Estudo das três dimensões do problema didático de sistemas de equações lineares
Autor(a) principal: | |
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Data de Publicação: | 2023 |
Tipo de documento: | Tese |
Idioma: | por |
Título da fonte: | Biblioteca Digital de Teses e Dissertações da PUC_SP |
Texto Completo: | https://repositorio.pucsp.br/jspui/handle/handle/32227 |
Resumo: | This research deals with the study of the three dimensions of the didactic problem of systems of linear equations This research deals with the study of the three dimensions of the didactic problem of systems of linear equations for initial teacher education. With the contribution of the Anthropological Theory of Didactics (ATD), we chose to start with the teaching question related to Systems of Linear Equations: how and why to teach systems of linear equations to students in initial teacher training? To answer it, we considered our teaching question and carried out our research based on the development of the didactic problem proposed by Gascón (2011), which led us to elaborate our research question: How different aspects referring to the Epistemological, Economic-institutional and Ecological dimensions of the didactic problem related to the mathematical object system of linear equations can they contribute to the development of a Didactic Reference Model (DRM) as a basis for proposing study and research pathways in teacher education? In search of answers with meanings inherent to the raison d'être of this mathematical object, we aim to understand how different aspects related to the Epistemological, Economic-institutional and Ecological dimensions of the didactic problem related to systems of linear equations can contribute to the development of a Reference Didactic Model (RDM) as a basis for proposing study and research pathways in teacher education. With the contribution of the ATD, we chose to start with the teaching question related to Systems of Linear Equations: how and why to teach systems of linear equations to students in initial teacher training? To answer it, we considered our teaching question and carried out our research based on the development of the didactic problem proposed by Gascón (2011), which led us to elaborate our research question: How different aspects referring to the epistemological, economic-institutional and Ecological dimensions of the didactic problem related to the mathematical object system of linear equations can they contribute to the development of a Didactic Reference Model (DRM) as a basis for proposing study and research pathways in teacher education? In search of answers with meanings inherent to the raison d'être of this mathematical object, we aim to understand how different aspects related to the epistemological, economic-institutional and ecological dimensions of the didactic problem related to systems of linear equations can contribute to the development of a Reference Didactic Model (RDM) as a basis for proposing study and research pathways in teacher education. To achieve this objective, we carried out a study based on the assumptions of the Anthropological Theory of Didactics (ATD) and sustaining ourselves, initially in the analysis of the epistemological dimension related to the origins and development of mathematical knowledge associated with systems of linear equations, we generate an Epistemological Reference Model (ERM). Based on this model, we carried out a study of the economic-institutional and ecological dimension of the praxeologies relevant to the development of the study of linear systems of thought in the scope of teacher training in search of the peculiarities of the Dominant Epistemological Model (DEM), described and interpreted in the documents official and teaching materials. The economic study allowed us to locate the systems of linear equations in four disciplines in the undergraduate curriculum (Analytical Geometry, Linear Algebra, Numerical Calculus and Ordinary Differential Equations). On the other hand, the ecological analysis of the object revealed conditions and restrictions that favor and hinder putting into practice the imposed tasks identified by the MED. With the analysis of these studies, we propose an Alternative Reference Didactic Model (ARDM) correlating the ERM and the MED for the analysis of a possible change in the raison d'être linear systems of equation. Finally, when considering the contributions revealed by the theory through the research, we proposed an Alternative Reference Didactic Model (ARDM) with a map of questions for the realization of possible study and research pathways |
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Manrique, Ana Lúciahttp://lattes.cnpq.br/0510953419404742http://lattes.cnpq.br/1956767163550045Paiva, Renne Garcia2023-04-28T13:49:03Z2023-04-28T13:49:03Z2023-03-01Paiva, Renne Garcia. Estudo das três dimensões do problema didático de sistemas de equações lineares. 2023. Tese (Doutorado em Educação Matemática) - Programa de Estudos Pós-Graduados em Educação Matemática da Pontifícia Universidade Católica de São Paulo, São Paulo, 2023.https://repositorio.pucsp.br/jspui/handle/handle/32227This research deals with the study of the three dimensions of the didactic problem of systems of linear equations This research deals with the study of the three dimensions of the didactic problem of systems of linear equations for initial teacher education. With the contribution of the Anthropological Theory of Didactics (ATD), we chose to start with the teaching question related to Systems of Linear Equations: how and why to teach systems of linear equations to students in initial teacher training? To answer it, we considered our teaching question and carried out our research based on the development of the didactic problem proposed by Gascón (2011), which led us to elaborate our research question: How different aspects referring to the Epistemological, Economic-institutional and Ecological dimensions of the didactic problem related to the mathematical object system of linear equations can they contribute to the development of a Didactic Reference Model (DRM) as a basis for proposing study and research pathways in teacher education? In search of answers with meanings inherent to the raison d'être of this mathematical object, we aim to understand how different aspects related to the Epistemological, Economic-institutional and Ecological dimensions of the didactic problem related to systems of linear equations can contribute to the development of a Reference Didactic Model (RDM) as a basis for proposing study and research pathways in teacher education. With the contribution of the ATD, we chose to start with the teaching question related to Systems of Linear Equations: how and why to teach systems of linear equations to students in initial teacher training? To answer it, we considered our teaching question and carried out our research based on the development of the didactic problem proposed by Gascón (2011), which led us to elaborate our research question: How different aspects referring to the epistemological, economic-institutional and Ecological dimensions of the didactic problem related to the mathematical object system of linear equations can they contribute to the development of a Didactic Reference Model (DRM) as a basis for proposing study and research pathways in teacher education? In search of answers with meanings inherent to the raison d'être of this mathematical object, we aim to understand how different aspects related to the epistemological, economic-institutional and ecological dimensions of the didactic problem related to systems of linear equations can contribute to the development of a Reference Didactic Model (RDM) as a basis for proposing study and research pathways in teacher education. To achieve this objective, we carried out a study based on the assumptions of the Anthropological Theory of Didactics (ATD) and sustaining ourselves, initially in the analysis of the epistemological dimension related to the origins and development of mathematical knowledge associated with systems of linear equations, we generate an Epistemological Reference Model (ERM). Based on this model, we carried out a study of the economic-institutional and ecological dimension of the praxeologies relevant to the development of the study of linear systems of thought in the scope of teacher training in search of the peculiarities of the Dominant Epistemological Model (DEM), described and interpreted in the documents official and teaching materials. The economic study allowed us to locate the systems of linear equations in four disciplines in the undergraduate curriculum (Analytical Geometry, Linear Algebra, Numerical Calculus and Ordinary Differential Equations). On the other hand, the ecological analysis of the object revealed conditions and restrictions that favor and hinder putting into practice the imposed tasks identified by the MED. With the analysis of these studies, we propose an Alternative Reference Didactic Model (ARDM) correlating the ERM and the MED for the analysis of a possible change in the raison d'être linear systems of equation. Finally, when considering the contributions revealed by the theory through the research, we proposed an Alternative Reference Didactic Model (ARDM) with a map of questions for the realization of possible study and research pathwaysEsta pesquisa trata do estudo das três dimensões do problema didático de sistemas de equações lineares para formação inicial de professores. Com o aporte da Teoria Antropológica do Didático (TAD), optamos por iniciar com a questão docente relacionada aos Sistemas de Equações Lineares: como e o porquê de ensinar de sistemas de equações lineares para estudantes na formação inicial de professores? Para respondê-la, consideramos nossa questão docente e realizamos nossa pesquisa apoiada no desenvolvimento do problema didático proposto por Gascón (2011) o que nos levou a elaborar nossa questão de pesquisa: De que maneira distintos aspectos referentes às dimensões epistemológica, econômico-institucional e ecológica do problema didático relativo ao objeto matemático sistema de equações lineares podem contribuir com um desenvolvimento de um Modelo Didático de Referência (MDR) como base para proposta de percursos de estudo e pesquisa na formação de professores? Em busca de repostas com significados inerentes a razão de ser desse objeto matemático, temos o objetivo compreender de que maneira distintos aspectos referentes às dimensões epistemológica, econômico-institucional e ecológica do problema didático relativo aos sistemas de equações lineares podem contribuir com o desenvolvimento de um Modelo Didático de Referência (MDR) como base para a proposta de percursos de estudo e pesquisa na formação de professores. Para atingir esse objetivo, realizamos um estudo apoiando-se nos pressupostos da Teoria Antropológica do Didático (TAD) e sustentando-nos, inicialmente na análise da dimensão epistemológica relacionada às origens ao desenvolvimento do saber matemático associado aos sistemas de equações lineares , geramos um modelo epistemológico de referência (MER). Baseando-nos por esse modelo realizamos um estudo da dimensão econômico -institucional e ecológico das praxeologias pertinentes ao desenvolvimento do estudo dos sistemas de equações lineares no âmbito da formação de professores em busca das peculiaridades do modelo epistemológico dominante (MED), descrito e interpretado a partir dos documentos oficiais e materiais didáticos. O estudo econômico nos proporcionou localizar os sistemas de equações lineares em quatro disciplinas no currículo de licenciaturas (Geometria Analítica, Álgebra Linear, Cálculo Numérico e Equações Diferenciais Ordinárias ). Por outro lado, a análise ecológica do objeto nos revelou condições e restrições que favorecem e dificultam pôr em prática as tarefas impostas identificadas pelo MED. Com a análise desses estudos, propomos um Modelo Didático de Referência Alternativo (MDRA) correlacionando o MER e o MED para análise de uma possível mudança da razão de ser dos sistemas de equações lineares . Por fim, ao considerarmos as contribuições reveladas da teoria pela pesquisa, propusemos um modelo didático de referência (MDR A) com mapa de questões para realizações de possíveis PEPporPontifícia Universidade Católica de São PauloPrograma de Estudos Pós-Graduados em Educação MatemáticaPUC-SPBrasilFaculdade de Ciências Exatas e TecnologiaCNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICASistemas de equações linearesDimensão epistemológicaDimensão econômico-institucionalDimensão ecológicaPraxeologiaLinear systems of equationsEpistemological dimensionEconomicInstitutional dimensionEcological dimensionPraxeologyEstudo das três dimensões do problema didático de sistemas de equações linearesinfo: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_SPORIGINALRenne Garcia Paiva.PDFapplication/pdf3290293https://repositorio.pucsp.br/xmlui/bitstream/handle/32227/1/Renne%20Garcia%20Paiva.PDF27f8fd316968d9a99cd2a74c5130fb4cMD51TEXTRenne Garcia Paiva.PDF.txtRenne Garcia Paiva.PDF.txtExtracted texttext/plain297641https://repositorio.pucsp.br/xmlui/bitstream/handle/32227/2/Renne%20Garcia%20Paiva.PDF.txt0f9b0202977733ee049e1ea9984acc62MD52THUMBNAILRenne Garcia Paiva.PDF.jpgRenne Garcia Paiva.PDF.jpgGenerated Thumbnailimage/jpeg1308https://repositorio.pucsp.br/xmlui/bitstream/handle/32227/3/Renne%20Garcia%20Paiva.PDF.jpg9dd95329ac085237290e23e4b268e95aMD53handle/322272023-04-29 01:05:38.997oai:repositorio.pucsp.br:handle/32227Biblioteca Digital de Teses e Dissertaçõeshttps://sapientia.pucsp.br/https://sapientia.pucsp.br/oai/requestbngkatende@pucsp.br||rapassi@pucsp.bropendoar:2023-04-29T04:05:38Biblioteca Digital de Teses e Dissertações da PUC_SP - Pontifícia Universidade Católica de São Paulo (PUC-SP)false |
dc.title.pt_BR.fl_str_mv |
Estudo das três dimensões do problema didático de sistemas de equações lineares |
title |
Estudo das três dimensões do problema didático de sistemas de equações lineares |
spellingShingle |
Estudo das três dimensões do problema didático de sistemas de equações lineares Paiva, Renne Garcia CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA Sistemas de equações lineares Dimensão epistemológica Dimensão econômico-institucional Dimensão ecológica Praxeologia Linear systems of equations Epistemological dimension Economic Institutional dimension Ecological dimension Praxeology |
title_short |
Estudo das três dimensões do problema didático de sistemas de equações lineares |
title_full |
Estudo das três dimensões do problema didático de sistemas de equações lineares |
title_fullStr |
Estudo das três dimensões do problema didático de sistemas de equações lineares |
title_full_unstemmed |
Estudo das três dimensões do problema didático de sistemas de equações lineares |
title_sort |
Estudo das três dimensões do problema didático de sistemas de equações lineares |
author |
Paiva, Renne Garcia |
author_facet |
Paiva, Renne Garcia |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Manrique, Ana Lúcia |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/0510953419404742 |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/1956767163550045 |
dc.contributor.author.fl_str_mv |
Paiva, Renne Garcia |
contributor_str_mv |
Manrique, Ana Lúcia |
dc.subject.cnpq.fl_str_mv |
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
topic |
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA Sistemas de equações lineares Dimensão epistemológica Dimensão econômico-institucional Dimensão ecológica Praxeologia Linear systems of equations Epistemological dimension Economic Institutional dimension Ecological dimension Praxeology |
dc.subject.por.fl_str_mv |
Sistemas de equações lineares Dimensão epistemológica Dimensão econômico-institucional Dimensão ecológica Praxeologia |
dc.subject.eng.fl_str_mv |
Linear systems of equations Epistemological dimension Economic Institutional dimension Ecological dimension Praxeology |
description |
This research deals with the study of the three dimensions of the didactic problem of systems of linear equations This research deals with the study of the three dimensions of the didactic problem of systems of linear equations for initial teacher education. With the contribution of the Anthropological Theory of Didactics (ATD), we chose to start with the teaching question related to Systems of Linear Equations: how and why to teach systems of linear equations to students in initial teacher training? To answer it, we considered our teaching question and carried out our research based on the development of the didactic problem proposed by Gascón (2011), which led us to elaborate our research question: How different aspects referring to the Epistemological, Economic-institutional and Ecological dimensions of the didactic problem related to the mathematical object system of linear equations can they contribute to the development of a Didactic Reference Model (DRM) as a basis for proposing study and research pathways in teacher education? In search of answers with meanings inherent to the raison d'être of this mathematical object, we aim to understand how different aspects related to the Epistemological, Economic-institutional and Ecological dimensions of the didactic problem related to systems of linear equations can contribute to the development of a Reference Didactic Model (RDM) as a basis for proposing study and research pathways in teacher education. With the contribution of the ATD, we chose to start with the teaching question related to Systems of Linear Equations: how and why to teach systems of linear equations to students in initial teacher training? To answer it, we considered our teaching question and carried out our research based on the development of the didactic problem proposed by Gascón (2011), which led us to elaborate our research question: How different aspects referring to the epistemological, economic-institutional and Ecological dimensions of the didactic problem related to the mathematical object system of linear equations can they contribute to the development of a Didactic Reference Model (DRM) as a basis for proposing study and research pathways in teacher education? In search of answers with meanings inherent to the raison d'être of this mathematical object, we aim to understand how different aspects related to the epistemological, economic-institutional and ecological dimensions of the didactic problem related to systems of linear equations can contribute to the development of a Reference Didactic Model (RDM) as a basis for proposing study and research pathways in teacher education. To achieve this objective, we carried out a study based on the assumptions of the Anthropological Theory of Didactics (ATD) and sustaining ourselves, initially in the analysis of the epistemological dimension related to the origins and development of mathematical knowledge associated with systems of linear equations, we generate an Epistemological Reference Model (ERM). Based on this model, we carried out a study of the economic-institutional and ecological dimension of the praxeologies relevant to the development of the study of linear systems of thought in the scope of teacher training in search of the peculiarities of the Dominant Epistemological Model (DEM), described and interpreted in the documents official and teaching materials. The economic study allowed us to locate the systems of linear equations in four disciplines in the undergraduate curriculum (Analytical Geometry, Linear Algebra, Numerical Calculus and Ordinary Differential Equations). On the other hand, the ecological analysis of the object revealed conditions and restrictions that favor and hinder putting into practice the imposed tasks identified by the MED. With the analysis of these studies, we propose an Alternative Reference Didactic Model (ARDM) correlating the ERM and the MED for the analysis of a possible change in the raison d'être linear systems of equation. Finally, when considering the contributions revealed by the theory through the research, we proposed an Alternative Reference Didactic Model (ARDM) with a map of questions for the realization of possible study and research pathways |
publishDate |
2023 |
dc.date.accessioned.fl_str_mv |
2023-04-28T13:49:03Z |
dc.date.available.fl_str_mv |
2023-04-28T13:49:03Z |
dc.date.issued.fl_str_mv |
2023-03-01 |
dc.type.status.fl_str_mv |
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 |
Paiva, Renne Garcia. Estudo das três dimensões do problema didático de sistemas de equações lineares. 2023. Tese (Doutorado em Educação Matemática) - Programa de Estudos Pós-Graduados em Educação Matemática da Pontifícia Universidade Católica de São Paulo, São Paulo, 2023. |
dc.identifier.uri.fl_str_mv |
https://repositorio.pucsp.br/jspui/handle/handle/32227 |
identifier_str_mv |
Paiva, Renne Garcia. Estudo das três dimensões do problema didático de sistemas de equações lineares. 2023. Tese (Doutorado em Educação Matemática) - Programa de Estudos Pós-Graduados em Educação Matemática da Pontifícia Universidade Católica de São Paulo, São Paulo, 2023. |
url |
https://repositorio.pucsp.br/jspui/handle/handle/32227 |
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por |
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por |
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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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