A concepção de educação matemática de Henri Lebesgue

• Ano de defesa: 2006
• Autor(a) principal: Palaro, Luzia Aparecida
• Orientador(a): Otte, Michael
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Pontifícia Universidade Católica de São Paulo
• Programa de Pós-Graduação: Programa de Estudos Pós-Graduados em Educação Matemática
• Departamento: Educação
• País: BR
• Palavras-chave em Português: Concepção de educação matemática; Henri Lebesgue; Filosofia da matemática; História do cálculo integral; Integral de Lebesgue; Medida das grandezas; Lebesgue, Henri Leon 1875-1941; Educacao matematica; Matematica > Estudo e ensino
• Palavras-chave em Inglês: Conceptions of mathematics education; Henri Lebesgue; Philosophy of mathematical; History of calculus; Lebesgue s integral; Measure of magnitudes
• Área do conhecimento CNPq: CNPQ::CIENCIAS HUMANAS::EDUCACAO
• Link de acesso: https://tede2.pucsp.br/handle/handle/11058

The main aim of this study was to consider the aspects which characterises Henri Lebesgue s conception of Mathematics Education. Lebesgue (1875-1941), as well as being one of the most eminent mathematicians of the twentieth century and revolutionising Mathematical Analysis with the creation of a new theory of measure and hence a new definition of the integral, was also a extremely dedicated teacher. Concerned about teacher education, he contributed much to debates on didactical, historical and philosophical issues related to Mathematics. The methodology adopted for this study was based on research with a bibliographic character, with a historic-descriptive approach employed, beginning with a brief presentation of the life and works of Lebesgue. Following this, a historicphilosophical contextualisation of Mathematics of his epoch is presented, along with a description of the philosophy of Mathematics he defended. To highlight the originality of Lebesgue s mathematical practices, a study of the historical development of Calculus from the seventeenth century until his time is presented, with the theory of functions serving as the leading thread of this development. Using as a basis this historical development, a study is made of how some Calculus and Analysis textbooks define Integration and how they approach the Fundamental Theorem of Calculus. Finally, a study of the work About the Measure of Magnitude is presented, which identifies aspects of the process that Lebesgue proposed for the teaching of mathematics. The study concludes that Lebesgue, given his constructivist stance: was not keen in the axiomatic tendency that characterised the practice of Mathematics during his time; that he placed emphasis on activity considering Mathematics as a tool without its own objects: that he defended a philosophy of Mathematics as simple and utilitarian, which would be a mere report on the practices of mathematician: and that he believed that teaching like the practice of Mathematicians, should begin with an activity which could be used as the basis from which to abstract concepts and make generalization, leaving the axiomatic definitions until the end