Uma abordagem sobre a operação de adição de frações por meio de classes de equivalências

Abstract

This work presents a didactic sequence applied in a second-year high school class at a public school in the municipality of Estância Velha/RS, where the author is a reference math teacher. The didactic proposal addresses the addition of fractions through equivalence classes, aiming to reframe fractional numbers through an algebraic approach typically introduced in higher education. To this end, the work begins by exploring teaching experiences and the weaknesses present in the teaching and learning process of fractions. Subsequently, a brief introduction to the Theory of Didactic Transposition is presented, which was chosen as the methodology for this work, serving as a strategy to adapt complex concepts to make them accessible at the students level of understanding. Following this, the exercise script is presented, organized to challenge students to read, interpret, and discuss resolutions in groups. The class reports, containing the definition of relationships, properties, demonstrations, and operations, provide a detailed view of the development of teaching over time. Initially, there was resistance from students to the proposed new educational approach, which quickly gave way to phases of overcoming, integration, and a growing interest in the concepts addressed. This evolution mainly highlights the relevance of differentiated pedagogical approaches and underscores the importance of active teacher intervention when difficulties or resistance arise from students. The ability of teachers to deal with these challenges plays a crucial role in the success of implementing new methodologies, ensuring that objectives are achieved, as was the case in this proposal.