Um estudo ontossemiótico sobre os conhecimentos didático-matemáticos de aplicações da integral definida com estudantes de matemática

Detalhes bibliográficos
Autor(a) principal: Mota, Janine Freitas
Data de Publicação: 2021
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/23641
Resumo: This research aims to analyze the way a group of licenciate in Mathematics students mobilizes competencies and develop didactic-mathematical knowledge during the implementation of a didactic proposal that approaches the meanings of the Definite Integral, involving digital technologies. The theoretical contribution lies in the Ontossemiotic Approach to Knowledge and Mathematical Instruction (OAK) and in the Didactic-Mathematical Knowledge of the teacher (DMK). Using the methodological aspects of Didactic Engineering interpreted according to the OAK, through the epistemic-ecological, cognitive-affective and instructional facets, we conducted the Preliminary Study, Design, Implementation of the Didactic Trajectory and Evaluation phases which enabled the systematic analysis of the development and implementation of the didactic proposal. The Preliminary Study phase highlighted the contributions of investigations that approached cognitive, didactic, epistemological aspects related to Definite Integral. In the Design phase, we planned the activities that compose the didactic proposal, starting from problem situations developed in intra and extra-mathematical contexts, assisted by GeoGebra. In the Implementation Phase of the Didactic Trajectory, the activities were applied to students of the third semester of the Licentiate degree in Mathematics at the State University of Montes Claros (Unimontes) in two face-to-face meetings and one remote meeting. The data were collected through recordings of the research participants’ dialogues, written and digital records containing the development of the activities, in addition to observation notes written during the activities. The tools and notions of mathematical object and OAK process configuration used in the Evaluation Phase enabled to identify the didactic configurations identification that permitted to determine how much the students institutionalized the knowledge about the studied mathematical objects. The analysis of the data showed that the didactic proposal in experimentation contributed to the didactic-mathematical knowledge of students in relation to the Definite Integral in the aspects: connections between theory and practice using intra and extra-mathematical contexts; formalization, generalization and institutionalization of knowledge; mobilization of skills; development of autonomy; use of interdisciplinarity; use of different types of representation records and mobilization of cognitive processes. The educational process in the perspective of the Didactic Analysis model proposed by OAK obtained a satisfactory level of didactic adequacy. We concluded that a didactic proposal referenced in the categories of OAK in which an adequate digital resource is used can enhance the construction of personal meanings and once the activities involve contexts that bring meaning and meaning to the knowledge about the mathematical object under study, students tend to understand it better
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spelling Abar, Celina Aparecida Almeida PereiraMota, Janine Freitas2021-07-29T11:24:23Z2021-06-25Mota, Janine Freitas. Um estudo ontossemiótico sobre os conhecimentos didático-matemáticos de aplicações da integral definida com estudantes de matemática. 2021. 292 f. Tese (Doutorado em Educação Matemática) - Programa de Estudos Pós-Graduados em Educação Matemática, Pontifícia Universidade Católica de São Paulo, São Paulo, 2020.https://tede2.pucsp.br/handle/handle/23641This research aims to analyze the way a group of licenciate in Mathematics students mobilizes competencies and develop didactic-mathematical knowledge during the implementation of a didactic proposal that approaches the meanings of the Definite Integral, involving digital technologies. The theoretical contribution lies in the Ontossemiotic Approach to Knowledge and Mathematical Instruction (OAK) and in the Didactic-Mathematical Knowledge of the teacher (DMK). Using the methodological aspects of Didactic Engineering interpreted according to the OAK, through the epistemic-ecological, cognitive-affective and instructional facets, we conducted the Preliminary Study, Design, Implementation of the Didactic Trajectory and Evaluation phases which enabled the systematic analysis of the development and implementation of the didactic proposal. The Preliminary Study phase highlighted the contributions of investigations that approached cognitive, didactic, epistemological aspects related to Definite Integral. In the Design phase, we planned the activities that compose the didactic proposal, starting from problem situations developed in intra and extra-mathematical contexts, assisted by GeoGebra. In the Implementation Phase of the Didactic Trajectory, the activities were applied to students of the third semester of the Licentiate degree in Mathematics at the State University of Montes Claros (Unimontes) in two face-to-face meetings and one remote meeting. The data were collected through recordings of the research participants’ dialogues, written and digital records containing the development of the activities, in addition to observation notes written during the activities. The tools and notions of mathematical object and OAK process configuration used in the Evaluation Phase enabled to identify the didactic configurations identification that permitted to determine how much the students institutionalized the knowledge about the studied mathematical objects. The analysis of the data showed that the didactic proposal in experimentation contributed to the didactic-mathematical knowledge of students in relation to the Definite Integral in the aspects: connections between theory and practice using intra and extra-mathematical contexts; formalization, generalization and institutionalization of knowledge; mobilization of skills; development of autonomy; use of interdisciplinarity; use of different types of representation records and mobilization of cognitive processes. The educational process in the perspective of the Didactic Analysis model proposed by OAK obtained a satisfactory level of didactic adequacy. We concluded that a didactic proposal referenced in the categories of OAK in which an adequate digital resource is used can enhance the construction of personal meanings and once the activities involve contexts that bring meaning and meaning to the knowledge about the mathematical object under study, students tend to understand it betterEsta pesquisa tem por objetivo analisar como um grupo de estudantes de Licenciatura em Matemática mobiliza competências e desenvolve conhecimentos didático-matemáticos, durante a implementação de uma proposta didática que aborda significados da Integral Definida, envolvendo tecnologias digitais. O aporte teórico situa-se no Enfoque Ontossemiótico do Conhecimento e da Instrução Matemática (EOS) e no Conhecimento Didático-Matemático do professor (CDM). Recorrendo aos aspectos metodológicos da Engenharia Didática, interpretados de acordo com o EOS, por meio das facetas epistêmica-ecológica, cognitiva-afetiva, instrucional, realizamos as fases Estudo Preliminar, Desenho, Implementação da Trajetória Didática e Avaliação, o que possibilitou a análise sistemática do desenvolvimento e implementação da proposta didática. A fase do Estudo Preliminar evidenciou as contribuições das investigações que abordaram aspectos cognitivos, didáticos, epistemológicos, relacionados à Integral Definida. Na fase do Desenho, planejamos as atividades que compõem a proposta didática, partindo de situações-problema elaboradas em contextos intra e extramatemáticos, assistidas pelo GeoGebra. Na Fase de Implementação da Trajetória Didática, as atividades foram aplicadas a estudantes do terceiro período da Licenciatura em Matemática da Universidade Estadual de Montes Claros em dois encontros presenciais e um encontro remoto. Os dados foram coletados por meio de gravações dos diálogos entre os participantes da pesquisa, registros escritos e digitais contendo o desenvolvimento das atividades, além de anotações das observações realizadas no momento de aplicação das atividades. As ferramentas e noções de objeto matemático e configuração de processos do EOS, utilizados na Fase de Avaliação, tornaram possíveis identificar as configurações didáticas que permitiram determinar o quanto os estudantes institucionalizaram os conhecimentos acerca dos objetos matemáticos em estudo. A análise dos dados mostrou que a proposta didática em experimentação contribuiu para os conhecimentos didático-matemáticos de estudantes em relação à Integral Definida nos aspectos: conexões entre teoria e prática, com a utilização de contextos intra e extramatemáticos; formalização, generalização e institucionalização de conhecimentos; mobilização de competências; desenvolvimento da autonomia; utilização da interdisciplinaridade; uso de diferentes tipos de registros de representação e mobilização de processos cognitivos. O processo educativo, na perspectiva do modelo de Análise Didática proposto pelo EOS, obteve um nível satisfatório de adequação didática. Concluímos que uma proposta didática referenciada nas categorias do EOS, em que se utiliza um recurso digital adequado, pode potencializar a construção de significados pessoais, uma vez que, quando as atividades envolvem contextos que trazem sentido e significado aos conhecimentos sobre o objeto matemático em estudo, os estudantes tendem a compreendê-lo melhorCoordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESapplication/pdfhttp://tede2.pucsp.br/tede/retrieve/53717/Janine%20Freitas%20Mota.pdf.jpgporPontifícia Universidade Católica de São PauloPrograma de Estudos Pós-Graduados em Educação MatemáticaPUC-SPBrasilFaculdade de Ciências Exatas e TecnologiaMatemática - Estudo e ensino (Superior)Licenciatura em MatemáticaIntegral definidaMathematics - Study and teaching (Higher Education)Licenciate degree in MathematicsDefinite integralCNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICAUm estudo ontossemiótico sobre os conhecimentos didático-matemáticos de aplicações da integral definida com estudantes de matemáticaAn ontossemiotic study on the didactic-mathematical knowledge of Integral Definite Integral applications with Mathematics studentsinfo: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_SPTEXTJanine Freitas Mota.pdf.txtJanine Freitas Mota.pdf.txtExtracted texttext/plain756763https://repositorio.pucsp.br/xmlui/bitstream/handle/23641/4/Janine%20Freitas%20Mota.pdf.txte08b9807e402849ba045e1b2895a55c0MD54LICENSElicense.txtlicense.txttext/plain; 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dc.title.por.fl_str_mv Um estudo ontossemiótico sobre os conhecimentos didático-matemáticos de aplicações da integral definida com estudantes de matemática
dc.title.alternative.eng.fl_str_mv An ontossemiotic study on the didactic-mathematical knowledge of Integral Definite Integral applications with Mathematics students
title Um estudo ontossemiótico sobre os conhecimentos didático-matemáticos de aplicações da integral definida com estudantes de matemática
spellingShingle Um estudo ontossemiótico sobre os conhecimentos didático-matemáticos de aplicações da integral definida com estudantes de matemática
Mota, Janine Freitas
Matemática - Estudo e ensino (Superior)
Licenciatura em Matemática
Integral definida
Mathematics - Study and teaching (Higher Education)
Licenciate degree in Mathematics
Definite integral
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
title_short Um estudo ontossemiótico sobre os conhecimentos didático-matemáticos de aplicações da integral definida com estudantes de matemática
title_full Um estudo ontossemiótico sobre os conhecimentos didático-matemáticos de aplicações da integral definida com estudantes de matemática
title_fullStr Um estudo ontossemiótico sobre os conhecimentos didático-matemáticos de aplicações da integral definida com estudantes de matemática
title_full_unstemmed Um estudo ontossemiótico sobre os conhecimentos didático-matemáticos de aplicações da integral definida com estudantes de matemática
title_sort Um estudo ontossemiótico sobre os conhecimentos didático-matemáticos de aplicações da integral definida com estudantes de matemática
author Mota, Janine Freitas
author_facet Mota, Janine Freitas
author_role author
dc.contributor.advisor1.fl_str_mv Abar, Celina Aparecida Almeida Pereira
dc.contributor.author.fl_str_mv Mota, Janine Freitas
contributor_str_mv Abar, Celina Aparecida Almeida Pereira
dc.subject.por.fl_str_mv Matemática - Estudo e ensino (Superior)
Licenciatura em Matemática
Integral definida
topic Matemática - Estudo e ensino (Superior)
Licenciatura em Matemática
Integral definida
Mathematics - Study and teaching (Higher Education)
Licenciate degree in Mathematics
Definite integral
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
dc.subject.eng.fl_str_mv Mathematics - Study and teaching (Higher Education)
Licenciate degree in Mathematics
Definite integral
dc.subject.cnpq.fl_str_mv CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
description This research aims to analyze the way a group of licenciate in Mathematics students mobilizes competencies and develop didactic-mathematical knowledge during the implementation of a didactic proposal that approaches the meanings of the Definite Integral, involving digital technologies. The theoretical contribution lies in the Ontossemiotic Approach to Knowledge and Mathematical Instruction (OAK) and in the Didactic-Mathematical Knowledge of the teacher (DMK). Using the methodological aspects of Didactic Engineering interpreted according to the OAK, through the epistemic-ecological, cognitive-affective and instructional facets, we conducted the Preliminary Study, Design, Implementation of the Didactic Trajectory and Evaluation phases which enabled the systematic analysis of the development and implementation of the didactic proposal. The Preliminary Study phase highlighted the contributions of investigations that approached cognitive, didactic, epistemological aspects related to Definite Integral. In the Design phase, we planned the activities that compose the didactic proposal, starting from problem situations developed in intra and extra-mathematical contexts, assisted by GeoGebra. In the Implementation Phase of the Didactic Trajectory, the activities were applied to students of the third semester of the Licentiate degree in Mathematics at the State University of Montes Claros (Unimontes) in two face-to-face meetings and one remote meeting. The data were collected through recordings of the research participants’ dialogues, written and digital records containing the development of the activities, in addition to observation notes written during the activities. The tools and notions of mathematical object and OAK process configuration used in the Evaluation Phase enabled to identify the didactic configurations identification that permitted to determine how much the students institutionalized the knowledge about the studied mathematical objects. The analysis of the data showed that the didactic proposal in experimentation contributed to the didactic-mathematical knowledge of students in relation to the Definite Integral in the aspects: connections between theory and practice using intra and extra-mathematical contexts; formalization, generalization and institutionalization of knowledge; mobilization of skills; development of autonomy; use of interdisciplinarity; use of different types of representation records and mobilization of cognitive processes. The educational process in the perspective of the Didactic Analysis model proposed by OAK obtained a satisfactory level of didactic adequacy. We concluded that a didactic proposal referenced in the categories of OAK in which an adequate digital resource is used can enhance the construction of personal meanings and once the activities involve contexts that bring meaning and meaning to the knowledge about the mathematical object under study, students tend to understand it better
publishDate 2021
dc.date.accessioned.fl_str_mv 2021-07-29T11:24:23Z
dc.date.issued.fl_str_mv 2021-06-25
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dc.identifier.citation.fl_str_mv Mota, Janine Freitas. Um estudo ontossemiótico sobre os conhecimentos didático-matemáticos de aplicações da integral definida com estudantes de matemática. 2021. 292 f. Tese (Doutorado em Educação Matemática) - Programa de Estudos Pós-Graduados em Educação Matemática, Pontifícia Universidade Católica de São Paulo, São Paulo, 2020.
dc.identifier.uri.fl_str_mv https://tede2.pucsp.br/handle/handle/23641
identifier_str_mv Mota, Janine Freitas. Um estudo ontossemiótico sobre os conhecimentos didático-matemáticos de aplicações da integral definida com estudantes de matemática. 2021. 292 f. Tese (Doutorado em Educação Matemática) - Programa de Estudos Pós-Graduados em Educação Matemática, Pontifícia Universidade Católica de São Paulo, São Paulo, 2020.
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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
publisher.none.fl_str_mv Pontifícia Universidade Católica de São Paulo
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