Um estudo sobre o ensino do conceito de número e suas relações a partir da análise de um conjunto de manuscritos de Charles Sanders Peirce (1839-1914)
Autor(a) principal: | |
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Data de Publicação: | 2020 |
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/23465 |
Resumo: | In this work we present a study on the teaching of the concept of number and its relations from the analysis of a set of manuscripts dedicated to arithmetic, which is organized in a collection entitled The New Elements of Mathematics by Charles Sanders Peirce, organized and published in 1976 by Carolyn Eisele. For that, we selected some manuscripts in which Peirce not only criticizes the textbooks dedicated to the teaching of arithmetic in his time, but also others that propose new ways to introduce the notion of number in elementary education. This study shows that Peirce's criticism, as well as his teaching proposal, were related to the expansion of elementary education programs in the United States of America in the 19th century, motivated by the need to propose a curriculum revision of the teaching of school mathematics. This review involved debates with the objective of proposing new teaching methods, as well as training teachers who were qualified to meet new demands related to commerce, industry and scientific research. In this context, Peirce stated that the teaching of elementary arithmetic did not sufficiently meet the practical and scientific demands of that time. Thus, through the analysis of Peirce's proposal to introduce the notion of number in the teaching of elementary arithmetic, we aim here to point to aspects that sometimes approximate and sometimes separate Peirce's proposal from other textbooks published at that time. In this respect, our research indicated that the concept of number in textbooks published in the last quarter of the 19th century was approached in its most practical sense, using resources that would allow to apprehend it through its application, always emphasizing the relationship of the number to the quantity it expresses. In this way, the proposal sought, through counting and, therefore, the concrete quantity of objects counted, to generalize the concept of number and, in an inverse movement, apply it to practical and concrete everyday situations. Faced with this, Peirce proposes an alternative way, to make children understand that the number is not a mere quantity, nor an intrinsic property of the objects counted, but an idea related to them in some way. It deals with the number in its most essential aspect and proposes a more “scientific” teaching, without, however, departing from the reality of children. This research was based on original documents on which we focus an analytical look based on the three spheres of analysis, namely, historiographic, epistemological and contextual |
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Saito, Fumikazuhttp://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4204670J2Oliveira, Alexandre Souza de2021-02-04T13:54:26Z2020-09-16Oliveira, Alexandre Souza de. Um estudo sobre o ensino do conceito de número e suas relações a partir da análise de um conjunto de manuscritos de Charles Sanders Peirce (1839-1914). 2020. 103 f. Tese (Doutorado em Educação Matemática) - Programa de Estudos Pós-Graduados em Educação Matemática, Pontifícia Universidade Católica de São Paulo, São Paulo, 2020.https://tede2.pucsp.br/handle/handle/23465In this work we present a study on the teaching of the concept of number and its relations from the analysis of a set of manuscripts dedicated to arithmetic, which is organized in a collection entitled The New Elements of Mathematics by Charles Sanders Peirce, organized and published in 1976 by Carolyn Eisele. For that, we selected some manuscripts in which Peirce not only criticizes the textbooks dedicated to the teaching of arithmetic in his time, but also others that propose new ways to introduce the notion of number in elementary education. This study shows that Peirce's criticism, as well as his teaching proposal, were related to the expansion of elementary education programs in the United States of America in the 19th century, motivated by the need to propose a curriculum revision of the teaching of school mathematics. This review involved debates with the objective of proposing new teaching methods, as well as training teachers who were qualified to meet new demands related to commerce, industry and scientific research. In this context, Peirce stated that the teaching of elementary arithmetic did not sufficiently meet the practical and scientific demands of that time. Thus, through the analysis of Peirce's proposal to introduce the notion of number in the teaching of elementary arithmetic, we aim here to point to aspects that sometimes approximate and sometimes separate Peirce's proposal from other textbooks published at that time. In this respect, our research indicated that the concept of number in textbooks published in the last quarter of the 19th century was approached in its most practical sense, using resources that would allow to apprehend it through its application, always emphasizing the relationship of the number to the quantity it expresses. In this way, the proposal sought, through counting and, therefore, the concrete quantity of objects counted, to generalize the concept of number and, in an inverse movement, apply it to practical and concrete everyday situations. Faced with this, Peirce proposes an alternative way, to make children understand that the number is not a mere quantity, nor an intrinsic property of the objects counted, but an idea related to them in some way. It deals with the number in its most essential aspect and proposes a more “scientific” teaching, without, however, departing from the reality of children. This research was based on original documents on which we focus an analytical look based on the three spheres of analysis, namely, historiographic, epistemological and contextualNeste trabalho apresentamos um estudo sobre o ensino do conceito de número e suas relações a partir da análise de um conjunto de manuscritos dedidados à aritmética, que se encontra organizado numa coletânea intitulada The New Elements of Mathematics by Charles Sanders Peirce, organizada e publicada em 1976 por Carolyn Eisele. Para tanto, selecionamos alguns manuscritos em que Peirce não só critica os livros-textos dedicados ao ensino de aritmética em sua época, como também outros que propõem novos caminhos para introduzir a noção de número no ensino elementar. Este estudo mostra que a crítica de Peirce, bem como sua proposta de ensino, estavam relacionadas à ampliação dos programas de ensino elementar nos Estados Unidos da América no século XIX, motivada pela necessidade de propor uma revisão curricular do ensino de Matemática escolar. Essa revisão envolveu debates com objetivo de propor novos métodos de ensino, bem como formar professores que estivessem capacitados para atender por novas demandas ligadas ao comércio, à indústria e à pesquisa científica. Nesse contexto, Peirce afirmava que o ensino de aritmética elementar não atendia suficientemente às demandas práticas e científicas daquela época. Desse modo, por meio da análise da proposta de Peirce para introduzir a noção de número no ensino de aritmética elementar, buscamos aqui apontar para aspectos que ora aproximam e ora afastam a proposta de Peirce de outros livros-textos publicados naquela época. Nesse aspecto, a nossa pesquisa indicou que o conceito de número nos livros-textos publicados no último quarto do século XIX foi abordado em seu sentido mais prático, recorrendo-se a recursos que permitissem apreendê-lo por meio de sua aplicação, sempre enfatizando a relação do número com a quantidade que expressa. Desse modo, a proposta buscava, por meio da contagem e, portanto, da quantidade concreta de objetos contados, generalizar o conceito de número e, num movimento inverso, aplicá-lo a situações práticas e concretas do cotidiano. Frente a isso, Peirce propõe um caminho alternativo, fazer com que as crianças compreendam que o número não é mera quantidade, nem uma propriedade intrínseca dos objetos contados, mas uma ideia relacionada entre eles de alguma forma. Ele trata do número em seu aspecto mais essencial e, propõe um ensino mais “científico”, sem, entretanto, afastar-se da realidade das crianças. Esta pesquisa se baseou em documentos originais sobre os quais incidimos um olhar analítico com base nas três esferas de análise, a saber, historiográfica, epistemológica e contextualCoordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESapplication/pdfhttp://tede2.pucsp.br/tede/retrieve/53127/ALEXANDRE%20SOUZA%20DE%20OLIVEIRA.pdf.jpgporPontifícia Universidade Católica de São PauloPrograma de Estudos Pós-Graduados em Educação MatemáticaPUC-SPBrasilFaculdade de Ciências Exatas e TecnologiaNúmeros naturaisMatemática - Estudo e ensinoAritmética - Estudo e ensinoPeirce, Charles Sanders [1839-1914] - Crítica e interpretaçãoNumbers, NaturalMathematics - Study and teachingArithmetic - Study and teachingPeirce, Charles Sanders [1839-1914] - Criticism and interpretationCNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICAUm estudo sobre o ensino do conceito de número e suas relações a partir da análise de um conjunto de manuscritos de Charles Sanders Peirce (1839-1914)info: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_SPTEXTALEXANDRE SOUZA DE OLIVEIRA.pdf.txtALEXANDRE SOUZA DE OLIVEIRA.pdf.txtExtracted texttext/plain220994https://repositorio.pucsp.br/xmlui/bitstream/handle/23465/4/ALEXANDRE%20SOUZA%20DE%20OLIVEIRA.pdf.txte93756ad24dd48d2aadb10f064ed895eMD54LICENSElicense.txtlicense.txttext/plain; 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dc.title.por.fl_str_mv |
Um estudo sobre o ensino do conceito de número e suas relações a partir da análise de um conjunto de manuscritos de Charles Sanders Peirce (1839-1914) |
title |
Um estudo sobre o ensino do conceito de número e suas relações a partir da análise de um conjunto de manuscritos de Charles Sanders Peirce (1839-1914) |
spellingShingle |
Um estudo sobre o ensino do conceito de número e suas relações a partir da análise de um conjunto de manuscritos de Charles Sanders Peirce (1839-1914) Oliveira, Alexandre Souza de Números naturais Matemática - Estudo e ensino Aritmética - Estudo e ensino Peirce, Charles Sanders [1839-1914] - Crítica e interpretação Numbers, Natural Mathematics - Study and teaching Arithmetic - Study and teaching Peirce, Charles Sanders [1839-1914] - Criticism and interpretation CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
title_short |
Um estudo sobre o ensino do conceito de número e suas relações a partir da análise de um conjunto de manuscritos de Charles Sanders Peirce (1839-1914) |
title_full |
Um estudo sobre o ensino do conceito de número e suas relações a partir da análise de um conjunto de manuscritos de Charles Sanders Peirce (1839-1914) |
title_fullStr |
Um estudo sobre o ensino do conceito de número e suas relações a partir da análise de um conjunto de manuscritos de Charles Sanders Peirce (1839-1914) |
title_full_unstemmed |
Um estudo sobre o ensino do conceito de número e suas relações a partir da análise de um conjunto de manuscritos de Charles Sanders Peirce (1839-1914) |
title_sort |
Um estudo sobre o ensino do conceito de número e suas relações a partir da análise de um conjunto de manuscritos de Charles Sanders Peirce (1839-1914) |
author |
Oliveira, Alexandre Souza de |
author_facet |
Oliveira, Alexandre Souza de |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Saito, Fumikazu |
dc.contributor.authorLattes.fl_str_mv |
http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4204670J2 |
dc.contributor.author.fl_str_mv |
Oliveira, Alexandre Souza de |
contributor_str_mv |
Saito, Fumikazu |
dc.subject.por.fl_str_mv |
Números naturais Matemática - Estudo e ensino Aritmética - Estudo e ensino Peirce, Charles Sanders [1839-1914] - Crítica e interpretação |
topic |
Números naturais Matemática - Estudo e ensino Aritmética - Estudo e ensino Peirce, Charles Sanders [1839-1914] - Crítica e interpretação Numbers, Natural Mathematics - Study and teaching Arithmetic - Study and teaching Peirce, Charles Sanders [1839-1914] - Criticism and interpretation CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
dc.subject.eng.fl_str_mv |
Numbers, Natural Mathematics - Study and teaching Arithmetic - Study and teaching Peirce, Charles Sanders [1839-1914] - Criticism and interpretation |
dc.subject.cnpq.fl_str_mv |
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
description |
In this work we present a study on the teaching of the concept of number and its relations from the analysis of a set of manuscripts dedicated to arithmetic, which is organized in a collection entitled The New Elements of Mathematics by Charles Sanders Peirce, organized and published in 1976 by Carolyn Eisele. For that, we selected some manuscripts in which Peirce not only criticizes the textbooks dedicated to the teaching of arithmetic in his time, but also others that propose new ways to introduce the notion of number in elementary education. This study shows that Peirce's criticism, as well as his teaching proposal, were related to the expansion of elementary education programs in the United States of America in the 19th century, motivated by the need to propose a curriculum revision of the teaching of school mathematics. This review involved debates with the objective of proposing new teaching methods, as well as training teachers who were qualified to meet new demands related to commerce, industry and scientific research. In this context, Peirce stated that the teaching of elementary arithmetic did not sufficiently meet the practical and scientific demands of that time. Thus, through the analysis of Peirce's proposal to introduce the notion of number in the teaching of elementary arithmetic, we aim here to point to aspects that sometimes approximate and sometimes separate Peirce's proposal from other textbooks published at that time. In this respect, our research indicated that the concept of number in textbooks published in the last quarter of the 19th century was approached in its most practical sense, using resources that would allow to apprehend it through its application, always emphasizing the relationship of the number to the quantity it expresses. In this way, the proposal sought, through counting and, therefore, the concrete quantity of objects counted, to generalize the concept of number and, in an inverse movement, apply it to practical and concrete everyday situations. Faced with this, Peirce proposes an alternative way, to make children understand that the number is not a mere quantity, nor an intrinsic property of the objects counted, but an idea related to them in some way. It deals with the number in its most essential aspect and proposes a more “scientific” teaching, without, however, departing from the reality of children. This research was based on original documents on which we focus an analytical look based on the three spheres of analysis, namely, historiographic, epistemological and contextual |
publishDate |
2020 |
dc.date.issued.fl_str_mv |
2020-09-16 |
dc.date.accessioned.fl_str_mv |
2021-02-04T13:54:26Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
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info:eu-repo/semantics/doctoralThesis |
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doctoralThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
Oliveira, Alexandre Souza de. Um estudo sobre o ensino do conceito de número e suas relações a partir da análise de um conjunto de manuscritos de Charles Sanders Peirce (1839-1914). 2020. 103 f. Tese (Doutorado em Educação Matemática) - Programa de Estudos Pós-Graduados em Educação Matemática, Pontifícia Universidade Católica de São Paulo, São Paulo, 2020. |
dc.identifier.uri.fl_str_mv |
https://tede2.pucsp.br/handle/handle/23465 |
identifier_str_mv |
Oliveira, Alexandre Souza de. Um estudo sobre o ensino do conceito de número e suas relações a partir da análise de um conjunto de manuscritos de Charles Sanders Peirce (1839-1914). 2020. 103 f. Tese (Doutorado em Educação Matemática) - Programa de Estudos Pós-Graduados em Educação Matemática, Pontifícia Universidade Católica de São Paulo, São Paulo, 2020. |
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https://tede2.pucsp.br/handle/handle/23465 |
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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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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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