Material para o ensino do cálculo diferencial e integral: referências de Tall, Gueudet e Trouche
Autor(a) principal: | |
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Data de Publicação: | 2017 |
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/20263 |
Resumo: | This thesis presents a material for the teaching of Differential and Integral Calculus, composed by seven activities, which were based on theoretical references of Mathematical Education. The concepts of function, continuity, differentiability, solution of a differential equation, integral and limit of sequences were approached in these activities. The intention was to defend that one of the ways to establish the narrowing of the relation of theory and practice in this area of investigation is done through the elaboration of materials for teaching with this goal. The concepts of generic organizer, cognitive root, and Three Worlds of Mathematics by Tall and collaborators and the idea of resource of Documental Genesis of Gueudet and Trouche were used. The use of the computer and the construction of tools on GeoGebra were productive procedures to obtain a material with the planned qualities. The research, which had as a result the material for teaching, followed the methodological orientation of a type of fundamental research, in which the goal is the filling of gaps in knowledge related to the solution of problems through practice. An explanatory, theoretical posture was adopted, the construction of considerations with rigor and logical coherence to validate the obtained results. In the scope of theoretic-methodological references seven activities were elaborated for the teaching of Calculus organized in three components which, compose a resource (mathematics, material and didactics) in the conception of Documental Genesis, incorporating cognitivist ideas of Tall and his associates. Using the components (mathematics, material and didactics) allows that the material may configure itself as an element of the set of resources, according to the Documental Genesis, which a teacher of Calculus can use for the development of a class. As a result it is possible to demonstrate that the way of elaboration proposed for a material for teaching, in which theories of Mathematical Education are elaborated and adequate software is used, may be a powerful way to favor the integration of theory and practice, pursued and necessary for Mathematic Education, besides contributing with learning |
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Igliori, Sonia Barbosa Camargohttp://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4471344A6Almeida, Marcio Vieira de2017-08-02T14:32:30Z2017-06-27Almeida, Marcio Vieira de. Material para o ensino do cálculo diferencial e integral: referências de Tall, Gueudet e Trouche. 2017. 261 f. Tese (Doutorado em Educação Matemática) - Doutorado Programa de Estudos Pós-Graduados em Educação Matemática, Pontifícia Universidade Católica de São Paulo, São Paulo, 2017.https://tede2.pucsp.br/handle/handle/20263This thesis presents a material for the teaching of Differential and Integral Calculus, composed by seven activities, which were based on theoretical references of Mathematical Education. The concepts of function, continuity, differentiability, solution of a differential equation, integral and limit of sequences were approached in these activities. The intention was to defend that one of the ways to establish the narrowing of the relation of theory and practice in this area of investigation is done through the elaboration of materials for teaching with this goal. The concepts of generic organizer, cognitive root, and Three Worlds of Mathematics by Tall and collaborators and the idea of resource of Documental Genesis of Gueudet and Trouche were used. The use of the computer and the construction of tools on GeoGebra were productive procedures to obtain a material with the planned qualities. The research, which had as a result the material for teaching, followed the methodological orientation of a type of fundamental research, in which the goal is the filling of gaps in knowledge related to the solution of problems through practice. An explanatory, theoretical posture was adopted, the construction of considerations with rigor and logical coherence to validate the obtained results. In the scope of theoretic-methodological references seven activities were elaborated for the teaching of Calculus organized in three components which, compose a resource (mathematics, material and didactics) in the conception of Documental Genesis, incorporating cognitivist ideas of Tall and his associates. Using the components (mathematics, material and didactics) allows that the material may configure itself as an element of the set of resources, according to the Documental Genesis, which a teacher of Calculus can use for the development of a class. As a result it is possible to demonstrate that the way of elaboration proposed for a material for teaching, in which theories of Mathematical Education are elaborated and adequate software is used, may be a powerful way to favor the integration of theory and practice, pursued and necessary for Mathematic Education, besides contributing with learningEsta tese apresenta um material para o ensino de Cálculo Diferencial e Integral composto por sete atividades que foram embasadas em referenciais teóricos da Educação Matemática. Nelas, foram abordados os conceitos de função, continuidade, diferenciabilidade, solução de uma equação diferencial, integral e limite de sequências. Pretendeu-se defender que uma das formas de se estabelecer o estreitamento da relação teoria e prática nessa área de investigação é feita por meio de elaboração de materiais para o ensino com essa finalidade. Foram utilizadas as noções de organizador genérico, raiz cognitiva e Três Mundos da Matemática de Tall e colaboradores, e a noção de recurso da Gênese Documental de Gueudet e Trouche. O uso do computador e a construção de ferramentas no GeoGebra foram procedimentos férteis para se obter um material com as competências planejadas. A pesquisa, que teve por resultado o material para o ensino, seguiu orientação metodológica de uma do tipo pesquisa fundamental, na qual se objetiva o preenchimento de lacunas no conhecimento relativo à solução de problemas advindos da prática. Adotou-se uma postura teórica exploratória, a da construção de argumentos com rigor e coerência lógica para validar os resultados obtidos. Nesse âmbito de referenciais teórico- metodológicos, foram elaboradas sete atividades para o ensino de Cálculo, organizadas em três componentes, as quais compõem um recurso (matemática, material e didática) na concepção da Gênese Documental, incorporando noções cognitivistas de Tall e seus associados. A utilização das componentes (matemática, material e didática) possibilita que o material possa se configurar em um elemento do conjunto de recursos, conforme a Gênese Documental, de um professor de Cálculo, para o desenvolvimento de uma aula. Como resultado pode-se demonstrar que o modo de elaboração proposto para um material para o ensino, em que se incorporam teorias da Educação Matemática e se utiliza um software adequado, pode ser um meio potente para favorecer a integração teoria e prática, almejada e necessária pela Educação Matemática, além de contribuir com a aprendizagemCoordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESapplication/pdfhttp://tede2.pucsp.br/tede/retrieve/42827/Marcio%20Vieira%20de%20Almeida.pdf.jpgporPontifícia Universidade Católica de São PauloPrograma de Estudos Pós-Graduados em Educação MatemáticaPUC-SPBrasilFaculdade de Ciências Exatas e TecnologiaCálculo diferencial - Estudo e ensinoCálculo integral - Estudo e ensinoEducação matemática - Ensino com auxilio do computadorDifferential calculus - Study and teachingIntegral calculus - Study and teachingMathematics Education - Computer-aided teachingCNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICAMaterial para o ensino do cálculo diferencial e integral: referências de Tall, Gueudet e Troucheinfo: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_SPTEXTMarcio Vieira de Almeida.pdf.txtMarcio Vieira de Almeida.pdf.txtExtracted texttext/plain571805https://repositorio.pucsp.br/xmlui/bitstream/handle/20263/4/Marcio%20Vieira%20de%20Almeida.pdf.txtc08b6dbbf99198337b12cd1662a89520MD54LICENSElicense.txtlicense.txttext/plain; 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dc.title.por.fl_str_mv |
Material para o ensino do cálculo diferencial e integral: referências de Tall, Gueudet e Trouche |
title |
Material para o ensino do cálculo diferencial e integral: referências de Tall, Gueudet e Trouche |
spellingShingle |
Material para o ensino do cálculo diferencial e integral: referências de Tall, Gueudet e Trouche Almeida, Marcio Vieira de Cálculo diferencial - Estudo e ensino Cálculo integral - Estudo e ensino Educação matemática - Ensino com auxilio do computador Differential calculus - Study and teaching Integral calculus - Study and teaching Mathematics Education - Computer-aided teaching CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
title_short |
Material para o ensino do cálculo diferencial e integral: referências de Tall, Gueudet e Trouche |
title_full |
Material para o ensino do cálculo diferencial e integral: referências de Tall, Gueudet e Trouche |
title_fullStr |
Material para o ensino do cálculo diferencial e integral: referências de Tall, Gueudet e Trouche |
title_full_unstemmed |
Material para o ensino do cálculo diferencial e integral: referências de Tall, Gueudet e Trouche |
title_sort |
Material para o ensino do cálculo diferencial e integral: referências de Tall, Gueudet e Trouche |
author |
Almeida, Marcio Vieira de |
author_facet |
Almeida, Marcio Vieira de |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Igliori, Sonia Barbosa Camargo |
dc.contributor.authorLattes.fl_str_mv |
http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4471344A6 |
dc.contributor.author.fl_str_mv |
Almeida, Marcio Vieira de |
contributor_str_mv |
Igliori, Sonia Barbosa Camargo |
dc.subject.por.fl_str_mv |
Cálculo diferencial - Estudo e ensino Cálculo integral - Estudo e ensino Educação matemática - Ensino com auxilio do computador |
topic |
Cálculo diferencial - Estudo e ensino Cálculo integral - Estudo e ensino Educação matemática - Ensino com auxilio do computador Differential calculus - Study and teaching Integral calculus - Study and teaching Mathematics Education - Computer-aided teaching CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
dc.subject.eng.fl_str_mv |
Differential calculus - Study and teaching Integral calculus - Study and teaching Mathematics Education - Computer-aided teaching |
dc.subject.cnpq.fl_str_mv |
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
description |
This thesis presents a material for the teaching of Differential and Integral Calculus, composed by seven activities, which were based on theoretical references of Mathematical Education. The concepts of function, continuity, differentiability, solution of a differential equation, integral and limit of sequences were approached in these activities. The intention was to defend that one of the ways to establish the narrowing of the relation of theory and practice in this area of investigation is done through the elaboration of materials for teaching with this goal. The concepts of generic organizer, cognitive root, and Three Worlds of Mathematics by Tall and collaborators and the idea of resource of Documental Genesis of Gueudet and Trouche were used. The use of the computer and the construction of tools on GeoGebra were productive procedures to obtain a material with the planned qualities. The research, which had as a result the material for teaching, followed the methodological orientation of a type of fundamental research, in which the goal is the filling of gaps in knowledge related to the solution of problems through practice. An explanatory, theoretical posture was adopted, the construction of considerations with rigor and logical coherence to validate the obtained results. In the scope of theoretic-methodological references seven activities were elaborated for the teaching of Calculus organized in three components which, compose a resource (mathematics, material and didactics) in the conception of Documental Genesis, incorporating cognitivist ideas of Tall and his associates. Using the components (mathematics, material and didactics) allows that the material may configure itself as an element of the set of resources, according to the Documental Genesis, which a teacher of Calculus can use for the development of a class. As a result it is possible to demonstrate that the way of elaboration proposed for a material for teaching, in which theories of Mathematical Education are elaborated and adequate software is used, may be a powerful way to favor the integration of theory and practice, pursued and necessary for Mathematic Education, besides contributing with learning |
publishDate |
2017 |
dc.date.accessioned.fl_str_mv |
2017-08-02T14:32:30Z |
dc.date.issued.fl_str_mv |
2017-06-27 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/doctoralThesis |
format |
doctoralThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
Almeida, Marcio Vieira de. Material para o ensino do cálculo diferencial e integral: referências de Tall, Gueudet e Trouche. 2017. 261 f. Tese (Doutorado em Educação Matemática) - Doutorado Programa de Estudos Pós-Graduados em Educação Matemática, Pontifícia Universidade Católica de São Paulo, São Paulo, 2017. |
dc.identifier.uri.fl_str_mv |
https://tede2.pucsp.br/handle/handle/20263 |
identifier_str_mv |
Almeida, Marcio Vieira de. Material para o ensino do cálculo diferencial e integral: referências de Tall, Gueudet e Trouche. 2017. 261 f. Tese (Doutorado em Educação Matemática) - Doutorado Programa de Estudos Pós-Graduados em Educação Matemática, Pontifícia Universidade Católica de São Paulo, São Paulo, 2017. |
url |
https://tede2.pucsp.br/handle/handle/20263 |
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por |
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por |
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info:eu-repo/semantics/openAccess |
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openAccess |
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Pontifícia Universidade Católica de São Paulo |
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Programa de Estudos Pós-Graduados em Educação Matemática |
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PUC-SP |
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Brasil |
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Faculdade de Ciências Exatas e Tecnologia |
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Pontifícia Universidade Católica de São Paulo |
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