaching situations involving the matrix of repetition, with an emphasis on the development of mathematical reasoning and the investigation of numerical patterns. This study is based on the methodological approaches of Didactic Engineering (DE) and Didactic Situation Theory (DST), giving priority to the preliminary analysis and a priori analysis phases. The proposed activities aim to investigate algebraic, structural, and recursive properties related to the repunity matrix, with the goal of fostering the construction of mathematical knowledge through intentional teaching situations. Based on the theoretical results obtained, it was possible to understand that the object of study and its characteristics can be considered a relevant tool for teaching mathematics, promoting the articulation between conceptual knowledge. In this sense, it is expected that this work will contribute to the formation of active, reflective, and autonomous thinking in students and that it will also serve as inspiration for new research in the field of mathematics education.