Irrational numbers on basic education: the didactical and epistemological contributions from Hystory of Mathematics.

Detalhes bibliográficos
Autor(a) principal: Pommer, Wagner Marcelo
Data de Publicação: 2018
Tipo de documento: Artigo
Idioma: por
Título da fonte: Revista de Ensino de Ciências e Matemática - REnCiMa
Texto Completo: https://revistapos.cruzeirodosul.edu.br/rencima/article/view/1360
Resumo: Irrational numbers’ presentation and development underwent a very simplified process of didactic transposition that is polarized between pragmatical and theoretical aspects. This text aimed to analyze the historical and epistemological contexts and contributions of irrational numbers, in a way to situate how it is presented the pragmatical and theoretical aspects revealed along the development of this theme on the references books where it is found the ‘academical university knowledge’, inspired in Resende (2007). We aimed our research on two reference books: ‘Mathematics’ Fundamentals Concepts’, by Caraça (1970) and 'The Fundamental Ideas of Mathematics', by Costa (1981). Caraça (1970) indicated the possibility of addressing and developing the 'Incommensurable Measurement Problem', where it is possible to perform commensurable and incommensurable segments. Costa (1981) pointed to the development of irrational numbers by real number line, an issue that goes back to the idea of continuity and ‘Dedekind cut’. The narratives discussed in these two books may contribute to a didactic transposition concerning to irrational numbers. Facing such analyzes, imbued on narrative and qualitative approach, we point out some contributions that can promote a retelling of mathematical facts, namely by approaching irrational numbers’ by the fundamental ideas expressed by counting&measure, finite&infinite and exact&approximate pairs.
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spelling Irrational numbers on basic education: the didactical and epistemological contributions from Hystory of Mathematics.Números irracionais na escolaridade básica: as contribuições didático-epistemológicas advindas da História da Matemática.Números IrracionaisHistória da MatemáticaBento de Jesus CaraçaManuel Amoroso CostaIdeias FundamentaisIrrational NumbersHystory of MathematicsBento de Jesus CaraçaManuel Amoroso CostaFundamental IdeasIrrational numbers’ presentation and development underwent a very simplified process of didactic transposition that is polarized between pragmatical and theoretical aspects. This text aimed to analyze the historical and epistemological contexts and contributions of irrational numbers, in a way to situate how it is presented the pragmatical and theoretical aspects revealed along the development of this theme on the references books where it is found the ‘academical university knowledge’, inspired in Resende (2007). We aimed our research on two reference books: ‘Mathematics’ Fundamentals Concepts’, by Caraça (1970) and 'The Fundamental Ideas of Mathematics', by Costa (1981). Caraça (1970) indicated the possibility of addressing and developing the 'Incommensurable Measurement Problem', where it is possible to perform commensurable and incommensurable segments. Costa (1981) pointed to the development of irrational numbers by real number line, an issue that goes back to the idea of continuity and ‘Dedekind cut’. The narratives discussed in these two books may contribute to a didactic transposition concerning to irrational numbers. Facing such analyzes, imbued on narrative and qualitative approach, we point out some contributions that can promote a retelling of mathematical facts, namely by approaching irrational numbers’ by the fundamental ideas expressed by counting&measure, finite&infinite and exact&approximate pairs.A apresentação e desenvolvimento dos números irracionais sofreram um processo de transposição didática muito simplificado e polarizado entre o pragmático e o teórico. Este texto objetivou analisar os contextos e contribuições histórico-epistemológicos dos números irracionais, de modo a situar como se apresentam os aspectos pragmáticos e teóricos surgidos ao longo do desenvolvimento do referido tema em livros de referência onde se encontram os ‘saberes acadêmicos universitários’, inspirados em Resende (2007). Realizamos uma busca em dois livros de referência: ‘Conceitos Fundamentais da Matemática’, de Caraça (1970) e ‘As Ideias Fundamentais da Matemática’, de Costa (1981). Caraça (1970) indica a possibilidade de se desenvolver o ‘Problema da Medida’, onde é possível se apresentar os segmentos comensuráveis e os segmentos incomensuráveis. Costa (1981) aponta para o desenvolvimento dos números irracionais por meio da reta real, questão que remonta a ideia de continuidade e ao corte de Dedekind. As narrativas presentes nesses livros podem contribuir para uma transposição didática com relação aos números irracionais. Em face de tais análises, centradas na narrativa e na abordagem qualitativa, destacamos alguns aportes que podem promover uma releitura dos fatos matemáticos, pela abordagem dos números irracionais por meio das ideias fundamentais representadas pelos pares contagem&medida, finito&infinito e exato&aproximado.Editora Cruzeiro do Sul2018-06-28info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://revistapos.cruzeirodosul.edu.br/rencima/article/view/136010.26843/rencima.v9i3.1360Revista de Ensino de Ciências e Matemática; v. 9 n. 3 (2018): abr./jun.; 183-1992179-426X10.26843/rencima.v9i3reponame:Revista de Ensino de Ciências e Matemática - REnCiMainstname:Universidade de Caxias do Sul (UCS)instacron:UCSporhttps://revistapos.cruzeirodosul.edu.br/rencima/article/view/1360/1008https://creativecommons.org/licenses/by-nc-sa/4.0/deed.pt_BRinfo:eu-repo/semantics/openAccessPommer, Wagner Marcelo2023-04-20T23:11:50Zoai:ojs.pkp.sfu.ca:article/1360Revistahttps://revistapos.cruzeirodosul.edu.br/index.php/rencima/indexPRIhttps://revistapos.cruzeirodosul.edu.br/index.php/rencima/oai||rencima@cruzeirodosul.edu.br2179-426X2179-426Xopendoar:2023-04-20T23:11:50Revista de Ensino de Ciências e Matemática - REnCiMa - Universidade de Caxias do Sul (UCS)false
dc.title.none.fl_str_mv Irrational numbers on basic education: the didactical and epistemological contributions from Hystory of Mathematics.
Números irracionais na escolaridade básica: as contribuições didático-epistemológicas advindas da História da Matemática.
title Irrational numbers on basic education: the didactical and epistemological contributions from Hystory of Mathematics.
spellingShingle Irrational numbers on basic education: the didactical and epistemological contributions from Hystory of Mathematics.
Pommer, Wagner Marcelo
Números Irracionais
História da Matemática
Bento de Jesus Caraça
Manuel Amoroso Costa
Ideias Fundamentais
Irrational Numbers
Hystory of Mathematics
Bento de Jesus Caraça
Manuel Amoroso Costa
Fundamental Ideas
title_short Irrational numbers on basic education: the didactical and epistemological contributions from Hystory of Mathematics.
title_full Irrational numbers on basic education: the didactical and epistemological contributions from Hystory of Mathematics.
title_fullStr Irrational numbers on basic education: the didactical and epistemological contributions from Hystory of Mathematics.
title_full_unstemmed Irrational numbers on basic education: the didactical and epistemological contributions from Hystory of Mathematics.
title_sort Irrational numbers on basic education: the didactical and epistemological contributions from Hystory of Mathematics.
author Pommer, Wagner Marcelo
author_facet Pommer, Wagner Marcelo
author_role author
dc.contributor.author.fl_str_mv Pommer, Wagner Marcelo
dc.subject.por.fl_str_mv Números Irracionais
História da Matemática
Bento de Jesus Caraça
Manuel Amoroso Costa
Ideias Fundamentais
Irrational Numbers
Hystory of Mathematics
Bento de Jesus Caraça
Manuel Amoroso Costa
Fundamental Ideas
topic Números Irracionais
História da Matemática
Bento de Jesus Caraça
Manuel Amoroso Costa
Ideias Fundamentais
Irrational Numbers
Hystory of Mathematics
Bento de Jesus Caraça
Manuel Amoroso Costa
Fundamental Ideas
description Irrational numbers’ presentation and development underwent a very simplified process of didactic transposition that is polarized between pragmatical and theoretical aspects. This text aimed to analyze the historical and epistemological contexts and contributions of irrational numbers, in a way to situate how it is presented the pragmatical and theoretical aspects revealed along the development of this theme on the references books where it is found the ‘academical university knowledge’, inspired in Resende (2007). We aimed our research on two reference books: ‘Mathematics’ Fundamentals Concepts’, by Caraça (1970) and 'The Fundamental Ideas of Mathematics', by Costa (1981). Caraça (1970) indicated the possibility of addressing and developing the 'Incommensurable Measurement Problem', where it is possible to perform commensurable and incommensurable segments. Costa (1981) pointed to the development of irrational numbers by real number line, an issue that goes back to the idea of continuity and ‘Dedekind cut’. The narratives discussed in these two books may contribute to a didactic transposition concerning to irrational numbers. Facing such analyzes, imbued on narrative and qualitative approach, we point out some contributions that can promote a retelling of mathematical facts, namely by approaching irrational numbers’ by the fundamental ideas expressed by counting&measure, finite&infinite and exact&approximate pairs.
publishDate 2018
dc.date.none.fl_str_mv 2018-06-28
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://revistapos.cruzeirodosul.edu.br/rencima/article/view/1360
10.26843/rencima.v9i3.1360
url https://revistapos.cruzeirodosul.edu.br/rencima/article/view/1360
identifier_str_mv 10.26843/rencima.v9i3.1360
dc.language.iso.fl_str_mv por
language por
dc.relation.none.fl_str_mv https://revistapos.cruzeirodosul.edu.br/rencima/article/view/1360/1008
dc.rights.driver.fl_str_mv https://creativecommons.org/licenses/by-nc-sa/4.0/deed.pt_BR
info:eu-repo/semantics/openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/4.0/deed.pt_BR
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Editora Cruzeiro do Sul
publisher.none.fl_str_mv Editora Cruzeiro do Sul
dc.source.none.fl_str_mv Revista de Ensino de Ciências e Matemática; v. 9 n. 3 (2018): abr./jun.; 183-199
2179-426X
10.26843/rencima.v9i3
reponame:Revista de Ensino de Ciências e Matemática - REnCiMa
instname:Universidade de Caxias do Sul (UCS)
instacron:UCS
instname_str Universidade de Caxias do Sul (UCS)
instacron_str UCS
institution UCS
reponame_str Revista de Ensino de Ciências e Matemática - REnCiMa
collection Revista de Ensino de Ciências e Matemática - REnCiMa
repository.name.fl_str_mv Revista de Ensino de Ciências e Matemática - REnCiMa - Universidade de Caxias do Sul (UCS)
repository.mail.fl_str_mv ||rencima@cruzeirodosul.edu.br
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