O teorema fundamental da aritmética: jogos e problemas com alunos do sexto ano do ensino fundamental
Autor(a) principal: | |
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Data de Publicação: | 2008 |
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/11358 |
Resumo: | The present thesis has the purpose of carrying out an interventionist study for the introduction of the Fundamental Theorem of Arithmetic (FTA) and main concepts associated to it to students of the 6th Grade of Basic Education. In the research we intend to answer the following question: What are the arguments used by students in the significance process of the Fundamental Theorem of Arithmetic? For that purpose, we carried out a study with 22 students of a private school situated in the north zone of Rio de Janeiro. The group had already been in touch, according to the school s formal point of view, with the concepts related to the Fundamental Theorem of Arithmetic: multiples, divisors, prime and compound numbers and prime factors decomposition. The research has as theoretical fundamental, the Conceptual Fields Theory proposed by Vergnaud (1983, 2001) and the ideas of Campbell and Zazquis (2002) related to the learning process of concepts associated with the Basic Number Theory, which TFA belongs to. The method used a study divided into three stages. The first stage was the collective use of an initial evaluation. The second addressed the intervention stage, which was divided into three activity groups, and inserted into them, there were two intermediary evaluations. And, at last, the third corresponds to the use, also collective, of a final evaluation, with the same questions as the initial evaluation. Data was analysed from two perspectives, one directed to quantitative analysis, where we tried to relate the percentages of rights, with the help of the statistic package SPSS (Statistical Package for Social Sciences). The second perspective was data analysis from the qualitative point of view, aiming at identifying the type of mistakes made by students, as well as their strategies to solve problem-situations. The results showed that students had developed their own scheme to deal with concepts in construction. In this process, even if implicitly, a series of mathematic concepts present in students actions; is the teacher s function to create favourable conditions for the students to explain them |
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Magina, Sandra Maria PintoBarbosa, Gabriela dos Santos2016-04-27T16:58:49Z2009-01-212008-12-16Barbosa, Gabriela dos Santos. O teorema fundamental da aritmética: jogos e problemas com alunos do sexto ano do ensino fundamental. 2008. 304 f. Tese (Doutorado em Educação) - Pontifícia Universidade Católica de São Paulo, São Paulo, 2008.https://tede2.pucsp.br/handle/handle/11358The present thesis has the purpose of carrying out an interventionist study for the introduction of the Fundamental Theorem of Arithmetic (FTA) and main concepts associated to it to students of the 6th Grade of Basic Education. In the research we intend to answer the following question: What are the arguments used by students in the significance process of the Fundamental Theorem of Arithmetic? For that purpose, we carried out a study with 22 students of a private school situated in the north zone of Rio de Janeiro. The group had already been in touch, according to the school s formal point of view, with the concepts related to the Fundamental Theorem of Arithmetic: multiples, divisors, prime and compound numbers and prime factors decomposition. The research has as theoretical fundamental, the Conceptual Fields Theory proposed by Vergnaud (1983, 2001) and the ideas of Campbell and Zazquis (2002) related to the learning process of concepts associated with the Basic Number Theory, which TFA belongs to. The method used a study divided into three stages. The first stage was the collective use of an initial evaluation. The second addressed the intervention stage, which was divided into three activity groups, and inserted into them, there were two intermediary evaluations. And, at last, the third corresponds to the use, also collective, of a final evaluation, with the same questions as the initial evaluation. Data was analysed from two perspectives, one directed to quantitative analysis, where we tried to relate the percentages of rights, with the help of the statistic package SPSS (Statistical Package for Social Sciences). The second perspective was data analysis from the qualitative point of view, aiming at identifying the type of mistakes made by students, as well as their strategies to solve problem-situations. The results showed that students had developed their own scheme to deal with concepts in construction. In this process, even if implicitly, a series of mathematic concepts present in students actions; is the teacher s function to create favourable conditions for the students to explain themA presente tese teve por objetivo realizar um estudo intervencionista para a introdução do Teorema Fundamental da Aritmética (TFA) e dos principais conceitos associados a ele com alunos do 6º ano do Ensino Fundamental. Na pesquisa, propomo-nos a responder a seguinte questão: De que argumentos os alunos se valem no processo de significação do Teorema Fundamental da Aritmética? Para tanto, realizamos um estudo com 22 alunos, advindos de uma turma de uma escola particular da zona norte do Rio de Janeiro. O grupo já havia tido contato, do ponto de vista formal da escola, com conceitos associados ao Teorema Fundamental da Aritmética: múltiplo, divisor, números primos e compostos e decomposição em fatores primos. A fundamentação teórica da pesquisa contou com a Teoria dos Campos Conceituais proposta por Vergnaud (1983, 2001) e as idéias de Campbell e Zazquis (2002) com relação à aprendizagem dos conceitos associados à Teoria Elementar dos Números, de que o TFA é parte integrante. O método constou de um estudo dividido em três etapas. A primeira referiu-se a aplicação coletiva de uma avaliação inicial. A segunda voltou-se para a fase de intervenção, que foi divida em três grupos de atividades intercalados por duas avaliações intermediárias. E, por fim, a terceira corresponde à aplicação, também coletiva, de uma avaliação final, com as mesmas questões da avaliação inicial. Os dados foram analisados em duas perspectivas: uma voltada à análise quantitativa, em que se buscou relacionar os percentuais de acerto, com a ajuda do pacote estatístico SPSS (Statistical Package for Social Science). A segunda perspectiva referiu-se à análise dos dados do ponto de vista qualitativo, visando identificar os tipos de erros cometidos pelos alunos, bem como suas estratégias na resolução de situações-problema. Os resultados mostraram que os alunos desenvolvem esquemas próprios para lidar com os conceitos em construção. Nesse processo, uma série de conceitos matemáticos está presente, ainda que implicitamente, em suas ações. É função do professor criar condições que favoreçam aos alunos explicitá-losCoordenação de Aperfeiçoamento de Pessoal de Nível Superiorapplication/pdfhttp://tede2.pucsp.br/tede/retrieve/23673/Gabriela%20dos%20Santos%20Barbosa.pdf.jpgporPontifícia Universidade Católica de São PauloPrograma de Estudos Pós-Graduados em Educação MatemáticaPUC-SPBREducaçãoTeorema fundamental da aritméticaTeoria dos campos conceituaisEstruturas multiplicativasAritmetica -- Estudo e ensinoMatematica (Ensino fundamental)Fundamental theorem of arithmeticConceptual Fields TheoryMultiplicative structuresCNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICAO teorema fundamental da aritmética: jogos e problemas com alunos do sexto ano do ensino fundamentalinfo: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_SPTEXTGabriela dos Santos Barbosa.pdf.txtGabriela dos Santos Barbosa.pdf.txtExtracted texttext/plain495342https://repositorio.pucsp.br/xmlui/bitstream/handle/11358/3/Gabriela%20dos%20Santos%20Barbosa.pdf.txt36b1e58772d929e8e90ea08a2e7a6c72MD53ORIGINALGabriela dos Santos Barbosa.pdfapplication/pdf4377226https://repositorio.pucsp.br/xmlui/bitstream/handle/11358/1/Gabriela%20dos%20Santos%20Barbosa.pdf1fa1ce1a13b0a16668f868acafcd63efMD51THUMBNAILGabriela dos Santos Barbosa.pdf.jpgGabriela dos Santos Barbosa.pdf.jpgGenerated Thumbnailimage/jpeg1943https://repositorio.pucsp.br/xmlui/bitstream/handle/11358/2/Gabriela%20dos%20Santos%20Barbosa.pdf.jpgcc73c4c239a4c332d642ba1e7c7a9fb2MD52handle/113582022-04-27 12:24:49.953oai:repositorio.pucsp.br:handle/11358Biblioteca Digital de Teses e Dissertaçõeshttps://sapientia.pucsp.br/https://sapientia.pucsp.br/oai/requestbngkatende@pucsp.br||rapassi@pucsp.bropendoar:2022-04-27T15:24:49Biblioteca Digital de Teses e Dissertações da PUC_SP - Pontifícia Universidade Católica de São Paulo (PUC-SP)false |
dc.title.por.fl_str_mv |
O teorema fundamental da aritmética: jogos e problemas com alunos do sexto ano do ensino fundamental |
title |
O teorema fundamental da aritmética: jogos e problemas com alunos do sexto ano do ensino fundamental |
spellingShingle |
O teorema fundamental da aritmética: jogos e problemas com alunos do sexto ano do ensino fundamental Barbosa, Gabriela dos Santos Teorema fundamental da aritmética Teoria dos campos conceituais Estruturas multiplicativas Aritmetica -- Estudo e ensino Matematica (Ensino fundamental) Fundamental theorem of arithmetic Conceptual Fields Theory Multiplicative structures CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
title_short |
O teorema fundamental da aritmética: jogos e problemas com alunos do sexto ano do ensino fundamental |
title_full |
O teorema fundamental da aritmética: jogos e problemas com alunos do sexto ano do ensino fundamental |
title_fullStr |
O teorema fundamental da aritmética: jogos e problemas com alunos do sexto ano do ensino fundamental |
title_full_unstemmed |
O teorema fundamental da aritmética: jogos e problemas com alunos do sexto ano do ensino fundamental |
title_sort |
O teorema fundamental da aritmética: jogos e problemas com alunos do sexto ano do ensino fundamental |
author |
Barbosa, Gabriela dos Santos |
author_facet |
Barbosa, Gabriela dos Santos |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Magina, Sandra Maria Pinto |
dc.contributor.author.fl_str_mv |
Barbosa, Gabriela dos Santos |
contributor_str_mv |
Magina, Sandra Maria Pinto |
dc.subject.por.fl_str_mv |
Teorema fundamental da aritmética Teoria dos campos conceituais Estruturas multiplicativas Aritmetica -- Estudo e ensino Matematica (Ensino fundamental) |
topic |
Teorema fundamental da aritmética Teoria dos campos conceituais Estruturas multiplicativas Aritmetica -- Estudo e ensino Matematica (Ensino fundamental) Fundamental theorem of arithmetic Conceptual Fields Theory Multiplicative structures CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
dc.subject.eng.fl_str_mv |
Fundamental theorem of arithmetic Conceptual Fields Theory Multiplicative structures |
dc.subject.cnpq.fl_str_mv |
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
description |
The present thesis has the purpose of carrying out an interventionist study for the introduction of the Fundamental Theorem of Arithmetic (FTA) and main concepts associated to it to students of the 6th Grade of Basic Education. In the research we intend to answer the following question: What are the arguments used by students in the significance process of the Fundamental Theorem of Arithmetic? For that purpose, we carried out a study with 22 students of a private school situated in the north zone of Rio de Janeiro. The group had already been in touch, according to the school s formal point of view, with the concepts related to the Fundamental Theorem of Arithmetic: multiples, divisors, prime and compound numbers and prime factors decomposition. The research has as theoretical fundamental, the Conceptual Fields Theory proposed by Vergnaud (1983, 2001) and the ideas of Campbell and Zazquis (2002) related to the learning process of concepts associated with the Basic Number Theory, which TFA belongs to. The method used a study divided into three stages. The first stage was the collective use of an initial evaluation. The second addressed the intervention stage, which was divided into three activity groups, and inserted into them, there were two intermediary evaluations. And, at last, the third corresponds to the use, also collective, of a final evaluation, with the same questions as the initial evaluation. Data was analysed from two perspectives, one directed to quantitative analysis, where we tried to relate the percentages of rights, with the help of the statistic package SPSS (Statistical Package for Social Sciences). The second perspective was data analysis from the qualitative point of view, aiming at identifying the type of mistakes made by students, as well as their strategies to solve problem-situations. The results showed that students had developed their own scheme to deal with concepts in construction. In this process, even if implicitly, a series of mathematic concepts present in students actions; is the teacher s function to create favourable conditions for the students to explain them |
publishDate |
2008 |
dc.date.issued.fl_str_mv |
2008-12-16 |
dc.date.available.fl_str_mv |
2009-01-21 |
dc.date.accessioned.fl_str_mv |
2016-04-27T16:58:49Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/doctoralThesis |
format |
doctoralThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
Barbosa, Gabriela dos Santos. O teorema fundamental da aritmética: jogos e problemas com alunos do sexto ano do ensino fundamental. 2008. 304 f. Tese (Doutorado em Educação) - Pontifícia Universidade Católica de São Paulo, São Paulo, 2008. |
dc.identifier.uri.fl_str_mv |
https://tede2.pucsp.br/handle/handle/11358 |
identifier_str_mv |
Barbosa, Gabriela dos Santos. O teorema fundamental da aritmética: jogos e problemas com alunos do sexto ano do ensino fundamental. 2008. 304 f. Tese (Doutorado em Educação) - Pontifícia Universidade Católica de São Paulo, São Paulo, 2008. |
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https://tede2.pucsp.br/handle/handle/11358 |
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por |
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Pontifícia Universidade Católica de São Paulo |
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Programa de Estudos Pós-Graduados em Educação Matemática |
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PUC-SP |
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BR |
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Educação |
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Pontifícia Universidade Católica de São Paulo |
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