A aprendizagem da geometria analítica do ensino médio e suas representações semióticas no GrafEq
Autor(a) principal: | |
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Data de Publicação: | 2015 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Manancial - Repositório Digital da UFSM |
Texto Completo: | http://repositorio.ufsm.br/handle/1/6751 |
Resumo: | This thesis presents the design of a master's research involving students of the third year of high school, which has as its objective understanding the concepts and properties of Analytic Geometry using GrafEq software in high school. It is a qualitative research, and the methodology adopted for teaching and research is the Didactic Engineering, which allows the systemization research in theoretical and experimental fields. The activities deal with the straight, circumference and parabola objects, and were made with a group of students from a school in the city of Santa Maria / RS. As a theoretical framework, the Theory of Semiotics Representation Registers from Raymond Duval has been adopted due to the important role of representations in the understanding of mathematical concepts. Aiming to facilitate the coordination between the graphic and algebraic representation registers of Analytic Geometry, activities in the teaching sequence were designed using the GrafEq software, allowing the student to perform many activities involving these records. In some activities, GeoGebra software was used in order to formalize properties and mathematical results. The main results emphasize the recognition of the covered objects in their different registers of semiotic representation, considered a priority condition for their understanding. The activities in the sequence contributed for the recognition and understanding of relevant visual variables of algebraic records objects. It has been found that, in general, the development of students beem found along the dynamics of the didactic sequence, it means an improvement in the mathematical objets understanding approach. The engagement of students in solving activities has been emphasized along the activities. |
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2016-03-172016-03-172015-08-07HALBERSTADT, Fabrício Fernando. ANALYTIC GEOMETRY LEARNING IN HIGH SCHOOL AND ITS SEMIOTICS REPRESENTATION IN GRAFEQ. 2015. 174 f. Dissertação (Mestrado em Educação Matemática e Ensino de Física) - Universidade Federal de Santa Maria, Santa Maria, 2015.http://repositorio.ufsm.br/handle/1/6751This thesis presents the design of a master's research involving students of the third year of high school, which has as its objective understanding the concepts and properties of Analytic Geometry using GrafEq software in high school. It is a qualitative research, and the methodology adopted for teaching and research is the Didactic Engineering, which allows the systemization research in theoretical and experimental fields. The activities deal with the straight, circumference and parabola objects, and were made with a group of students from a school in the city of Santa Maria / RS. As a theoretical framework, the Theory of Semiotics Representation Registers from Raymond Duval has been adopted due to the important role of representations in the understanding of mathematical concepts. Aiming to facilitate the coordination between the graphic and algebraic representation registers of Analytic Geometry, activities in the teaching sequence were designed using the GrafEq software, allowing the student to perform many activities involving these records. In some activities, GeoGebra software was used in order to formalize properties and mathematical results. The main results emphasize the recognition of the covered objects in their different registers of semiotic representation, considered a priority condition for their understanding. The activities in the sequence contributed for the recognition and understanding of relevant visual variables of algebraic records objects. It has been found that, in general, the development of students beem found along the dynamics of the didactic sequence, it means an improvement in the mathematical objets understanding approach. The engagement of students in solving activities has been emphasized along the activities.Esta dissertação apresenta o delineamento de uma pesquisa de mestrado envolvendo alunos do terceiro ano do Ensino Médio, a qual tem por objetivo estudar a compreensão de conceitos e propriedades da Geometria Analítica do Ensino Médio com o uso do software GrafEq. Trata-se de uma pesquisa de cunho qualitativo cuja metodologia de ensino e pesquisa adotada é a Engenharia Didática, que possibilita sistematizar a realização da pesquisa nos âmbitos teórico e experimental. As atividades elaboradas versam sobre os objetos reta, circunferência e parábola e foram dinamizadas junto a uma turma de alunos de uma escola da cidade de Santa Maria/RS. Como aporte teórico adota-se a Teoria dos Registros de Representação Semiótica de Raymond Duval devido ao papel importante das representações na compreensão dos conceitos matemáticos. Com o intuito de propiciar a coordenação entre os registros de representação gráfico e algébrico da Geometria Analítica, as atividades que compõem a sequência didática foram planejadas com o uso do software GrafEq, permitindo que o aluno realize diversas experimentações envolvendo esses registros. Em algumas atividades faz-se uso do software GeoGebra a fim de formalizar propriedades e resultados matemáticos. Os resultados apontam para a consolidação do reconhecimento dos objetos abordados nos seus diferentes registros de representação semiótica, condição prioritária para a sua compreensão. As atividades da sequência contribuíram para o reconhecimento e compreensão das variáveis visuais pertinentes dos registros algébricos dos objetos abordados. Verifica-se que, de modo geral, houve um desenvolvimento dos alunos ao longo da dinamização da sequência didática, isto é, uma melhora na compreensão dos objetos matemáticos abordados. Destaca-se, também, o engajamento por parte dos alunos na resolução das atividades.Coordenação de Aperfeiçoamento de Pessoal de Nível Superiorapplication/pdfporUniversidade Federal de Santa MariaPrograma de Pós-Graduação em Educação Matemática e Ensino de FísicaUFSMBREducação Matemática e Ensino de FísicaGeometria analíticaTeoria dos registros de representação semióticaEngenharia didáticaGrafEqAnalytic geometryTheory of semiotics representation registersDidactic engineeringGrafEqCNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICAA aprendizagem da geometria analítica do ensino médio e suas representações semióticas no GrafEqAnalytic geometry learning in high school and its semiotics representation in GrafEqinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisFioreze, Leandra Anversahttp://lattes.cnpq.br/9910618131721810Notare, Márcia Rodrigueshttp://lattes.cnpq.br/9321196983141007Mariani, Rita de Cássia Pistóiahttp://lattes.cnpq.br/8330933788557081http://lattes.cnpq.br/1711424528391215Halberstadt, Fabrício Fernando1001000000084003003003003001240556f-aa87-4f8d-8fc3-9082bf27f4c14e3b02d4-3fae-4340-b0ed-9b260ca03412d5c19cad-9858-48e7-89aa-8081154c2e4dcdaf48f6-d0d6-4dac-a0d5-dcc6949d13f9info:eu-repo/semantics/openAccessreponame:Manancial - Repositório Digital da UFSMinstname:Universidade Federal de Santa Maria (UFSM)instacron:UFSMORIGINALHALBERSTADT, FABRICIO FERNANDO.pdfapplication/pdf15537132http://repositorio.ufsm.br/bitstream/1/6751/1/HALBERSTADT%2c%20FABRICIO%20FERNANDO.pdf414aa65378719311af95cc58200ad734MD51TEXTHALBERSTADT, FABRICIO FERNANDO.pdf.txtHALBERSTADT, FABRICIO FERNANDO.pdf.txtExtracted texttext/plain285210http://repositorio.ufsm.br/bitstream/1/6751/2/HALBERSTADT%2c%20FABRICIO%20FERNANDO.pdf.txtafcb5c5725b2075706500b1e43d2dedfMD52THUMBNAILHALBERSTADT, FABRICIO FERNANDO.pdf.jpgHALBERSTADT, FABRICIO FERNANDO.pdf.jpgIM Thumbnailimage/jpeg5418http://repositorio.ufsm.br/bitstream/1/6751/3/HALBERSTADT%2c%20FABRICIO%20FERNANDO.pdf.jpg90d73b7ce2187ef2a4d4a21a81fec256MD531/67512022-04-07 15:45:14.62oai:repositorio.ufsm.br:1/6751Repositório Institucionalhttp://repositorio.ufsm.br/PUBhttp://repositorio.ufsm.br/oai/requestopendoar:39132022-04-07T18:45:14Manancial - Repositório Digital da UFSM - Universidade Federal de Santa Maria (UFSM)false |
dc.title.por.fl_str_mv |
A aprendizagem da geometria analítica do ensino médio e suas representações semióticas no GrafEq |
dc.title.alternative.eng.fl_str_mv |
Analytic geometry learning in high school and its semiotics representation in GrafEq |
title |
A aprendizagem da geometria analítica do ensino médio e suas representações semióticas no GrafEq |
spellingShingle |
A aprendizagem da geometria analítica do ensino médio e suas representações semióticas no GrafEq Halberstadt, Fabrício Fernando Geometria analítica Teoria dos registros de representação semiótica Engenharia didática GrafEq Analytic geometry Theory of semiotics representation registers Didactic engineering GrafEq CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
title_short |
A aprendizagem da geometria analítica do ensino médio e suas representações semióticas no GrafEq |
title_full |
A aprendizagem da geometria analítica do ensino médio e suas representações semióticas no GrafEq |
title_fullStr |
A aprendizagem da geometria analítica do ensino médio e suas representações semióticas no GrafEq |
title_full_unstemmed |
A aprendizagem da geometria analítica do ensino médio e suas representações semióticas no GrafEq |
title_sort |
A aprendizagem da geometria analítica do ensino médio e suas representações semióticas no GrafEq |
author |
Halberstadt, Fabrício Fernando |
author_facet |
Halberstadt, Fabrício Fernando |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Fioreze, Leandra Anversa |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/9910618131721810 |
dc.contributor.referee1.fl_str_mv |
Notare, Márcia Rodrigues |
dc.contributor.referee1Lattes.fl_str_mv |
http://lattes.cnpq.br/9321196983141007 |
dc.contributor.referee2.fl_str_mv |
Mariani, Rita de Cássia Pistóia |
dc.contributor.referee2Lattes.fl_str_mv |
http://lattes.cnpq.br/8330933788557081 |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/1711424528391215 |
dc.contributor.author.fl_str_mv |
Halberstadt, Fabrício Fernando |
contributor_str_mv |
Fioreze, Leandra Anversa Notare, Márcia Rodrigues Mariani, Rita de Cássia Pistóia |
dc.subject.por.fl_str_mv |
Geometria analítica Teoria dos registros de representação semiótica Engenharia didática GrafEq |
topic |
Geometria analítica Teoria dos registros de representação semiótica Engenharia didática GrafEq Analytic geometry Theory of semiotics representation registers Didactic engineering GrafEq CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
dc.subject.eng.fl_str_mv |
Analytic geometry Theory of semiotics representation registers Didactic engineering GrafEq |
dc.subject.cnpq.fl_str_mv |
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
description |
This thesis presents the design of a master's research involving students of the third year of high school, which has as its objective understanding the concepts and properties of Analytic Geometry using GrafEq software in high school. It is a qualitative research, and the methodology adopted for teaching and research is the Didactic Engineering, which allows the systemization research in theoretical and experimental fields. The activities deal with the straight, circumference and parabola objects, and were made with a group of students from a school in the city of Santa Maria / RS. As a theoretical framework, the Theory of Semiotics Representation Registers from Raymond Duval has been adopted due to the important role of representations in the understanding of mathematical concepts. Aiming to facilitate the coordination between the graphic and algebraic representation registers of Analytic Geometry, activities in the teaching sequence were designed using the GrafEq software, allowing the student to perform many activities involving these records. In some activities, GeoGebra software was used in order to formalize properties and mathematical results. The main results emphasize the recognition of the covered objects in their different registers of semiotic representation, considered a priority condition for their understanding. The activities in the sequence contributed for the recognition and understanding of relevant visual variables of algebraic records objects. It has been found that, in general, the development of students beem found along the dynamics of the didactic sequence, it means an improvement in the mathematical objets understanding approach. The engagement of students in solving activities has been emphasized along the activities. |
publishDate |
2015 |
dc.date.issued.fl_str_mv |
2015-08-07 |
dc.date.accessioned.fl_str_mv |
2016-03-17 |
dc.date.available.fl_str_mv |
2016-03-17 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
HALBERSTADT, Fabrício Fernando. ANALYTIC GEOMETRY LEARNING IN HIGH SCHOOL AND ITS SEMIOTICS REPRESENTATION IN GRAFEQ. 2015. 174 f. Dissertação (Mestrado em Educação Matemática e Ensino de Física) - Universidade Federal de Santa Maria, Santa Maria, 2015. |
dc.identifier.uri.fl_str_mv |
http://repositorio.ufsm.br/handle/1/6751 |
identifier_str_mv |
HALBERSTADT, Fabrício Fernando. ANALYTIC GEOMETRY LEARNING IN HIGH SCHOOL AND ITS SEMIOTICS REPRESENTATION IN GRAFEQ. 2015. 174 f. Dissertação (Mestrado em Educação Matemática e Ensino de Física) - Universidade Federal de Santa Maria, Santa Maria, 2015. |
url |
http://repositorio.ufsm.br/handle/1/6751 |
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UFSM |
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BR |
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Educação Matemática e Ensino de Física |
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