A Atividade de Situações Problema Discente no ensino de limites e continuidade

Contribuições do Sistema Didático Galperin–Talízina–Majmutov

Abstract

Teaching Differential and Integral Calculus faces recurrent challenges, such as mechanical and decontextualized approaches to learning its fundamental concepts. In this context, this article presents a didactic proposal for teaching limits and continuity, grounded in the Galperin–Talízina–Majmutov Didactic System. The aim is to describe a Complete Orienting Basis of Action Scheme (EBOCA) designed for Student Problem Situation Activity, focusing on introductory notions of limits and continuity. The structure of the EBOCA is organized into stages that include problem formulation, construction of the conceptual and procedural core, problem solving, and solution analysis. The proposal also incorporates multiple representations—algebraic, graphical, and numerical—which foster a comprehensive understanding of the concepts. As a result, the proposed EBOCA guides instructional planning, provides criteria for formative assessment, and supports the progressive internalization of scientific concepts, contributing to overcoming mechanistic practices in Calculus teaching. It is concluded that the EBOCA constitutes a flexible tool for organizing instruction within the Zone of Proximal Development, enabling teachers to diagnose students’ initial learning levels and to plan interventions that promote theoretical thinking in Mathematics, particularly in the study of limits and continuity of functions.