O cálculo integral sob uma perspectiva de resolução de problemas: uma proposta de ensino-aprendizagem com aplicações práticas e teóricas

Resumo

This dissertation aims to seek to understand how Problem Solving can contribute to the teaching-learning process of Integral Calculus. The choice of this approach in the context of Integral Calculus is justified by the fact that this area of Mathematics has been one of the main sources of difficulty for undergraduate students in both mathematics and engineering programs. The teaching of Differential and Integral Calculus has been extensively studied in Brazilian academia, given the persistent high failure rates and difficulties in conceptual understanding. Despite theoretical advances made in recent decades, existing contributions have proven insufficient to effectively transform pedagogical practice in the classroom. Thus, to understand this issue, Problem Solving was adopted as the theoretical-methodological framework, underpinning both the development of activities and the analysis of research data. This descriptive, qualitative, and bibliographic study was organized into two complementary projects (P1 and P2). In the first project (P1), a teaching practicum was conducted, through which it was possible to conclude that Integral Calculus instruction remains predominantly lecture-based, with students struggling to mobilize their prior knowledge in the problem-solving process. In light of these observations, six lessons focused on Problem Solving were delivered, with the support of the History of Mathematics and digital technology, resulting in greater student willingness to understand the concepts. The second project (P2) involved selecting and adapting twelve textbook problems from textbooks, covering Integral Calculus topics, with the aim of implementing the teaching proposal based on this methodology. The results indicate that the proposal constitutes material that can be applied to different higher education courses, helping to address gaps in the conventional approach, particularly regarding conceptual understanding, and reinforcing the potential of Problem Solving as a strategy to improve the teaching-learning process of the subject matter in the classroom.

Dados da obra

Tipo

Dissertação (mestrado)

Instituição

UEPB

Programa

Programa de Pós-Graduação em Ensino de Ciências e Educação Matemática - PPGECEM

Ano

2026

Defesa

21/07/2026

Idioma

pt

Palavras-chave

CIENCIAS HUMANAS::EDUCACAO; Cálculo Integral.; Educação Matemática; Resolução de problemas matemáticos

Temas

Cálculo, História da Matemática, Resolução de Problemas, Tecnologias Digitais

Handle

https://repositorio.uepb.edu.br/handle/123456789/77830

Acesso

Texto completo na fonte

Fontes

BDTD/IBICT

Na Biblioteca desde

01/10/2026 · verificada em 03/10/2026