Overcoming obstacles: from Arithmetic to Algebra

Detalhes bibliográficos
Autor(a) principal: Sant'Anna, Neide
Data de Publicação: 2014
Outros Autores: Palis, Gilda de La Rocque, Neves, Maria Apparecida Campos Mamede
Tipo de documento: Artigo
Idioma: por
Título da fonte: Zetetiké (Online)
Texto Completo: https://periodicos.sbu.unicamp.br/ojs/index.php/zetetike/article/view/8646603
Resumo: This work demonstrates difficulties of students on recognizing fractions asnumbers and how to overcome them. For this purpose, a strategy was developed to teachfractions taking as reference the number line. By relating the fraction to a well-defined objective concept, students proceed quickly to master more complex concepts. Theidentification of fractions as numbers is initially performed in the measurement of linesegments. From the number line the student transposes to other contexts in a process ofsuccessive generalizations. A sequence of activities involving, e.g., equivalence betweenfractions and order in the set of fractions, is here described and results of this methodologyapplication are presented. These results are evaluated from a global point of view and ofgroups with different levels of previous qualification. Results obtained demonstrate thatfamiliarization with the algebraic field is more easily reached when the concept of fraction isdealt in the proposed way.
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spelling Overcoming obstacles: from Arithmetic to AlgebraTranspondo obstáculos: da aritmética para a álgebraFractionFraction as a numberProblems with fractionsAlgebraic reasoningTeaching arithmeticFraçãoFração como número Problemas com fraçõesPensamento algébricoEnsino de aritméticaFraçõesThis work demonstrates difficulties of students on recognizing fractions asnumbers and how to overcome them. For this purpose, a strategy was developed to teachfractions taking as reference the number line. By relating the fraction to a well-defined objective concept, students proceed quickly to master more complex concepts. Theidentification of fractions as numbers is initially performed in the measurement of linesegments. From the number line the student transposes to other contexts in a process ofsuccessive generalizations. A sequence of activities involving, e.g., equivalence betweenfractions and order in the set of fractions, is here described and results of this methodologyapplication are presented. These results are evaluated from a global point of view and ofgroups with different levels of previous qualification. Results obtained demonstrate thatfamiliarization with the algebraic field is more easily reached when the concept of fraction isdealt in the proposed way.Neste trabalho se demonstra a dificuldade dos alunos em reconhecer fração como número e indica-se como vencer essa dificuldade. Para isso, desenvolve-se uma estratégia de ensino de frações que toma como referência a reta numérica. Ao associar à fração um conceito objetivo bem determinado, rapidamente os alunos prosseguem no domínio de conceitos mais complexos. A identificação de fração como número é realizada inicialmente na medição de segmentos de reta. Da reta numérica se passa para outros contextos, em um processo de sucessivas generalizações. Este texto descreve atividades envolvendo, por exemplo, equivalência entre frações e ordem no conjunto das frações e apresenta resultados da aplicação da metodologia,  avaliados do ponto de vista global e do ponto de vista de grupos diferenciados de alunos em diferentes níveis de qualificação prévia. Os resultados demonstram que a familiarização com o campo algébrico é alcançada com mais facilidade, quando o conceito de fração é trabalhado como proposto.Universidade Estadual de Campinas2014-04-16info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionTextoinfo:eu-repo/semantics/otherapplication/pdfhttps://periodicos.sbu.unicamp.br/ojs/index.php/zetetike/article/view/864660310.20396/zet.v21i39.8646603Zetetike; Vol. 21 No. 1 (2013): jan./jun. [39]; 169-196Zetetike; Vol. 21 Núm. 1 (2013): jan./jun. [39]; 169-196Zetetike; v. 21 n. 1 (2013): jan./jun. [39]; 169-1962176-1744reponame:Zetetiké (Online)instname:Universidade Estadual de Campinas (UNICAMP)instacron:UNICAMPporhttps://periodicos.sbu.unicamp.br/ojs/index.php/zetetike/article/view/8646603/13505Brazil; 2013Brasil; 2013Copyright (c) 2014 Zetetiké: Revista de Educação Matemáticahttps://creativecommons.org/licenses/by-nc-nd/4.0info:eu-repo/semantics/openAccessSant'Anna, NeidePalis, Gilda de La RocqueNeves, Maria Apparecida Campos Mamede2023-11-23T16:41:20Zoai:ojs.periodicos.sbu.unicamp.br:article/8646603Revistahttp://www.fe.unicamp.br/zetetike/PUBhttps://periodicos.sbu.unicamp.br/ojs/index.php/zetetike/oaizetetike@unicamp.br2176-17440104-4877opendoar:2023-11-23T16:41:20Zetetiké (Online) - Universidade Estadual de Campinas (UNICAMP)false
dc.title.none.fl_str_mv Overcoming obstacles: from Arithmetic to Algebra
Transpondo obstáculos: da aritmética para a álgebra
title Overcoming obstacles: from Arithmetic to Algebra
spellingShingle Overcoming obstacles: from Arithmetic to Algebra
Sant'Anna, Neide
Fraction
Fraction as a number
Problems with fractions
Algebraic reasoning
Teaching arithmetic
Fração
Fração como número
Problemas com frações
Pensamento algébrico
Ensino de aritmética
Frações
title_short Overcoming obstacles: from Arithmetic to Algebra
title_full Overcoming obstacles: from Arithmetic to Algebra
title_fullStr Overcoming obstacles: from Arithmetic to Algebra
title_full_unstemmed Overcoming obstacles: from Arithmetic to Algebra
title_sort Overcoming obstacles: from Arithmetic to Algebra
author Sant'Anna, Neide
author_facet Sant'Anna, Neide
Palis, Gilda de La Rocque
Neves, Maria Apparecida Campos Mamede
author_role author
author2 Palis, Gilda de La Rocque
Neves, Maria Apparecida Campos Mamede
author2_role author
author
dc.contributor.author.fl_str_mv Sant'Anna, Neide
Palis, Gilda de La Rocque
Neves, Maria Apparecida Campos Mamede
dc.subject.por.fl_str_mv Fraction
Fraction as a number
Problems with fractions
Algebraic reasoning
Teaching arithmetic
Fração
Fração como número
Problemas com frações
Pensamento algébrico
Ensino de aritmética
Frações
topic Fraction
Fraction as a number
Problems with fractions
Algebraic reasoning
Teaching arithmetic
Fração
Fração como número
Problemas com frações
Pensamento algébrico
Ensino de aritmética
Frações
description This work demonstrates difficulties of students on recognizing fractions asnumbers and how to overcome them. For this purpose, a strategy was developed to teachfractions taking as reference the number line. By relating the fraction to a well-defined objective concept, students proceed quickly to master more complex concepts. Theidentification of fractions as numbers is initially performed in the measurement of linesegments. From the number line the student transposes to other contexts in a process ofsuccessive generalizations. A sequence of activities involving, e.g., equivalence betweenfractions and order in the set of fractions, is here described and results of this methodologyapplication are presented. These results are evaluated from a global point of view and ofgroups with different levels of previous qualification. Results obtained demonstrate thatfamiliarization with the algebraic field is more easily reached when the concept of fraction isdealt in the proposed way.
publishDate 2014
dc.date.none.fl_str_mv 2014-04-16
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/8646603
10.20396/zet.v21i39.8646603
url https://periodicos.sbu.unicamp.br/ojs/index.php/zetetike/article/view/8646603
identifier_str_mv 10.20396/zet.v21i39.8646603
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/8646603/13505
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; 2013
Brasil; 2013
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. 21 No. 1 (2013): jan./jun. [39]; 169-196
Zetetike; Vol. 21 Núm. 1 (2013): jan./jun. [39]; 169-196
Zetetike; v. 21 n. 1 (2013): jan./jun. [39]; 169-196
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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