O Sistema de Numeração Decimal: um estudo sobre o valor posicional
Autor(a) principal: | |
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Data de Publicação: | 2018 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Biblioteca Digital de Teses e Dissertações da PUC_SP |
Texto Completo: | https://tede2.pucsp.br/handle/handle/21279 |
Resumo: | As soon as children begin their school life, they already carry with them an idea about the numbers and operation of the Decimal Number System (DNS). However, this knowledge need to be systematized, extended and deepened appropriately in order to assist in the construction of other mathematical concepts. Given this problem, the present research aims to investigate the mobilized knowledge of the positional value in the DNS and the understanding of the characteristics of number zero in the same system by students of the fourth year of Elementary School. Therefore, it is done a brief historical context to rescue how the development of this kind of knowledge by ancient people has developed over time. As theoretical contributions, it is used the researches of Piaget & Szeminska, and of Kamii on the constructions of the number concept by the students. Regarding to the acquisition of the properties of the DNS, it is discussed the researches of Fayol, Lerner & Sadovsky as well as Zunino, who also studies the issue of the number zero in this system. To achieve the research objective, it is adopted the qualitative methodology, since the focus of it is on the mobilized knowledge by the students in the search for a solution to proposed activities. It was also developed an instrument with six exercises involving the positional value and the number zero, based on the proposed sequence in the Brandt version. One week after an application of the instrument, it was conducted a semistructured interview, which was of very important to understand the answers provided by the students. In the analysis and discussion of the obtained data, it is understand that the students mobilized knowledge about the numerical sequence and the criteria of comparison pointed out by Lerner & Sadovsky. In addition to these mobilized knowledge, the participants also used the contextualization of activities to justify their responses, using a comparison with everyday situations, such as, for example, age observation among children. Regarding the number zero, it was analyzed the meanings attributed to this number by the students during interviews. During the research phases, all students stated that zero “worth nothing”, but they have provided justifications that meet the historical facts pointed out in the brief contextualization carried out in the third chapter of the research. It is also noted that the participants are building their knowledge about DNS, presenting an unstable knowledge that changes according to the question asked regarding the proposed situation. The results found in this research indicate that the work with DNS needs to be continuous throughout the initial years of Elementary School, as the students continue to build their knowledge about DNS and expand their understanding of the number zero in the years after the literacy cycle |
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Bianchini, Barbara Lutaifhttp://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K8383728Y0Tracanella, Aline Tafarelo2018-07-27T13:29:57Z2018-05-09Tracanella, Aline Tafarelo. O Sistema de Numeração Decimal: um estudo sobre o valor posicional. 2018. 174 f. Dissertação (Mestrado em Educação Matemática) - Programa de Estudos Pós-Graduados em Educação Matemática, Pontifícia Universidade Católica de São Paulo, São Paulo, 2018.https://tede2.pucsp.br/handle/handle/21279As soon as children begin their school life, they already carry with them an idea about the numbers and operation of the Decimal Number System (DNS). However, this knowledge need to be systematized, extended and deepened appropriately in order to assist in the construction of other mathematical concepts. Given this problem, the present research aims to investigate the mobilized knowledge of the positional value in the DNS and the understanding of the characteristics of number zero in the same system by students of the fourth year of Elementary School. Therefore, it is done a brief historical context to rescue how the development of this kind of knowledge by ancient people has developed over time. As theoretical contributions, it is used the researches of Piaget & Szeminska, and of Kamii on the constructions of the number concept by the students. Regarding to the acquisition of the properties of the DNS, it is discussed the researches of Fayol, Lerner & Sadovsky as well as Zunino, who also studies the issue of the number zero in this system. To achieve the research objective, it is adopted the qualitative methodology, since the focus of it is on the mobilized knowledge by the students in the search for a solution to proposed activities. It was also developed an instrument with six exercises involving the positional value and the number zero, based on the proposed sequence in the Brandt version. One week after an application of the instrument, it was conducted a semistructured interview, which was of very important to understand the answers provided by the students. In the analysis and discussion of the obtained data, it is understand that the students mobilized knowledge about the numerical sequence and the criteria of comparison pointed out by Lerner & Sadovsky. In addition to these mobilized knowledge, the participants also used the contextualization of activities to justify their responses, using a comparison with everyday situations, such as, for example, age observation among children. Regarding the number zero, it was analyzed the meanings attributed to this number by the students during interviews. During the research phases, all students stated that zero “worth nothing”, but they have provided justifications that meet the historical facts pointed out in the brief contextualization carried out in the third chapter of the research. It is also noted that the participants are building their knowledge about DNS, presenting an unstable knowledge that changes according to the question asked regarding the proposed situation. The results found in this research indicate that the work with DNS needs to be continuous throughout the initial years of Elementary School, as the students continue to build their knowledge about DNS and expand their understanding of the number zero in the years after the literacy cycleAssim que as crianças iniciam sua vida escolar, já carregam consigo alguma ideia sobre os números e sobre o funcionamento do Sistema de Numeração Decimal (SND). Todavia esses conhecimentos precisam ser sistematizados, ampliados e aprofundados adequadamente, para auxiliar na construção de outros conceitos matemáticos. Diante dessa problemática, a presente pesquisa tem por objetivo investigar que conhecimentos são mobilizados por alunos do quarto ano do Ensino Fundamental acerca do valor posicional no SND e sobre a compreensão do número zero nesse mesmo sistema. Para isso, buscamos em uma breve contextualização histórica resgatar como se deu o desenvolvimento desses saberes por povos antigos no decorrer do tempo. Como aportes teóricos, nos baseamos nas pesquisas de Piaget e Szeminska e de Kamii sobre a construção do conceito de número pelos alunos. Com relação à aquisição das propriedades do SND, discorremos sobre as pesquisas de Fayol e de Lerner e Sadovsky, bem como de Zunino, que aborda também a questão do número zero nesse sistema. Para atender ao objetivo da pesquisa, adotamos a metodologia de cunho qualitativo, pois o foco da investigação está nos conhecimentos mobilizados pelos educandos na busca por uma solução para as atividades propostas. Elaboramos um instrumento com seis exercícios envolvendo o valor posicional e o número zero, baseado na sequência proposta na tese de Brandt. Uma semana após a aplicação do instrumento, realizamos uma entrevista semiestruturada, que foi de suma importância para compreender com maior clareza as respostas fornecidas pelos alunos. Na análise e discussão dos dados obtidos, compreendemos que os estudantes mobilizaram conhecimentos acerca da sequência numérica e dos critérios de comparação apontados por Lerner e Sadovsky. Além desses conhecimentos mobilizados, os participantes também recorreram à contextualização das atividades para justificar suas respostas, usando a comparação com situações cotidianas, como, por exemplo, a observação da idade entre crianças. Com relação ao número zero, analisamos os significados atribuídos a esse número pelos alunos durante as entrevistas. Durante as fases da pesquisa, todos os educandos afirmaram que o zero “não vale nada”, mas trouxeram justificativas que vão ao encontro dos fatos histórico apontados na breve contextualização realizada no primeiro capítulo da investigação. Notamos também que os participantes estão construindo seus conhecimentos acerca do SND, apresentando um conhecimento não estável, ou seja, que se altera de acordo com a pergunta feita referente à situação proposta. Os resultados encontrados nessa pesquisa apontam que o trabalho com o SND precisa ser contínuo, durante todos os anos iniciais do Ensino Fundamental, pois os alunos continuam construindo seus conhecimentos acerca do SND e ampliando sua compreensão sobre o número zero nos anos posteriores ao ciclo de alfabetizaçãoCoordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESapplication/pdfhttp://tede2.pucsp.br/tede/retrieve/46219/Aline%20Tafarelo%20Tracanella.pdf.jpgporPontifícia Universidade Católica de São PauloPrograma de Estudos Pós-Graduados em Educação MatemáticaPUC-SPBrasilFaculdade de Ciências Exatas e TecnologiaNúmeros naturaisSistema de Numeração DecimalNúmero - Conceito em criançasMatemática - Estudo e ensinoNumbers, NaturalDecimal Number SystemNumber concept in childrenMathematics - Study and teachingCNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICAO Sistema de Numeração Decimal: um estudo sobre o valor posicionalinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/openAccessreponame:Biblioteca Digital de Teses e Dissertações da PUC_SPinstname:Pontifícia Universidade Católica de São Paulo (PUC-SP)instacron:PUC_SPTEXTAline Tafarelo Tracanella.pdf.txtAline Tafarelo Tracanella.pdf.txtExtracted texttext/plain376775https://repositorio.pucsp.br/xmlui/bitstream/handle/21279/4/Aline%20Tafarelo%20Tracanella.pdf.txtf86a59185ae692bdf1b8aa49b1f1fac2MD54LICENSElicense.txtlicense.txttext/plain; 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dc.title.por.fl_str_mv |
O Sistema de Numeração Decimal: um estudo sobre o valor posicional |
title |
O Sistema de Numeração Decimal: um estudo sobre o valor posicional |
spellingShingle |
O Sistema de Numeração Decimal: um estudo sobre o valor posicional Tracanella, Aline Tafarelo Números naturais Sistema de Numeração Decimal Número - Conceito em crianças Matemática - Estudo e ensino Numbers, Natural Decimal Number System Number concept in children Mathematics - Study and teaching CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
title_short |
O Sistema de Numeração Decimal: um estudo sobre o valor posicional |
title_full |
O Sistema de Numeração Decimal: um estudo sobre o valor posicional |
title_fullStr |
O Sistema de Numeração Decimal: um estudo sobre o valor posicional |
title_full_unstemmed |
O Sistema de Numeração Decimal: um estudo sobre o valor posicional |
title_sort |
O Sistema de Numeração Decimal: um estudo sobre o valor posicional |
author |
Tracanella, Aline Tafarelo |
author_facet |
Tracanella, Aline Tafarelo |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Bianchini, Barbara Lutaif |
dc.contributor.authorLattes.fl_str_mv |
http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K8383728Y0 |
dc.contributor.author.fl_str_mv |
Tracanella, Aline Tafarelo |
contributor_str_mv |
Bianchini, Barbara Lutaif |
dc.subject.eng.fl_str_mv |
Números naturais Sistema de Numeração Decimal Número - Conceito em crianças Matemática - Estudo e ensino Numbers, Natural Decimal Number System Number concept in children Mathematics - Study and teaching |
topic |
Números naturais Sistema de Numeração Decimal Número - Conceito em crianças Matemática - Estudo e ensino Numbers, Natural Decimal Number System Number concept in children Mathematics - Study and teaching CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
dc.subject.cnpq.fl_str_mv |
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
description |
As soon as children begin their school life, they already carry with them an idea about the numbers and operation of the Decimal Number System (DNS). However, this knowledge need to be systematized, extended and deepened appropriately in order to assist in the construction of other mathematical concepts. Given this problem, the present research aims to investigate the mobilized knowledge of the positional value in the DNS and the understanding of the characteristics of number zero in the same system by students of the fourth year of Elementary School. Therefore, it is done a brief historical context to rescue how the development of this kind of knowledge by ancient people has developed over time. As theoretical contributions, it is used the researches of Piaget & Szeminska, and of Kamii on the constructions of the number concept by the students. Regarding to the acquisition of the properties of the DNS, it is discussed the researches of Fayol, Lerner & Sadovsky as well as Zunino, who also studies the issue of the number zero in this system. To achieve the research objective, it is adopted the qualitative methodology, since the focus of it is on the mobilized knowledge by the students in the search for a solution to proposed activities. It was also developed an instrument with six exercises involving the positional value and the number zero, based on the proposed sequence in the Brandt version. One week after an application of the instrument, it was conducted a semistructured interview, which was of very important to understand the answers provided by the students. In the analysis and discussion of the obtained data, it is understand that the students mobilized knowledge about the numerical sequence and the criteria of comparison pointed out by Lerner & Sadovsky. In addition to these mobilized knowledge, the participants also used the contextualization of activities to justify their responses, using a comparison with everyday situations, such as, for example, age observation among children. Regarding the number zero, it was analyzed the meanings attributed to this number by the students during interviews. During the research phases, all students stated that zero “worth nothing”, but they have provided justifications that meet the historical facts pointed out in the brief contextualization carried out in the third chapter of the research. It is also noted that the participants are building their knowledge about DNS, presenting an unstable knowledge that changes according to the question asked regarding the proposed situation. The results found in this research indicate that the work with DNS needs to be continuous throughout the initial years of Elementary School, as the students continue to build their knowledge about DNS and expand their understanding of the number zero in the years after the literacy cycle |
publishDate |
2018 |
dc.date.accessioned.fl_str_mv |
2018-07-27T13:29:57Z |
dc.date.issued.fl_str_mv |
2018-05-09 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
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masterThesis |
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publishedVersion |
dc.identifier.citation.fl_str_mv |
Tracanella, Aline Tafarelo. O Sistema de Numeração Decimal: um estudo sobre o valor posicional. 2018. 174 f. Dissertação (Mestrado em Educação Matemática) - Programa de Estudos Pós-Graduados em Educação Matemática, Pontifícia Universidade Católica de São Paulo, São Paulo, 2018. |
dc.identifier.uri.fl_str_mv |
https://tede2.pucsp.br/handle/handle/21279 |
identifier_str_mv |
Tracanella, Aline Tafarelo. O Sistema de Numeração Decimal: um estudo sobre o valor posicional. 2018. 174 f. Dissertação (Mestrado em Educação Matemática) - Programa de Estudos Pós-Graduados em Educação Matemática, Pontifícia Universidade Católica de São Paulo, São Paulo, 2018. |
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por |
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por |
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Pontifícia Universidade Católica de São Paulo |
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Brasil |
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Faculdade de Ciências Exatas e Tecnologia |
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Pontifícia Universidade Católica de São Paulo |
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