Uma proposta de ensino-aprendizagem de números reais em análise real através da exploração-proposição-resolução de problemas

Resumo

This dissertation investigates the contributions of the Problem Exploration-Posing-Solving (Exploração-Proposição-Resolução de Problemas - EPR) approach to the teaching and learning of Real Numbers in the Real Analysis within Mathematics teacher education programs. The research stems from issues discussed in the academical literature concerning the difficulties faced by preservice mathematics teachers in understanding concepts, definitions, and proofs in Real Analysis, often associated with excessively formalistic approaches that are disconnected from their future teaching practice. In this context, the study aims to identify how the EPR approach can enhance the learning of fundamental concepts related to the set of real numbers and contribute to the mathematical and pedagogical education of preservice mathematics teachers. This is a qualitative study characterized as pedagogical research and grounded in Charmaz's Grounded Theory, with the aim of constructing a Substantive Theory. Data were generated during the development of a Thematic Unit implemented with 11 undergraduate Mathematics students at a public university in northeastern Brazil, using an e-book specifically developed for the research as the main instructional resource. The posed activities addressed concepts related to finite and infinite sets, incommensurability, limits, and properties of real numbers, mediated throughout by Problem Posing and Problem Solving through Problem Exploration. Data were generated through written records, classroom dialogues, researcher observations, and activities developed by the participants. The analysis led to the construction of analytical categories that revealed the potential of the EPR approach for the teaching and learning of Real Analysis. The results indicate that the approach fostered active participation among preservice mathematics teachers, expanding opportunities for argumentation, Problem Posing, Problem Solving, and the collective construction of mathematical knowledge. Furthermore, the approach contributed to a deeper understanding of abstract concepts, enabling students to establish connections between higher mathematics and Basic Education, particularly with regard to real numbers, infinite sets, and continuity. The study concludes that the Problem Exploration-Problem-Posing constitutes a relevant approach for the teaching and learning of Real Numbers in the Real Analysis within Mathematics teacher education programs, as it promotes the collaborative construction of mathematical knowledge, active participation among preservice mathematics teachers, and a deeper understanding of mathematical concepts and proofs. The results also demonstrate that the approach enabled students to experience the practice of exploring problems, collectively constructing mathematical definitions and results, and recognizing relationships between Real Analysis and Basic Education, and other higher education subjects. In addition, the research indicates that the EPR approach contributes to a more reflective approach to Real Analysis by bringing mathematical rigor closer to the educational needs of preservice mathematics teachers.

Dados da obra

Tipo

Tese (doutorado)

Instituição

UEPB

Programa

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

Ano

2026

Defesa

30/06/2026

Idioma

pt

Palavras-chave

CIENCIAS HUMANAS::EDUCACAO::ENSINO-APRENDIZAGEM::METODOS E TECNICAS DE ENSINO; CIENCIAS EXATAS E DA TERRA::MATEMATICA; exploração de problemas; números reais; ensino-aprendizagem de matemática

Temas

Formação de Professores de Matemática, Práticas Pedagógicas, Resolução de Problemas

Handle

https://repositorio.uepb.edu.br/handle/123456789/77682

Acesso

Texto completo na fonte

Fontes

BDTD/IBICT

Na Biblioteca desde

01/10/2026 · verificada em 03/10/2026