Análise de processos de construções de modelos: o movimento de translação
Autor(a) principal: | |
---|---|
Data de Publicação: | 2021 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFG |
Texto Completo: | http://repositorio.bc.ufg.br/tede/handle/tede/11600 |
Resumo: | This work aims to analyze the construction processes of mathematical models carried out by first-year high school students, to represent the changes in the plane, specifically the horizontal movement. Geometric transformations, isometries, rigid movements and symmetries are common, either formally or in a simple way. With the purpose of mediating the work between these two extremes, a workshop was carried out, with the students developing the mutual teaching of algebra, geometry and arithmetic so that they could make use of creativity and mathematical language to descrive the actions observed. The workshop was supported by ideas about mathematical modeling, with the intention of mathematically interpreting and describing the horizontal translation movement through the manipulation of the concrete material, then providing a better visualization of the situation investigated by the participants. Therefore, two workshops were held with students during the 1st year of high school (14 – 15 years) in a public school in Goiás. It is important to emphasize that the objective was not to find the correct solution, the ideal answer, but to create a space of construction of significant knowledge where students, with the help of the teacher, were instructed to discover, criticize and question their decisions and the creation of a model based on the concrete world. To gather data, activity forms, questionnaires and audio recordings were used. Regarding the results, the arithmetic, algebraic and geometric approaches were analyzed when representing the phenomenon, and students showed difficulties related to the elementary operations and the use of symbology. It was noticed that students used one of the languages, the mathematics or the written mother tongue, or both, to solve problems by choosing the one that is more convenient for them to understand. It is possible to conclude that these difficulties are reflections of a mechanical teaching without meaning production in the previous grades. In addition, the research results can contribute to the interdisciplinary treatment of this topic and boost the development of mathematics, in addition to highlighting its applicability in everyday life. |
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Alvarenga, Karly Barbosahttp://lattes.cnpq.br/8950541327384418Alvarenga, Karly BarbosaSilva, Jhone Caldeira daVilla-Ochoa, Jhony Alexanderhttp://lattes.cnpq.br/1954149370405356Costa Junior, Edson Ferreira da2021-08-27T11:22:19Z2021-08-27T11:22:19Z2021-07-19COSTA JUNIOR, E. F. Análise de processos de construções de modelos: o movimento de translação. 2021. 146 f. Dissertação (Mestrado em Educação em Ciências e Matemática) - Universidade Federal de Goiás, Goiânia, 2021.http://repositorio.bc.ufg.br/tede/handle/tede/11600This work aims to analyze the construction processes of mathematical models carried out by first-year high school students, to represent the changes in the plane, specifically the horizontal movement. Geometric transformations, isometries, rigid movements and symmetries are common, either formally or in a simple way. With the purpose of mediating the work between these two extremes, a workshop was carried out, with the students developing the mutual teaching of algebra, geometry and arithmetic so that they could make use of creativity and mathematical language to descrive the actions observed. The workshop was supported by ideas about mathematical modeling, with the intention of mathematically interpreting and describing the horizontal translation movement through the manipulation of the concrete material, then providing a better visualization of the situation investigated by the participants. Therefore, two workshops were held with students during the 1st year of high school (14 – 15 years) in a public school in Goiás. It is important to emphasize that the objective was not to find the correct solution, the ideal answer, but to create a space of construction of significant knowledge where students, with the help of the teacher, were instructed to discover, criticize and question their decisions and the creation of a model based on the concrete world. To gather data, activity forms, questionnaires and audio recordings were used. Regarding the results, the arithmetic, algebraic and geometric approaches were analyzed when representing the phenomenon, and students showed difficulties related to the elementary operations and the use of symbology. It was noticed that students used one of the languages, the mathematics or the written mother tongue, or both, to solve problems by choosing the one that is more convenient for them to understand. It is possible to conclude that these difficulties are reflections of a mechanical teaching without meaning production in the previous grades. In addition, the research results can contribute to the interdisciplinary treatment of this topic and boost the development of mathematics, in addition to highlighting its applicability in everyday life.Este trabalho tem por objetivo analisar os processos de construção de modelos matemáticos realizados por alunos do primeiro ano do ensino médio, para representar as transformações no plano, especificamente o movimento horizontal. É comum as transformações geométricas, as isometrias, os movimentos rígidos e as simetrias serem apresentados ou com formalidade, ou de maneira simplória. Com o propósito de gerar um trabalho intermediário entre esses dois extremos, elaborou-se uma oficina, com a finalidade de desenvolver o ensino conjunto de álgebra, de geometria e de aritmética para que, assim, os alunos pudessem fazer uso da criatividade e da linguagem matemática e descrever as ações observadas. A oficina foi subsidiada por ideias acerca da modelagem matemática, com a intenção de interpretar e descrever, matematicamente, o movimento de translação horizontal por meio da manipulação do material concreto, para, desse modo, proporcionar melhor visualização da situação investigada pelos participantes. Portanto, foram realizadas duas oficinas com alunos do 1° ano do ensino médio de uma escola pública de Goiás. É importante ressaltar que o objetivo não era encontrar a solução correta, a resposta ideal, mas, sim, possibilitar o contexto de construção do conhecimento fundamentado e significativo em que os estudantes, com o auxílio do professor, eram instruídos a descobrir, criticar e questionar as suas decisões e a criar um modelo com implicações no mundo concreto. Para a obtenção dos dados, foram empregados ficha de atividade, questionário e gravação em áudio. Em relação aos resultados, analisaram-se as abordagens aritmética, algébrica e geométrica, ao representar o fenômeno, e os estudantes apresentaram dificuldades relacionadas às operações elementares e ao uso da simbologia. Notou-se que eles recorrem a uma das linguagens, a matemática ou a materna escrita, ou a ambas, para resolver as situações problema com escolha da que é mais conveniente em seu entendimento. Conclui-se que essas dificuldades são reflexos de um ensino mecânico e sem produção de significado nas séries anteriores. Além disso, os resultados da pesquisa podem contribuir para o tratamento interdisciplinar desse tema e impulsionar o desenvolvimento da matemática, além de destacar a sua aplicabilidade no cotidiano.Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2021-08-25T18:02:29Z No. of bitstreams: 2 Dissertação - Edson Ferreira da Costa Junior - 2021.pdf: 9213536 bytes, checksum: 2fd14da950f8320eb6817d39b316e8d8 (MD5) license_rdf: 805 bytes, checksum: 4460e5956bc1d1639be9ae6146a50347 (MD5)Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2021-08-27T11:22:19Z (GMT) No. of bitstreams: 2 Dissertação - Edson Ferreira da Costa Junior - 2021.pdf: 9213536 bytes, checksum: 2fd14da950f8320eb6817d39b316e8d8 (MD5) license_rdf: 805 bytes, checksum: 4460e5956bc1d1639be9ae6146a50347 (MD5)Made available in DSpace on 2021-08-27T11:22:19Z (GMT). No. of bitstreams: 2 Dissertação - Edson Ferreira da Costa Junior - 2021.pdf: 9213536 bytes, checksum: 2fd14da950f8320eb6817d39b316e8d8 (MD5) license_rdf: 805 bytes, checksum: 4460e5956bc1d1639be9ae6146a50347 (MD5) Previous issue date: 2021-07-19porUniversidade Federal de GoiásPrograma de Pós-graduação em Educação em Ciências e Matemática (PRPG)UFGBrasilPró-Reitoria de Pós-graduação (PRPG)Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessÁlgebraAritméticaGeometriaEnsinoIsometriasAlgebraArithmeticGeometryTeachingIsometriesCIENCIAS EXATAS E DA TERRA::MATEMATICAAnálise de processos de construções de modelos: o movimento de translaçãoAnalysis of some model building processes: the translation movementinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesis4450050050033197reponame:Repositório Institucional da UFGinstname:Universidade Federal de Goiás (UFG)instacron:UFGLICENSElicense.txtlicense.txttext/plain; charset=utf-81748http://repositorio.bc.ufg.br/tede/bitstreams/6dd366df-57b8-4e81-b5e6-65d3061e24d1/download8a4605be74aa9ea9d79846c1fba20a33MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805http://repositorio.bc.ufg.br/tede/bitstreams/3056d43e-54be-48c8-aa8f-c333467e594c/download4460e5956bc1d1639be9ae6146a50347MD52ORIGINALDissertação - Edson Ferreira da Costa Junior - 2021.pdfDissertação - Edson Ferreira da Costa Junior - 2021.pdfapplication/pdf9213536http://repositorio.bc.ufg.br/tede/bitstreams/675a20fc-fe4f-46fe-bb28-7a6a6807852d/download2fd14da950f8320eb6817d39b316e8d8MD53tede/116002021-08-27 08:22:19.911http://creativecommons.org/licenses/by-nc-nd/4.0/Attribution-NonCommercial-NoDerivatives 4.0 Internationalopen.accessoai:repositorio.bc.ufg.br:tede/11600http://repositorio.bc.ufg.br/tedeRepositório InstitucionalPUBhttp://repositorio.bc.ufg.br/oai/requesttasesdissertacoes.bc@ufg.bropendoar:2021-08-27T11:22:19Repositório Institucional da UFG - Universidade Federal de Goiás (UFG)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 |
dc.title.pt_BR.fl_str_mv |
Análise de processos de construções de modelos: o movimento de translação |
dc.title.alternative.eng.fl_str_mv |
Analysis of some model building processes: the translation movement |
title |
Análise de processos de construções de modelos: o movimento de translação |
spellingShingle |
Análise de processos de construções de modelos: o movimento de translação Costa Junior, Edson Ferreira da Álgebra Aritmética Geometria Ensino Isometrias Algebra Arithmetic Geometry Teaching Isometries CIENCIAS EXATAS E DA TERRA::MATEMATICA |
title_short |
Análise de processos de construções de modelos: o movimento de translação |
title_full |
Análise de processos de construções de modelos: o movimento de translação |
title_fullStr |
Análise de processos de construções de modelos: o movimento de translação |
title_full_unstemmed |
Análise de processos de construções de modelos: o movimento de translação |
title_sort |
Análise de processos de construções de modelos: o movimento de translação |
author |
Costa Junior, Edson Ferreira da |
author_facet |
Costa Junior, Edson Ferreira da |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Alvarenga, Karly Barbosa |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/8950541327384418 |
dc.contributor.referee1.fl_str_mv |
Alvarenga, Karly Barbosa |
dc.contributor.referee2.fl_str_mv |
Silva, Jhone Caldeira da |
dc.contributor.referee3.fl_str_mv |
Villa-Ochoa, Jhony Alexander |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/1954149370405356 |
dc.contributor.author.fl_str_mv |
Costa Junior, Edson Ferreira da |
contributor_str_mv |
Alvarenga, Karly Barbosa Alvarenga, Karly Barbosa Silva, Jhone Caldeira da Villa-Ochoa, Jhony Alexander |
dc.subject.por.fl_str_mv |
Álgebra Aritmética Geometria Ensino Isometrias |
topic |
Álgebra Aritmética Geometria Ensino Isometrias Algebra Arithmetic Geometry Teaching Isometries CIENCIAS EXATAS E DA TERRA::MATEMATICA |
dc.subject.eng.fl_str_mv |
Algebra Arithmetic Geometry Teaching Isometries |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::MATEMATICA |
description |
This work aims to analyze the construction processes of mathematical models carried out by first-year high school students, to represent the changes in the plane, specifically the horizontal movement. Geometric transformations, isometries, rigid movements and symmetries are common, either formally or in a simple way. With the purpose of mediating the work between these two extremes, a workshop was carried out, with the students developing the mutual teaching of algebra, geometry and arithmetic so that they could make use of creativity and mathematical language to descrive the actions observed. The workshop was supported by ideas about mathematical modeling, with the intention of mathematically interpreting and describing the horizontal translation movement through the manipulation of the concrete material, then providing a better visualization of the situation investigated by the participants. Therefore, two workshops were held with students during the 1st year of high school (14 – 15 years) in a public school in Goiás. It is important to emphasize that the objective was not to find the correct solution, the ideal answer, but to create a space of construction of significant knowledge where students, with the help of the teacher, were instructed to discover, criticize and question their decisions and the creation of a model based on the concrete world. To gather data, activity forms, questionnaires and audio recordings were used. Regarding the results, the arithmetic, algebraic and geometric approaches were analyzed when representing the phenomenon, and students showed difficulties related to the elementary operations and the use of symbology. It was noticed that students used one of the languages, the mathematics or the written mother tongue, or both, to solve problems by choosing the one that is more convenient for them to understand. It is possible to conclude that these difficulties are reflections of a mechanical teaching without meaning production in the previous grades. In addition, the research results can contribute to the interdisciplinary treatment of this topic and boost the development of mathematics, in addition to highlighting its applicability in everyday life. |
publishDate |
2021 |
dc.date.accessioned.fl_str_mv |
2021-08-27T11:22:19Z |
dc.date.available.fl_str_mv |
2021-08-27T11:22:19Z |
dc.date.issued.fl_str_mv |
2021-07-19 |
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 |
COSTA JUNIOR, E. F. Análise de processos de construções de modelos: o movimento de translação. 2021. 146 f. Dissertação (Mestrado em Educação em Ciências e Matemática) - Universidade Federal de Goiás, Goiânia, 2021. |
dc.identifier.uri.fl_str_mv |
http://repositorio.bc.ufg.br/tede/handle/tede/11600 |
identifier_str_mv |
COSTA JUNIOR, E. F. Análise de processos de construções de modelos: o movimento de translação. 2021. 146 f. Dissertação (Mestrado em Educação em Ciências e Matemática) - Universidade Federal de Goiás, Goiânia, 2021. |
url |
http://repositorio.bc.ufg.br/tede/handle/tede/11600 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.program.fl_str_mv |
44 |
dc.relation.confidence.fl_str_mv |
500 500 500 |
dc.relation.department.fl_str_mv |
33 |
dc.relation.cnpq.fl_str_mv |
197 |
dc.rights.driver.fl_str_mv |
Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess |
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Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de Goiás |
dc.publisher.program.fl_str_mv |
Programa de Pós-graduação em Educação em Ciências e Matemática (PRPG) |
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UFG |
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Brasil |
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Pró-Reitoria de Pós-graduação (PRPG) |
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Universidade Federal de Goiás |
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