A construção do conceito de integral : uma viagem pelos três mundos da matemática

• Ano de defesa: 2021
• Autor(a) principal: Bueno, Rafael Winícius da Silva
• Orientador(a): Viali, Lori
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Pontifícia Universidade Católica do Rio Grande do Sul
• Programa de Pós-Graduação: Programa de Pós-Graduação em Educação em Ciências e Matemática
• Departamento: Escola Politénica
• País: Brasil
• Palavras-chave em Português: Ensino e Aprendizagem de Cálculo; História do Cálculo; Três Mundos da Matemática; Educação Matemática; Ensino Superior
• Palavras-chave em Inglês: Calculus Teaching and Learning; History of Calculus; The Tree Worlds of Mathematics; Mathematics Education; Higher Education
• Área do conhecimento CNPq: CIENCIAS HUMANAS::ENSINO
• Link de acesso: http://tede2.pucrs.br/tede2/handle/tede/10144

This thesis aimed to investigate the historical construction of the concept of integral and how this content is taught in the light of the Three Worlds of Mathematics Theory in the initial education of mathematics teachers in the state of Rio Grande do Sul. It seeks to understand how the future professionals realize the introduction of this concept, from the practice based on the theoretical principles studied and developed through mathematical modeling. This is a qualitative research that was started with the reconstruction of the path followed by the mankind for the development of the concepts of calculus, from the Mesopotamia and Ancient Egypt to the XX century. The next step was the construction of ideas referring to the Three Worlds of Mathematics, seeking to connect them with the conception of integral. After that, the current state of knowledge was reviewed to analyze how Brazilian research, produced in stricto sensu programs, has used this theory to contribute to the processes of teaching and learning calculus. Another step was the identification of the most used teaching materials in the initial education of mathematics teachers in higher education institutions in Rio Grande do Sul to understand how the concept of integral is introduced. A mathematical modeling activity was then applied to undergraduate students in the subject Calculus II in the Mathematics teaching course in a higher education institution in Rio Grande do Sul. Based on that experience, the students answered a questionnaire, whose subjective answers were interpreted using the methodological approach called Discursive Textual Analysis. In such context, our results pointed out that the students could start the study of the concept of integral from the met-before coming from the Embodied Conceptual and Symbolic Operational worlds. Moreover, the students thought that embodied experiences give more meaning to the lessons and that an education construction that does not prioritize algebraic manipulations and formal definitions is able to create more motivation for learning, and might even become a source of inspiration for their subsequent professional action.