Introdução ao estudo da Álgebra para alunos do ensino fundamental

Detalhes bibliográficos
Autor(a) principal: Kucinskas, Ricardo
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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spelling 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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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.
url https://repositorio.ufscar.br/handle/ufscar/9378
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Câmpus São Carlos
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publisher.none.fl_str_mv Universidade Federal de São Carlos
Câmpus São Carlos
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