A Repunidade no campo dos inteiros: Explorando Padrões no Contexto de Matemática

Abstract

The main objective of this work is to develop and propose Didactic Situations involving the repunity sequence, focusing on the development of mathematical reasoning and the exploration of numerical patterns. The research is based on the methodological approaches of Didactic Engineering (DE) and Didactic Situations Theory (DST), prioritizing the preliminary analysis and a priori analysis phases. The proposed activities aim to investigate the algebraic, structural, and recursive properties of the sequence, including its extension to negative integer indices, in order to promote the construction of mathematical knowledge through problematizing situations. The theoretical results indicate that the repunity sequence can be excellent content for teaching mathematics, promoting the articulation between conceptual knowledge. It is thus hoped that this will contribute to the formation of critical, reflective, and autonomous students and inspire new investigations in the field of mathematics education.