Uma organização didática em quadrilátero que aproxime o aluno de licenciatura das demonstrações geométricas
Autor(a) principal: | |
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Data de Publicação: | 2016 |
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/18952 |
Resumo: | This study investigated a didactic proposal whose tasks coordinate proofs and demonstrations as a teaching methodological strategy for easing some of the difficulties related to the topic ‘quadrilaterals’ on a teaching certification course in mathematics. The tasks involve geometric constructions within a paper-and-pencil setting in which students are asked to build figures and mathematically justify the techniques used. Upon carrying out the tasks, students perform conversions of registers and mobilize different understandings of a geometric figure (sequential, perceptive, operative, and discursive). In order to meet the objective, didactic engineering was elected as the investigative method and analyses were based on the theory of registers of semiotic representation, the theory of didactic situations, and the anthropological theory of the didactic. In a preliminary study, the conceptions of students regarding the proofs and demonstrations were investigated and three geometry books used on the teaching certification courses in mathematics were analyzed. The preliminary analyses showed that the conceptions of proofs and demonstrations of the students investigated were influenced by the didactic books. Analysis of the experience revealed that the students appeared to have become aware of the limitations of perceptive understanding, subsequently performing discursive interpretation of the figure, which led to evolution from pragmatic proofs to conceptual proofs, according to Balacheff. With regard to the functions of demonstration, the students performed these not only with the function of validation, but also with the functions of explanation, systematization, and communication, according to De Villiers. In summary, it was concluded that tasks which coordinate proofs and demonstrations are conducive for students to experience the phases of Brousseau’s theory of didactic situations; carry out conversion of registers, semiotic representation and treatments; and coordinate the understandings of the figure, thereby contributing to the (re)construction of implicit and formalized knowledge on quadrilaterals, proof, and demonstration |
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Ag Almouloud, Saddohttp://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4735271A9Ferreira, Maridete Brito Cunha2016-08-26T13:24:11Z2016-03-08Ferreira, Maridete Brito Cunha. Uma organização didática em quadrilátero que aproxime o aluno de licenciatura das demonstrações geométricas. 2016. 342 f. Tese (Doutorado em Educação Matemática) - Programa de Estudos Pós-Graduados em Educação Matemática, Pontifícia Universidade Católica de São Paulo, São Paulo, 2016.https://tede2.pucsp.br/handle/handle/18952This study investigated a didactic proposal whose tasks coordinate proofs and demonstrations as a teaching methodological strategy for easing some of the difficulties related to the topic ‘quadrilaterals’ on a teaching certification course in mathematics. The tasks involve geometric constructions within a paper-and-pencil setting in which students are asked to build figures and mathematically justify the techniques used. Upon carrying out the tasks, students perform conversions of registers and mobilize different understandings of a geometric figure (sequential, perceptive, operative, and discursive). In order to meet the objective, didactic engineering was elected as the investigative method and analyses were based on the theory of registers of semiotic representation, the theory of didactic situations, and the anthropological theory of the didactic. In a preliminary study, the conceptions of students regarding the proofs and demonstrations were investigated and three geometry books used on the teaching certification courses in mathematics were analyzed. The preliminary analyses showed that the conceptions of proofs and demonstrations of the students investigated were influenced by the didactic books. Analysis of the experience revealed that the students appeared to have become aware of the limitations of perceptive understanding, subsequently performing discursive interpretation of the figure, which led to evolution from pragmatic proofs to conceptual proofs, according to Balacheff. With regard to the functions of demonstration, the students performed these not only with the function of validation, but also with the functions of explanation, systematization, and communication, according to De Villiers. In summary, it was concluded that tasks which coordinate proofs and demonstrations are conducive for students to experience the phases of Brousseau’s theory of didactic situations; carry out conversion of registers, semiotic representation and treatments; and coordinate the understandings of the figure, thereby contributing to the (re)construction of implicit and formalized knowledge on quadrilaterals, proof, and demonstrationEsta pesquisa investiga uma proposta didática cujas tarefas articulam provas e demonstrações como estratégia metodológica de ensino para minimizar as dificuldades relacionadas ao tópico ‘quadriláteros’ em um curso de licenciatura em matemática. As tarefas envolvem construções geométricas em um ambiente de papel e lápis em que os alunos são solicitados a construir figuras geométricas e justificar matematicamente as técnicas utilizadas. Na execução das tarefas os alunos efetuam conversões de registros e mobilizam as diferentes apreensões de uma figura geométrica (sequencial, perceptiva, operatória e discursiva). Para cumprir o objetivo, elegemos a engenharia didática como metodologia de pesquisa e fundamentamos nossas análises na teoria dos registros de representação semiótica, na teoria das situações didáticas e na teoria antropológica do didático. Em um estudo preliminar, investigaram-se as concepções dos alunos com relação a provas e demonstrações e analisaram-se três livros de geometria utilizados nos cursos de licenciatura em matemática. As análises preliminares evidenciaram que as concepções de provas e demonstrações dos alunos investigados são influenciadas pelos livros didáticos. Na análise da experiência, evidenciamos que os alunos parecem ter tomado consciência das limitações da apreensão perceptiva, passando a realizar a interpretação discursiva da figura, o que provocou uma evolução de provas pragmáticas para provas conceituais, segundo Balacheff. Com relação às funções da demonstração, os alunos passaram a realizá-las não apenas com a função de validação, mas também com a função de explicação, sistematização e comunicação, segundo De Villiers. Em suma, concluímos que tarefas que articularam provas e demonstrações se mostraram férteis para que os alunos pudessem vivenciar as fases da teoria das situações didáticas, de Brousseau; efetuar conversões de registros representação semiótica e tratamentos; e coordenar as apreensões da figura, contribuindo assim para a (re)construção dos saberes/conhecimentos relativos a quadriláteros, prova e demonstraçãoapplication/pdfhttp://tede2.pucsp.br/tede/retrieve/38632/Maridete%20Brito%20Cunha%20Ferreira.pdf.jpgporPontifícia Universidade Católica de São PauloPrograma de Estudos Pós-Graduados em Educação MatemáticaPUC-SPBrasilFaculdade de Ciências Exatas e TecnologiaProva matemáticaGeometria analíticaQuadriláterosProof mathematicsAnalytic geometryQuadrilateralsCNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICAUma organização didática em quadrilátero que aproxime o aluno de licenciatura das demonstrações geométricasinfo: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_SPTEXTMaridete Brito Cunha Ferreira.pdf.txtMaridete Brito Cunha Ferreira.pdf.txtExtracted texttext/plain717759https://repositorio.pucsp.br/xmlui/bitstream/handle/18952/4/Maridete%20Brito%20Cunha%20Ferreira.pdf.txteac6c6846eda0b626f0d2cd2c8bf23baMD54LICENSElicense.txtlicense.txttext/plain; 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dc.title.por.fl_str_mv |
Uma organização didática em quadrilátero que aproxime o aluno de licenciatura das demonstrações geométricas |
title |
Uma organização didática em quadrilátero que aproxime o aluno de licenciatura das demonstrações geométricas |
spellingShingle |
Uma organização didática em quadrilátero que aproxime o aluno de licenciatura das demonstrações geométricas Ferreira, Maridete Brito Cunha Prova matemática Geometria analítica Quadriláteros Proof mathematics Analytic geometry Quadrilaterals CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
title_short |
Uma organização didática em quadrilátero que aproxime o aluno de licenciatura das demonstrações geométricas |
title_full |
Uma organização didática em quadrilátero que aproxime o aluno de licenciatura das demonstrações geométricas |
title_fullStr |
Uma organização didática em quadrilátero que aproxime o aluno de licenciatura das demonstrações geométricas |
title_full_unstemmed |
Uma organização didática em quadrilátero que aproxime o aluno de licenciatura das demonstrações geométricas |
title_sort |
Uma organização didática em quadrilátero que aproxime o aluno de licenciatura das demonstrações geométricas |
author |
Ferreira, Maridete Brito Cunha |
author_facet |
Ferreira, Maridete Brito Cunha |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Ag Almouloud, Saddo |
dc.contributor.authorLattes.fl_str_mv |
http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4735271A9 |
dc.contributor.author.fl_str_mv |
Ferreira, Maridete Brito Cunha |
contributor_str_mv |
Ag Almouloud, Saddo |
dc.subject.por.fl_str_mv |
Prova matemática Geometria analítica Quadriláteros |
topic |
Prova matemática Geometria analítica Quadriláteros Proof mathematics Analytic geometry Quadrilaterals CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
dc.subject.eng.fl_str_mv |
Proof mathematics Analytic geometry Quadrilaterals |
dc.subject.cnpq.fl_str_mv |
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
description |
This study investigated a didactic proposal whose tasks coordinate proofs and demonstrations as a teaching methodological strategy for easing some of the difficulties related to the topic ‘quadrilaterals’ on a teaching certification course in mathematics. The tasks involve geometric constructions within a paper-and-pencil setting in which students are asked to build figures and mathematically justify the techniques used. Upon carrying out the tasks, students perform conversions of registers and mobilize different understandings of a geometric figure (sequential, perceptive, operative, and discursive). In order to meet the objective, didactic engineering was elected as the investigative method and analyses were based on the theory of registers of semiotic representation, the theory of didactic situations, and the anthropological theory of the didactic. In a preliminary study, the conceptions of students regarding the proofs and demonstrations were investigated and three geometry books used on the teaching certification courses in mathematics were analyzed. The preliminary analyses showed that the conceptions of proofs and demonstrations of the students investigated were influenced by the didactic books. Analysis of the experience revealed that the students appeared to have become aware of the limitations of perceptive understanding, subsequently performing discursive interpretation of the figure, which led to evolution from pragmatic proofs to conceptual proofs, according to Balacheff. With regard to the functions of demonstration, the students performed these not only with the function of validation, but also with the functions of explanation, systematization, and communication, according to De Villiers. In summary, it was concluded that tasks which coordinate proofs and demonstrations are conducive for students to experience the phases of Brousseau’s theory of didactic situations; carry out conversion of registers, semiotic representation and treatments; and coordinate the understandings of the figure, thereby contributing to the (re)construction of implicit and formalized knowledge on quadrilaterals, proof, and demonstration |
publishDate |
2016 |
dc.date.accessioned.fl_str_mv |
2016-08-26T13:24:11Z |
dc.date.issued.fl_str_mv |
2016-03-08 |
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 |
Ferreira, Maridete Brito Cunha. Uma organização didática em quadrilátero que aproxime o aluno de licenciatura das demonstrações geométricas. 2016. 342 f. Tese (Doutorado em Educação Matemática) - Programa de Estudos Pós-Graduados em Educação Matemática, Pontifícia Universidade Católica de São Paulo, São Paulo, 2016. |
dc.identifier.uri.fl_str_mv |
https://tede2.pucsp.br/handle/handle/18952 |
identifier_str_mv |
Ferreira, Maridete Brito Cunha. Uma organização didática em quadrilátero que aproxime o aluno de licenciatura das demonstrações geométricas. 2016. 342 f. Tese (Doutorado em Educação Matemática) - Programa de Estudos Pós-Graduados em Educação Matemática, Pontifícia Universidade Católica de São Paulo, São Paulo, 2016. |
url |
https://tede2.pucsp.br/handle/handle/18952 |
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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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application/pdf |
dc.publisher.none.fl_str_mv |
Pontifícia Universidade Católica de São Paulo |
dc.publisher.program.fl_str_mv |
Programa de Estudos Pós-Graduados em Educação Matemática |
dc.publisher.initials.fl_str_mv |
PUC-SP |
dc.publisher.country.fl_str_mv |
Brasil |
dc.publisher.department.fl_str_mv |
Faculdade de Ciências Exatas e Tecnologia |
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Pontifícia Universidade Católica de São Paulo |
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Biblioteca Digital de Teses e Dissertações da PUC_SP |
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