A plataforma “desvendando o cálculo” aplicada na transição do pensamento matemático: uma análise pedagógica dos erros dos licenciandos no ensino de limites

Abstract

This study addresses the challenge of transitioning from elementary to advanced mathematical thinking in the teaching of Differential and Integral Calculus, with an emphasis on the concept of limit, whose limited understanding often leads to conceptual and procedural errors that hinder learning in subsequent courses. The investigation highlights the relevance of analyzing such errors as a pedagogical tool in pre-service teacher education and explores the potential of digital technologies to support the learning of abstract concepts. The objective was to develop the educational platform Desvendando o Cálculo (“Unveiling Calculus”), focusing on the pedagogical analysis of errors and on the contributions of students’ mathematical thinking regarding the concept of function limits. Grounded in the Didactical Engineering methodology, the research encompassed all its stages. The preliminary analyses supported the design of the platform and four didactical situations structured according to the Theory of Didactical Situations, applied in a 20-hour extension course with seven Mathematics pre-service teachers from the State University of Ceará. Data collection included questionnaires, photographic records, and audio recordings, which were analyzed through triangulation and the a posteriori and validation analysis. The results indicated advances in conceptual understanding and participant engagement, especially in the coordination between representation registers. Furthermore, the error analysis acted as a catalyst for conceptual reorganization, contributing to the improvement of learning despite persistent difficulties with the ε–δ formalization. It is concluded that the Desvendando o Cálculo platform proved to be an effective tool by integrating error analysis into an interactive digital environment, strengthening teacher education and pointing to promising directions for future research and improvements.