A prática que se investiga: entre Álgebra e Geometria, o ensino de produtos notáveis e fatoração nos anos finais do ensino fundamental

Abstract

This study investigates the articulation between the fields of Algebra and Geometry as a pedagogical strategy for teaching notable products and factorization in the final years of Elementary Education. Considering the difficulties students often experience in understanding abstract algebraic concepts, this research explores the complementarity between geometric and algebraic representations as a way to promote more integrated learning. The study is grounded in theoretical perspectives that advocate the articulation among different registers of mathematical representation, favoring the construction of meaning and conceptual understanding.This is a qualitative study guided by the interpretative paradigm, in which a didactic sequence was designed and implemented with a 9th-grade class in a public school located in the municipality of Conquista, Minas Gerais, Brazil. Data were collected through a field journal, classroom observations, students’ written productions, and audio and video recordings.The data analyzed so far indicate that the use of visual representations and manipulative materials supports the transition between perceptual experiences and symbolic representations, increasing students’ engagement and contributing to the understanding of mathematical concepts. The research also highlights the importance of teachers’ reflection in the reconfiguration of pedagogical practices. In this sense, the Investigation of One’s Own Practice (IPP) enables the teacher to critically analyze her actions, rethink didactic choices, and produce professional knowledge, contributing directly to teacher education.The study indicates that the integration between Algebra and Geometry, combined with an investigative stance from the teacher, has the potential to strengthen teaching and learning processes in Mathematics.