Álgebra e o pensamento algébrico: desafios e possibilidades para o ensino nos anos finais do ensino fundamental

Abstract

This Final Paper is a research that investigates the challenges and methodological possibilities for the development of algebraic thinking in students in the final years of Elementary School, in a public school in the city of Manaus. The research is motivated by the finding that the teaching of Algebra, often focused on technical and operational aspects, has generated significant difficulties, as evidenced in large-scale evaluations. The central problem that guided the study was: What are the challenges for the development of algebraic thinking in the final years of Elementary School, in the context of a public school in the city of Manaus, and how can we overcome them? To answer this question, the general objective was to identify the challenges and methodological possibilities for this development, in the context of the 9th grade of Elementary School, in a public school in the city of Manaus. The theoretical foundation was anchored in the distinction between arithmetic and algebraic thinking, in the dimensions of generalization, symbolization and modeling, and in learning theories, notably the Theory of Conceptual Fields and the APOS Theory (Actions, Processes, Objects, Schemas). The methodology adopted was qualitative research, with data collection carried out through questionnaires and activities applied to teachers and students, and content analysis. The results pointed to the persistence of a predominantly instrumental approach to Algebra, which hinders the transition to relational and structural understanding. However, potentials were identified in pedagogical practices that prioritize the identification of patterns and generalization, acting as conceptual bridges for the construction of algebraic thinking. It is concluded that a paradigm is imperative in teaching, shifting the focus from Algebra as a technique to Algebra as a language of generalization and modeling, and it is suggested the need for continuing education and elaboration of didactic materials aligned with this perspective.