O uso de figuras relacionadas à integral complexa e ao teorema integral de Cauchy em livros didáticos universitários de variável complexa usados na Espanha

Autores

DOI:

https://doi.org/10.23925/1983-3156.2024v26i3p303-326

Palavras-chave:

Modelo epistemológico de referência, Análise de conteúdo de livros didáticos, Figuras, Transposição didática, Variável complexa

Resumo

Este estudo aborda uma questão sobre as semelhanças e diferenças entre trabalhos matemáticos originais em análise complexa e livros didáticos contemporâneos, com relação ao uso de figures (concebidas como imagens bidimensionais) para abordar conceitos nesse ramo da matemática. Para responder essa pregunta, analisamos os quatro principais livros didáticos que são referenciados nos guias de professores de todas as universidades públicas espanholas que oferecem graduação em matemática. Especificamente, apresentamos como esses quatro livros didáticos estruturam o conceito de integral complexa e a prova do teorema da integral de Cauchy. Para realizar nossa análise, recuperamos um modelo de referência epistemológica que descreve como os sujeitos históricos usaram figuras para desenvolver a análise complexa desde o primeiro quarto do século XIX até a primeira metade do século XX. O estudo mostra que os quatro livros didáticos estruturam esses conceitos de tal forma que eles estão relacionados às formas mais contemporâneas em que foram utilizados em seu desenvolvimento histórico. Embora não sejamos contra a estruturação do conteúdo dos livros didáticos dessa forma, argumentaremos como o modelo de referência epistemológica pode servir como uma alternativa epistemológica para a elaboração de material didático que leve em conta o desenvolvimento histórico da variável complexa.

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Biografia do Autor

José Gerardo Piña-Aguirre, Cinvestav

MSc in Mathematics Education

Antonio M. Oller-Marcén, Departamento de Matemáticas – IUMA, Universidad de Zaragoza

PhD in Mathematics Education

Rosa María Farfán Márquez, Centro de investigación y de estudios avanzados (Cinvestav)

PhD in Mathematics Education

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Publicado

2024-11-03

Como Citar

PIÑA-AGUIRRE, J. G.; OLLER-MARCÉN, A. M.; FARFÁN MÁRQUEZ, R. M. O uso de figuras relacionadas à integral complexa e ao teorema integral de Cauchy em livros didáticos universitários de variável complexa usados na Espanha. Educação Matemática Pesquisa Revista do Programa de Estudos Pós-Graduados em Educação Matemática, São Paulo, v. 26, n. 3, p. 303–326, 2024. DOI: 10.23925/1983-3156.2024v26i3p303-326. Disponível em: https://revistas.pucsp.br/index.php/emp/article/view/66938. Acesso em: 14 dez. 2024.

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Seção

Modelo epistemológico de referência (MER) para o ensino de cálculo