A concepção de educação matemática de Henri Lebesgue
Autor(a) principal: | |
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Data de Publicação: | 2006 |
Tipo de documento: | Tese |
Idioma: | por |
Título da fonte: | Biblioteca Digital de Teses e Dissertações da PUC_SP |
Texto Completo: | https://tede2.pucsp.br/handle/handle/11058 |
Resumo: | 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 |
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Otte, MichaelPalaro, Luzia Aparecida2016-04-27T16:57:42Z2007-09-112006-05-22Palaro, Luzia Aparecida. A concepção de educação matemática de Henri Lebesgue. 2006. 340 f. Tese (Doutorado em Educação) - Pontifícia Universidade Católica de São Paulo, São Paulo, 2006.https://tede2.pucsp.br/handle/handle/11058The 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 endO objetivo geral deste trabalho foi levantar os aspectos caracterizadores da concepção de Educação Matemática de Henri Lebesgue (1875-1941), que além de ter sido um dos mais eminentes matemáticos do século XX pois revolucionou a Análise Matemática com a criação de uma nova teoria da medida e, fundamentado nesta, uma nova definição de integral , foi também um professor extremamente dedicado e que se preocupava com a formação de professores e, muito contribuiu para os assuntos didáticos, históricos e filosóficos da Matemática. A metodologia do estudo baseou-se em uma pesquisa de caráter bibliográfico, sob a abordagem histórico-descritiva; iniciando-se com uma breve apresentação da vida e das obras de Lebesgue. Em seguida, foram apresentadas uma contextualização histórico-filosófica da Matemática de sua época e a filosofia da Matemática que propagava. Buscando realçar a originalidade de Lebesgue, pela sua forma de fazer Matemática, foi apresentado um estudo do desenvolvimento histórico do Cálculo, do século XVII até Lebesgue, sendo a teoria das funções o fio condutor desse desenvolvimento. Tendo como base este desenvolvimento histórico, é apresentado um estudo de como alguns livros didáticos de Cálculo e Análise definem a integração e como abordam o Teorema Fundamental do Cálculo, identificando assim, a perspectiva adotada. Por fim, é apresentado um estudo da obra Sobre a Medida das Grandezas de autoria de Lebesgue, buscando identificar aspectos do processo que Lebesgue considerava para o ensino da Matemática. O estudo concluiu que Lebesgue, construtivista que era, não gostava da tendência axiomática de fazer Matemática de sua época; dava ênfase a atividade e considerava a Matemática um instrumento que não tem objetos próprios; propagava uma filosofia da Matemática simples e utilitária, que seria apenas um relato das práticas desenvolvidas pelos matemáticos; considerava que, no ensino assim como na prática de fazer matemática, se deveria iniciar com uma atividade, a partir da qual poderiam ser abstraídos conceitos, fazer generalizações, deixando as definições axiomáticas por últimoCoordenação de Aperfeiçoamento de Pessoal de Nível Superiorapplication/pdfhttp://tede2.pucsp.br/tede/retrieve/24306/tese_luzia_aparecida_palaro.pdf.jpgporPontifícia Universidade Católica de São PauloPrograma de Estudos Pós-Graduados em Educação MatemáticaPUC-SPBREducaçãoConcepção de educação matemáticaHenri LebesgueFilosofia da matemáticaHistória do cálculo integralIntegral de LebesgueMedida das grandezasLebesgue, Henri Leon 1875-1941Educacao matematicaMatematica -- Estudo e ensinoConceptions of mathematics educationHenri LebesguePhilosophy of mathematicalHistory of calculusLebesgue s integralMeasure of magnitudesCNPQ::CIENCIAS HUMANAS::EDUCACAOA concepção de educação matemática de Henri Lebesgueinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/openAccessreponame:Biblioteca Digital de Teses e Dissertações da PUC_SPinstname:Pontifícia Universidade Católica de São Paulo (PUC-SP)instacron:PUC_SPTEXTtese_luzia_aparecida_palaro.pdf.txttese_luzia_aparecida_palaro.pdf.txtExtracted texttext/plain612277https://repositorio.pucsp.br/xmlui/bitstream/handle/11058/3/tese_luzia_aparecida_palaro.pdf.txtbce0ca85b75f32f70fff3691911a09a2MD53ORIGINALtese_luzia_aparecida_palaro.pdfapplication/pdf27255885https://repositorio.pucsp.br/xmlui/bitstream/handle/11058/1/tese_luzia_aparecida_palaro.pdfd2ee8521118c71c7bfe212a84a1dfc70MD51THUMBNAILtese_luzia_aparecida_palaro.pdf.jpgtese_luzia_aparecida_palaro.pdf.jpgGenerated Thumbnailimage/jpeg1943https://repositorio.pucsp.br/xmlui/bitstream/handle/11058/2/tese_luzia_aparecida_palaro.pdf.jpgcc73c4c239a4c332d642ba1e7c7a9fb2MD52handle/110582022-04-27 13:20:58.645oai:repositorio.pucsp.br:handle/11058Biblioteca Digital de Teses e Dissertaçõeshttps://sapientia.pucsp.br/https://sapientia.pucsp.br/oai/requestbngkatende@pucsp.br||rapassi@pucsp.bropendoar:2022-04-27T16:20:58Biblioteca Digital de Teses e Dissertações da PUC_SP - Pontifícia Universidade Católica de São Paulo (PUC-SP)false |
dc.title.por.fl_str_mv |
A concepção de educação matemática de Henri Lebesgue |
title |
A concepção de educação matemática de Henri Lebesgue |
spellingShingle |
A concepção de educação matemática de Henri Lebesgue Palaro, Luzia Aparecida 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 Conceptions of mathematics education Henri Lebesgue Philosophy of mathematical History of calculus Lebesgue s integral Measure of magnitudes CNPQ::CIENCIAS HUMANAS::EDUCACAO |
title_short |
A concepção de educação matemática de Henri Lebesgue |
title_full |
A concepção de educação matemática de Henri Lebesgue |
title_fullStr |
A concepção de educação matemática de Henri Lebesgue |
title_full_unstemmed |
A concepção de educação matemática de Henri Lebesgue |
title_sort |
A concepção de educação matemática de Henri Lebesgue |
author |
Palaro, Luzia Aparecida |
author_facet |
Palaro, Luzia Aparecida |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Otte, Michael |
dc.contributor.author.fl_str_mv |
Palaro, Luzia Aparecida |
contributor_str_mv |
Otte, Michael |
dc.subject.por.fl_str_mv |
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 |
topic |
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 Conceptions of mathematics education Henri Lebesgue Philosophy of mathematical History of calculus Lebesgue s integral Measure of magnitudes CNPQ::CIENCIAS HUMANAS::EDUCACAO |
dc.subject.eng.fl_str_mv |
Conceptions of mathematics education Henri Lebesgue Philosophy of mathematical History of calculus Lebesgue s integral Measure of magnitudes |
dc.subject.cnpq.fl_str_mv |
CNPQ::CIENCIAS HUMANAS::EDUCACAO |
description |
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 |
publishDate |
2006 |
dc.date.issued.fl_str_mv |
2006-05-22 |
dc.date.available.fl_str_mv |
2007-09-11 |
dc.date.accessioned.fl_str_mv |
2016-04-27T16:57:42Z |
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info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/doctoralThesis |
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doctoralThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
Palaro, Luzia Aparecida. A concepção de educação matemática de Henri Lebesgue. 2006. 340 f. Tese (Doutorado em Educação) - Pontifícia Universidade Católica de São Paulo, São Paulo, 2006. |
dc.identifier.uri.fl_str_mv |
https://tede2.pucsp.br/handle/handle/11058 |
identifier_str_mv |
Palaro, Luzia Aparecida. A concepção de educação matemática de Henri Lebesgue. 2006. 340 f. Tese (Doutorado em Educação) - Pontifícia Universidade Católica de São Paulo, São Paulo, 2006. |
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https://tede2.pucsp.br/handle/handle/11058 |
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Programa de Estudos Pós-Graduados em Educação Matemática |
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Pontifícia Universidade Católica de São Paulo |
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