Combinatory reasoning in school problems of Cartesian product
Autor(a) principal: | |
---|---|
Data de Publicação: | 2010 |
Outros Autores: | , |
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. |
id |
UNICAMP-21_1bed2e38a0e18ab14fdca6d28dc8cc1b |
---|---|
oai_identifier_str |
oai:ojs.periodicos.sbu.unicamp.br:article/8646698 |
network_acronym_str |
UNICAMP-21 |
network_name_str |
Zetetiké (Online) |
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 |
_version_ |
1822181123629776896 |
dc.identifier.doi.none.fl_str_mv |
10.20396/zet.v18i33.8646698 |