Entre matrizes e códigos: uma sequência didática baseada em demandas cognitivas para a ressignificação do ensino de álgebra

Abstract

Amid matrix operations, codes, and processes of algebraic formalization, this study investigates how a didactic sequence articulated with Realistic Mathematics Education and cognitive-demand principles can transform the way high school students approach Algebra. The central purpose is to understand how such a sequence—designed through investigative situations and progressively challenging tasks—can foster new ways of giving meaning to and practicing Algebra in the classroom. Drawing on student-led workshops, tasks structured in increasing levels of complexity, and cryptography scenarios that spark curiosity, the study reveals movements of conceptual reorganization. The analyzes, conducted through Discursive Textual Analysis, highlight conceptual advances, stronger engagement, and a closer alignment of students with more investigative mathematical practices. Amid productive errors, creative interpretations, and conceptual shifts, the data suggest that learning Algebra may be less about repeating procedures and more about deciphering structures, almost like unraveling a code. What emerges, in the end, is not merely the account of a didactic experience but an invitation to reconsider the place of Algebra in education: a space in which meaning and form intertwine and where investigation becomes an essential part of mathematical learning.