Divisibilidade e congruência: aplicações didáticas no ensino médio

Abstract

This dissertation investigates high school students’ understanding of divisibility and congruences through a structured didactic intervention. Initially, a diagnostic activity was applied to identify the main difficulties and strategies used by students when solving problems involving modular arithmetic and cyclic patterns. Based on the results obtained, a sequence of four investigative lessons was designed, aimed at consolidating the fundamental concepts. Subsequently, a second application was conducted to assess students’ progress, revealing an increase in correct answers in questions related to simultaneous congruences, day-of-the-week cycles, and patterns of remainders in powers. The results indicate that the intervention contributed to the improvement of conceptual understanding and the ability to apply appropriate problem-solving strategies, although some more complex questions still posed significant challenges. The analysis highlights the importance of contextualized activities and continuous practice for the consolidation of mathematical reasoning at the high school level