Who dances with whom: the development of elementary school chidren’s combinatorial reasoning

Detalhes bibliográficos
Autor(a) principal: Pessoa, Cristiane
Data de Publicação: 2009
Outros Autores: Borba, Rute
Tipo de documento: Artigo
Idioma: por
Título da fonte: Zetetiké (Online)
DOI: 10.20396/zet.v17i31.8646726
Texto Completo: https://periodicos.sbu.unicamp.br/ojs/index.php/zetetike/article/view/8646726
Resumo: In the present study it was observed how Elementary School pupilsunderstand combinatorial problems and what strategies they use. Differenttypes of problems (Cartesian product, arrangements, permutations andcombinations) were present in the test applied and answers were analyzedaccording to age and problem type. Progress was observed through differentschool grades. Arrangements and permutations problems were the most difficult,probably because of the difficulty in exhausting all possibilities, in which theorder of presentation of the elements is important. Strategies varied from totalincomprehension of the relations involved, passing by relation comprehensionwithout exhaustion of possibilities, until the identification of the product thatsummarizes the situation. It is necessary to recognize that combinatorialreasoning may develop also out of school, being necessary emphasis on the totalexhaustion of possibilities whilst solving these types of problems in theclassroom.
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spelling Who dances with whom: the development of elementary school chidren’s combinatorial reasoningQuem dança com quem: o desenvolvimento do raciocínio combinatório de crianças de 1ª a 4ª sérieCombinatorial reasoningProblem typesSolving strategiesElementary schoolRaciocínio combinatórioTipos de problemasEstratégias de resoluçãoEnsino fundamentalIn the present study it was observed how Elementary School pupilsunderstand combinatorial problems and what strategies they use. Differenttypes of problems (Cartesian product, arrangements, permutations andcombinations) were present in the test applied and answers were analyzedaccording to age and problem type. Progress was observed through differentschool grades. Arrangements and permutations problems were the most difficult,probably because of the difficulty in exhausting all possibilities, in which theorder of presentation of the elements is important. Strategies varied from totalincomprehension of the relations involved, passing by relation comprehensionwithout exhaustion of possibilities, until the identification of the product thatsummarizes the situation. It is necessary to recognize that combinatorialreasoning may develop also out of school, being necessary emphasis on the totalexhaustion of possibilities whilst solving these types of problems in theclassroom.Neste estudo buscou-se levantar a compreensão de problemas combinatórios por alunos de 1ª a 4a série e observar as estratégias por eles utilizadas. Aplicou-se um teste envolvendo diferentes tipos de problemas (produto cartesiano, arranjo, combinação e permutação) e analisaram-se os acertos dos alunos, por série e por tipo de problema. Observaram-se avanços ao longo das séries, com melhores desempenhos nas séries posteriores. Os problemas de arranjo e permutação, nos quais a ordem dos elementos é importante, apresentaram percentuais baixos de acertos, provavelmente pela dificuldade em levantar todas as possibilidades. As estratégias variavam da total incompreensão das relações envolvidas, passando pela compreensão das relações sem esgotamento de possibilidades, até a identificação do produto que sintetizava a situação. Deve-se reconhecer que o raciocínio combinatório desenvolve-se dentro e fora da escola, sendo necessário que se enfatize a necessidade de os alunos levantarem de modo sistematizado todas as possibilidades de uma situação. Universidade Estadual de Campinas2009-12-19info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionTextoinfo:eu-repo/semantics/otherapplication/pdfhttps://periodicos.sbu.unicamp.br/ojs/index.php/zetetike/article/view/864672610.20396/zet.v17i31.8646726Zetetike; Vol. 17 No. 1 (2009): jan./jun. [31]; 105-150Zetetike; Vol. 17 Núm. 1 (2009): jan./jun. [31]; 105-150Zetetike; v. 17 n. 1 (2009): jan./jun. [31]; 105-1502176-1744reponame:Zetetiké (Online)instname:Universidade Estadual de Campinas (UNICAMP)instacron:UNICAMPporhttps://periodicos.sbu.unicamp.br/ojs/index.php/zetetike/article/view/8646726/13628Brazil; 2009Brasil; 2009Copyright (c) 2014 Zetetiké: Revista de Educação Matemáticahttps://creativecommons.org/licenses/by-nc-nd/4.0info:eu-repo/semantics/openAccessPessoa, CristianeBorba, Rute2023-11-10T11:59:24Zoai:ojs.periodicos.sbu.unicamp.br:article/8646726Revistahttp://www.fe.unicamp.br/zetetike/PUBhttps://periodicos.sbu.unicamp.br/ojs/index.php/zetetike/oaizetetike@unicamp.br2176-17440104-4877opendoar:2023-11-10T11:59:24Zetetiké (Online) - Universidade Estadual de Campinas (UNICAMP)false
dc.title.none.fl_str_mv Who dances with whom: the development of elementary school chidren’s combinatorial reasoning
Quem dança com quem: o desenvolvimento do raciocínio combinatório de crianças de 1ª a 4ª série
title Who dances with whom: the development of elementary school chidren’s combinatorial reasoning
spellingShingle Who dances with whom: the development of elementary school chidren’s combinatorial reasoning
Who dances with whom: the development of elementary school chidren’s combinatorial reasoning
Pessoa, Cristiane
Combinatorial reasoning
Problem types
Solving strategies
Elementary school
Raciocínio combinatório
Tipos de problemas
Estratégias de resolução
Ensino fundamental
Pessoa, Cristiane
Combinatorial reasoning
Problem types
Solving strategies
Elementary school
Raciocínio combinatório
Tipos de problemas
Estratégias de resolução
Ensino fundamental
title_short Who dances with whom: the development of elementary school chidren’s combinatorial reasoning
title_full Who dances with whom: the development of elementary school chidren’s combinatorial reasoning
title_fullStr Who dances with whom: the development of elementary school chidren’s combinatorial reasoning
Who dances with whom: the development of elementary school chidren’s combinatorial reasoning
title_full_unstemmed Who dances with whom: the development of elementary school chidren’s combinatorial reasoning
Who dances with whom: the development of elementary school chidren’s combinatorial reasoning
title_sort Who dances with whom: the development of elementary school chidren’s combinatorial reasoning
author Pessoa, Cristiane
author_facet Pessoa, Cristiane
Pessoa, Cristiane
Borba, Rute
Borba, Rute
author_role author
author2 Borba, Rute
author2_role author
dc.contributor.author.fl_str_mv Pessoa, Cristiane
Borba, Rute
dc.subject.por.fl_str_mv Combinatorial reasoning
Problem types
Solving strategies
Elementary school
Raciocínio combinatório
Tipos de problemas
Estratégias de resolução
Ensino fundamental
topic Combinatorial reasoning
Problem types
Solving strategies
Elementary school
Raciocínio combinatório
Tipos de problemas
Estratégias de resolução
Ensino fundamental
description In the present study it was observed how Elementary School pupilsunderstand combinatorial problems and what strategies they use. Differenttypes of problems (Cartesian product, arrangements, permutations andcombinations) were present in the test applied and answers were analyzedaccording to age and problem type. Progress was observed through differentschool grades. Arrangements and permutations problems were the most difficult,probably because of the difficulty in exhausting all possibilities, in which theorder of presentation of the elements is important. Strategies varied from totalincomprehension of the relations involved, passing by relation comprehensionwithout exhaustion of possibilities, until the identification of the product thatsummarizes the situation. It is necessary to recognize that combinatorialreasoning may develop also out of school, being necessary emphasis on the totalexhaustion of possibilities whilst solving these types of problems in theclassroom.
publishDate 2009
dc.date.none.fl_str_mv 2009-12-19
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/8646726
10.20396/zet.v17i31.8646726
url https://periodicos.sbu.unicamp.br/ojs/index.php/zetetike/article/view/8646726
identifier_str_mv 10.20396/zet.v17i31.8646726
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/8646726/13628
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; 2009
Brasil; 2009
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. 17 No. 1 (2009): jan./jun. [31]; 105-150
Zetetike; Vol. 17 Núm. 1 (2009): jan./jun. [31]; 105-150
Zetetike; v. 17 n. 1 (2009): jan./jun. [31]; 105-150
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.v17i31.8646726

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