Introdução ao estudo da Álgebra para alunos do ensino fundamental
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFSCAR |
Texto Completo: | https://repositorio.ufscar.br/handle/ufscar/9378 |
Resumo: | This dissertation of professional masters proposes the introduction of the Algebra study for elementary school students. Our main objective was to develop a work outlined in didactic sequence, based on instigating problems that would challenge the independent thinking, essential for the effectiveness of the meaningful learning. For this purpose, a didactic sequence will be presented by three phases: Algebraic Thinking, Algebraic Expressions and First Degree Equations. In order to develop algebraic thinking, students were mobilized to study models and regularities. After that, problems that explored the variation of quantities and the generalization of patterns led them to read and represent some algebraic expressions as well as to calculate its numeric value in various contexts. Finally, our intention was to translate situations through first degree equations, analyzing them, finding their respective roots and validating the results found. As for the development of this research and the data analysis, we were guided by a qualitative approach, since the interactive contact of the researcher as a teacher at a municipal school provided the construction of a reality of students inserted in a particular universe of beliefs, values and several meanings. As the most important result, we realized that 7th grade students initially had only intuitive conceptual notions and had some difficulty in dealing with algebraic calculations. Therefore, problem solving proved to be an effective methodology for students to appropriate Algebra as a meaningful knowledge. |
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Kucinskas, RicardoBarbosa, Grazielle Felicianihttp://lattes.cnpq.br/5368292206467565http://lattes.cnpq.br/1476150846493125ce14ce4a-f11b-4aa5-9771-a6a58cd7ea282018-02-05T16:03:17Z2018-02-05T16:03:17Z2017-10-11KUCINSKAS, Ricardo. Introdução ao estudo da Álgebra para alunos do ensino fundamental. 2017. Dissertação (Mestrado em Matemática em Rede Nacional) – Universidade Federal de São Carlos, São Carlos, 2017. Disponível em: https://repositorio.ufscar.br/handle/ufscar/9378.https://repositorio.ufscar.br/handle/ufscar/9378This dissertation of professional masters proposes the introduction of the Algebra study for elementary school students. Our main objective was to develop a work outlined in didactic sequence, based on instigating problems that would challenge the independent thinking, essential for the effectiveness of the meaningful learning. For this purpose, a didactic sequence will be presented by three phases: Algebraic Thinking, Algebraic Expressions and First Degree Equations. In order to develop algebraic thinking, students were mobilized to study models and regularities. After that, problems that explored the variation of quantities and the generalization of patterns led them to read and represent some algebraic expressions as well as to calculate its numeric value in various contexts. Finally, our intention was to translate situations through first degree equations, analyzing them, finding their respective roots and validating the results found. As for the development of this research and the data analysis, we were guided by a qualitative approach, since the interactive contact of the researcher as a teacher at a municipal school provided the construction of a reality of students inserted in a particular universe of beliefs, values and several meanings. As the most important result, we realized that 7th grade students initially had only intuitive conceptual notions and had some difficulty in dealing with algebraic calculations. Therefore, problem solving proved to be an effective methodology for students to appropriate Algebra as a meaningful knowledge.Esta dissertação de mestrado profissional tem como proposta a introdução do estudo da Álgebra para alunos do ensino fundamental. Nosso maior objetivo foi desenvolver um trabalho delineado em sequência didática, a partir de problemas instigantes que desafiassem o racicíonio independente, imprescindível para a efetivação da aprendizagem significativa. Para isso, será apresentada uma sequência didática composta por três fases: Pensamento Algébrico, Expressões Algébricas e Equações do 1º Grau. A fim de desenvolver o pensamento algébrico, os alunos foram mobilizados a estudar padrões e regularidades. Após isso, problemas que exploravam a variação de grandezas e a generalização de padrões os levaram a ler e representar expressões algébricas bem como calcular seu valor numérico em variados contextos. Por fim, nossa intenção foi traduzir situações por meio de equações de primeiro grau, analisando-as, encontrando suas respectivas raízes e validando os resultados encontrados. Quanto ao desenvolvimento desta pesquisa e à análise dos dados, nos pautamos numa abordagem qualitativa, uma vez que o contato interativo do pesquisador como professor de uma escola municipal proporcionou a construção de uma realidade de alunos inseridos num universo particular de crenças, valores e significados diversos. Como principal resultado, percebemos que os alunos do 7º ano tinham inicialmente apenas noções conceituais intuitivas e apresentavam certa dificuldade para lidar com cálculos algébricos. Diante disso, a resolução de problemas mostrou-se como metodologia eficaz para que os discentes se apropriassem da Álgebra como conhecimento significativo.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)porUniversidade Federal de São CarlosCâmpus São CarlosPrograma de Mestrado Profissional em Matemática em Rede Nacional - PROFMATUFSCarPensamento algébricoExpressões algébricasEquação do primeiro grauSequência didáticaAprendizagem significativaResolução de problemasAlgebraic thinkingAlgebraic expressionsFirst degree equationsDidactic sequenceMeaningful learningProblem solvingCIENCIAS HUMANAS::EDUCACAO::ENSINO-APRENDIZAGEMIntrodução ao estudo da Álgebra para alunos do ensino fundamentalinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisOnline600600f380e992-1637-45e0-90d0-2c659445c1b7info:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFSCARinstname:Universidade Federal de São Carlos (UFSCAR)instacron:UFSCARLICENSElicense.txtlicense.txttext/plain; charset=utf-81957https://repositorio.ufscar.br/bitstream/ufscar/9378/3/license.txtae0398b6f8b235e40ad82cba6c50031dMD53ORIGINALKUCINSKAS_Ricardo_2018.pdfKUCINSKAS_Ricardo_2018.pdfapplication/pdf28902108https://repositorio.ufscar.br/bitstream/ufscar/9378/4/KUCINSKAS_Ricardo_2018.pdfd482f02dff4233412daf9a9108935142MD54TEXTKUCINSKAS_Ricardo_2018.pdf.txtKUCINSKAS_Ricardo_2018.pdf.txtExtracted texttext/plain174055https://repositorio.ufscar.br/bitstream/ufscar/9378/5/KUCINSKAS_Ricardo_2018.pdf.txt79c9ff81f8cf032935b7994929ba14d9MD55THUMBNAILKUCINSKAS_Ricardo_2018.pdf.jpgKUCINSKAS_Ricardo_2018.pdf.jpgIM Thumbnailimage/jpeg7465https://repositorio.ufscar.br/bitstream/ufscar/9378/6/KUCINSKAS_Ricardo_2018.pdf.jpg552d7951452040347758944eeb384b98MD56ufscar/93782023-09-18 18:31:12.284oai:repositorio.ufscar.br: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Repositório InstitucionalPUBhttps://repositorio.ufscar.br/oai/requestopendoar:43222023-09-18T18:31:12Repositório Institucional da UFSCAR - Universidade Federal de São Carlos (UFSCAR)false |
dc.title.por.fl_str_mv |
Introdução ao estudo da Álgebra para alunos do ensino fundamental |
title |
Introdução ao estudo da Álgebra para alunos do ensino fundamental |
spellingShingle |
Introdução ao estudo da Álgebra para alunos do ensino fundamental Kucinskas, Ricardo Pensamento algébrico Expressões algébricas Equação do primeiro grau Sequência didática Aprendizagem significativa Resolução de problemas Algebraic thinking Algebraic expressions First degree equations Didactic sequence Meaningful learning Problem solving CIENCIAS HUMANAS::EDUCACAO::ENSINO-APRENDIZAGEM |
title_short |
Introdução ao estudo da Álgebra para alunos do ensino fundamental |
title_full |
Introdução ao estudo da Álgebra para alunos do ensino fundamental |
title_fullStr |
Introdução ao estudo da Álgebra para alunos do ensino fundamental |
title_full_unstemmed |
Introdução ao estudo da Álgebra para alunos do ensino fundamental |
title_sort |
Introdução ao estudo da Álgebra para alunos do ensino fundamental |
author |
Kucinskas, Ricardo |
author_facet |
Kucinskas, Ricardo |
author_role |
author |
dc.contributor.authorlattes.por.fl_str_mv |
http://lattes.cnpq.br/1476150846493125 |
dc.contributor.author.fl_str_mv |
Kucinskas, Ricardo |
dc.contributor.advisor1.fl_str_mv |
Barbosa, Grazielle Feliciani |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/5368292206467565 |
dc.contributor.authorID.fl_str_mv |
ce14ce4a-f11b-4aa5-9771-a6a58cd7ea28 |
contributor_str_mv |
Barbosa, Grazielle Feliciani |
dc.subject.por.fl_str_mv |
Pensamento algébrico Expressões algébricas Equação do primeiro grau Sequência didática Aprendizagem significativa Resolução de problemas |
topic |
Pensamento algébrico Expressões algébricas Equação do primeiro grau Sequência didática Aprendizagem significativa Resolução de problemas Algebraic thinking Algebraic expressions First degree equations Didactic sequence Meaningful learning Problem solving CIENCIAS HUMANAS::EDUCACAO::ENSINO-APRENDIZAGEM |
dc.subject.eng.fl_str_mv |
Algebraic thinking Algebraic expressions First degree equations Didactic sequence Meaningful learning Problem solving |
dc.subject.cnpq.fl_str_mv |
CIENCIAS HUMANAS::EDUCACAO::ENSINO-APRENDIZAGEM |
description |
This dissertation of professional masters proposes the introduction of the Algebra study for elementary school students. Our main objective was to develop a work outlined in didactic sequence, based on instigating problems that would challenge the independent thinking, essential for the effectiveness of the meaningful learning. For this purpose, a didactic sequence will be presented by three phases: Algebraic Thinking, Algebraic Expressions and First Degree Equations. In order to develop algebraic thinking, students were mobilized to study models and regularities. After that, problems that explored the variation of quantities and the generalization of patterns led them to read and represent some algebraic expressions as well as to calculate its numeric value in various contexts. Finally, our intention was to translate situations through first degree equations, analyzing them, finding their respective roots and validating the results found. As for the development of this research and the data analysis, we were guided by a qualitative approach, since the interactive contact of the researcher as a teacher at a municipal school provided the construction of a reality of students inserted in a particular universe of beliefs, values and several meanings. As the most important result, we realized that 7th grade students initially had only intuitive conceptual notions and had some difficulty in dealing with algebraic calculations. Therefore, problem solving proved to be an effective methodology for students to appropriate Algebra as a meaningful knowledge. |
publishDate |
2017 |
dc.date.issued.fl_str_mv |
2017-10-11 |
dc.date.accessioned.fl_str_mv |
2018-02-05T16:03:17Z |
dc.date.available.fl_str_mv |
2018-02-05T16:03:17Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
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info:eu-repo/semantics/masterThesis |
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masterThesis |
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publishedVersion |
dc.identifier.citation.fl_str_mv |
KUCINSKAS, Ricardo. Introdução ao estudo da Álgebra para alunos do ensino fundamental. 2017. Dissertação (Mestrado em Matemática em Rede Nacional) – Universidade Federal de São Carlos, São Carlos, 2017. Disponível em: https://repositorio.ufscar.br/handle/ufscar/9378. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufscar.br/handle/ufscar/9378 |
identifier_str_mv |
KUCINSKAS, Ricardo. Introdução ao estudo da Álgebra para alunos do ensino fundamental. 2017. Dissertação (Mestrado em Matemática em Rede Nacional) – Universidade Federal de São Carlos, São Carlos, 2017. Disponível em: https://repositorio.ufscar.br/handle/ufscar/9378. |
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https://repositorio.ufscar.br/handle/ufscar/9378 |
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Universidade Federal de São Carlos Câmpus São Carlos |
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Programa de Mestrado Profissional em Matemática em Rede Nacional - PROFMAT |
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UFSCar |
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Universidade Federal de São Carlos Câmpus São Carlos |
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