Combinatory reasoning in school problems of Cartesian product

Detalhes bibliográficos
Autor(a) principal: Moro, Maria Lúcia Faria
Data de Publicação: 2010
Outros Autores: Soares, Maria Teresa Carneiro, Filho, Jomar Antonio Camarinha
Tipo de documento: Artigo
Idioma: por
Título da fonte: Zetetiké (Online)
DOI: 10.20396/zet.v18i33.8646698
Texto Completo: https://periodicos.sbu.unicamp.br/ojs/index.php/zetetike/article/view/8646698
Resumo: The paper concerns the construction of the combinatory reasoningwhen problems of Cartesian product are solved by 3rd to 6th grade ElementarySchool students’. Stemming from the revision of hierarchies described in earlierstudies, it is based on Piaget’s and Vergnaud’s proposals. The participants, 110students attending State Elementary Schools (mean age 10;5), answered a paperand pencil instrument containing four multiplicative problems of Cartesianproduct. A qualitative and a quantitative analysis result in a revised hierarchy ofthe combinatory reasoning, and show its absence on solutions in all grades andproblems, but a significant tendency to advanced solutions in 4th grade to someproblems. Concerning the hierarchy, the discussion underlines the progressivecombination of variables; the passage from arithmetical to algebraic reasoningand from additive to multiplicative schemata; the progressive overture to thepossibilities in its interplay with the necessities. Methodological restrictions andimplications for mathematical education are presented.
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spelling Combinatory reasoning in school problems of Cartesian product Raciocínio combinatório em problemas escolares de produto cartesianoCombinatory reasoning constructionMultiplicative problems of Cartesian product Elementary School mathematicsConstrução do raciocínio combinatórioProblemas multiplicativos de produto cartesianoMatemática no ensino fundamentalThe paper concerns the construction of the combinatory reasoningwhen problems of Cartesian product are solved by 3rd to 6th grade ElementarySchool students’. Stemming from the revision of hierarchies described in earlierstudies, it is based on Piaget’s and Vergnaud’s proposals. The participants, 110students attending State Elementary Schools (mean age 10;5), answered a paperand pencil instrument containing four multiplicative problems of Cartesianproduct. A qualitative and a quantitative analysis result in a revised hierarchy ofthe combinatory reasoning, and show its absence on solutions in all grades andproblems, but a significant tendency to advanced solutions in 4th grade to someproblems. Concerning the hierarchy, the discussion underlines the progressivecombination of variables; the passage from arithmetical to algebraic reasoningand from additive to multiplicative schemata; the progressive overture to thepossibilities in its interplay with the necessities. Methodological restrictions andimplications for mathematical education are presented.São descritos níveis do raciocínio combinatório de alunos de 3ª a 6ª séries do Ensino Fundamental, ao solucionarem problemas de produto cartesiano. O trabalho decorre do reexame de hierarquias descritas em estudos anteriores, com base em proposições de Piaget e Vergnaud. Os participantes, 110 alunos de escolas públicas (média etária 10;5), solucionaram por escrito quatro problemas multiplicativos de produto cartesiano. A análise qualitativa e a quantitativa dos dados permitiram: redefinir patamares do raciocínio combinatório; apontar ausência de raciocínio combinatório nas soluções em todas as séries e problemas, mas tendência significativa a soluções de níveis mais adiantados na 4ª série em alguns problemas. A discussão destaca na hierarquia descrita: a combinação progressiva das variáveis; a passagem do raciocínio aritmético para o algébrico e a dos esquemas aditivos aos multiplicativos; marcas da progressiva abertura para os possíveis em relação ao necessário. Restrições metodológicas e implicações para a educação matemática são apresentadas.Universidade Estadual de Campinas2010-12-23info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionTexto info:eu-repo/semantics/otherapplication/pdfhttps://periodicos.sbu.unicamp.br/ojs/index.php/zetetike/article/view/864669810.20396/zet.v18i33.8646698Zetetike; Vol. 18 No. 1 (2010): jan./jun. [33]; 211-242Zetetike; Vol. 18 Núm. 1 (2010): jan./jun. [33]; 211-242Zetetike; v. 18 n. 1 (2010): jan./jun. [33]; 211-2422176-1744reponame:Zetetiké (Online)instname:Universidade Estadual de Campinas (UNICAMP)instacron:UNICAMPporhttps://periodicos.sbu.unicamp.br/ojs/index.php/zetetike/article/view/8646698/13600Brazil; 2010Brasil; 2010Copyright (c) 2014 Zetetiké: Revista de Educação Matemáticahttps://creativecommons.org/licenses/by-nc-nd/4.0info:eu-repo/semantics/openAccessMoro, Maria Lúcia FariaSoares, Maria Teresa CarneiroFilho, Jomar Antonio Camarinha2023-11-13T12:17:06Zoai:ojs.periodicos.sbu.unicamp.br:article/8646698Revistahttp://www.fe.unicamp.br/zetetike/PUBhttps://periodicos.sbu.unicamp.br/ojs/index.php/zetetike/oaizetetike@unicamp.br2176-17440104-4877opendoar:2023-11-13T12:17:06Zetetiké (Online) - Universidade Estadual de Campinas (UNICAMP)false
dc.title.none.fl_str_mv Combinatory reasoning in school problems of Cartesian product
Raciocínio combinatório em problemas escolares de produto cartesiano
title Combinatory reasoning in school problems of Cartesian product
spellingShingle Combinatory reasoning in school problems of Cartesian product
Combinatory reasoning in school problems of Cartesian product
Moro, Maria Lúcia Faria
Combinatory reasoning construction
Multiplicative problems of Cartesian product
Elementary School mathematics
Construção do raciocínio combinatório
Problemas multiplicativos de produto cartesiano
Matemática no ensino fundamental
Moro, Maria Lúcia Faria
Combinatory reasoning construction
Multiplicative problems of Cartesian product
Elementary School mathematics
Construção do raciocínio combinatório
Problemas multiplicativos de produto cartesiano
Matemática no ensino fundamental
title_short Combinatory reasoning in school problems of Cartesian product
title_full Combinatory reasoning in school problems of Cartesian product
title_fullStr Combinatory reasoning in school problems of Cartesian product
Combinatory reasoning in school problems of Cartesian product
title_full_unstemmed Combinatory reasoning in school problems of Cartesian product
Combinatory reasoning in school problems of Cartesian product
title_sort Combinatory reasoning in school problems of Cartesian product
author Moro, Maria Lúcia Faria
author_facet Moro, Maria Lúcia Faria
Moro, Maria Lúcia Faria
Soares, Maria Teresa Carneiro
Filho, Jomar Antonio Camarinha
Soares, Maria Teresa Carneiro
Filho, Jomar Antonio Camarinha
author_role author
author2 Soares, Maria Teresa Carneiro
Filho, Jomar Antonio Camarinha
author2_role author
author
dc.contributor.author.fl_str_mv Moro, Maria Lúcia Faria
Soares, Maria Teresa Carneiro
Filho, Jomar Antonio Camarinha
dc.subject.por.fl_str_mv Combinatory reasoning construction
Multiplicative problems of Cartesian product
Elementary School mathematics
Construção do raciocínio combinatório
Problemas multiplicativos de produto cartesiano
Matemática no ensino fundamental
topic Combinatory reasoning construction
Multiplicative problems of Cartesian product
Elementary School mathematics
Construção do raciocínio combinatório
Problemas multiplicativos de produto cartesiano
Matemática no ensino fundamental
description The paper concerns the construction of the combinatory reasoningwhen problems of Cartesian product are solved by 3rd to 6th grade ElementarySchool students’. Stemming from the revision of hierarchies described in earlierstudies, it is based on Piaget’s and Vergnaud’s proposals. The participants, 110students attending State Elementary Schools (mean age 10;5), answered a paperand pencil instrument containing four multiplicative problems of Cartesianproduct. A qualitative and a quantitative analysis result in a revised hierarchy ofthe combinatory reasoning, and show its absence on solutions in all grades andproblems, but a significant tendency to advanced solutions in 4th grade to someproblems. Concerning the hierarchy, the discussion underlines the progressivecombination of variables; the passage from arithmetical to algebraic reasoningand from additive to multiplicative schemata; the progressive overture to thepossibilities in its interplay with the necessities. Methodological restrictions andimplications for mathematical education are presented.
publishDate 2010
dc.date.none.fl_str_mv 2010-12-23
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Texto
info:eu-repo/semantics/other
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://periodicos.sbu.unicamp.br/ojs/index.php/zetetike/article/view/8646698
10.20396/zet.v18i33.8646698
url https://periodicos.sbu.unicamp.br/ojs/index.php/zetetike/article/view/8646698
identifier_str_mv 10.20396/zet.v18i33.8646698
dc.language.iso.fl_str_mv por
language por
dc.relation.none.fl_str_mv https://periodicos.sbu.unicamp.br/ojs/index.php/zetetike/article/view/8646698/13600
dc.rights.driver.fl_str_mv Copyright (c) 2014 Zetetiké: Revista de Educação Matemática
https://creativecommons.org/licenses/by-nc-nd/4.0
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Copyright (c) 2014 Zetetiké: Revista de Educação Matemática
https://creativecommons.org/licenses/by-nc-nd/4.0
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.coverage.none.fl_str_mv Brazil; 2010
Brasil; 2010
dc.publisher.none.fl_str_mv Universidade Estadual de Campinas
publisher.none.fl_str_mv Universidade Estadual de Campinas
dc.source.none.fl_str_mv Zetetike; Vol. 18 No. 1 (2010): jan./jun. [33]; 211-242
Zetetike; Vol. 18 Núm. 1 (2010): jan./jun. [33]; 211-242
Zetetike; v. 18 n. 1 (2010): jan./jun. [33]; 211-242
2176-1744
reponame:Zetetiké (Online)
instname:Universidade Estadual de Campinas (UNICAMP)
instacron:UNICAMP
instname_str Universidade Estadual de Campinas (UNICAMP)
instacron_str UNICAMP
institution UNICAMP
reponame_str Zetetiké (Online)
collection Zetetiké (Online)
repository.name.fl_str_mv Zetetiké (Online) - Universidade Estadual de Campinas (UNICAMP)
repository.mail.fl_str_mv zetetike@unicamp.br
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dc.identifier.doi.none.fl_str_mv 10.20396/zet.v18i33.8646698

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