The commercial model: a persistent obstacle to learning the rule of signs

Detalhes bibliográficos
Autor(a) principal: Hillesheim, Selma Felisbino
Data de Publicação: 2013
Outros Autores: Moretti, Méricles Thadeu
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/824
Resumo: The rule of signs theory for multiplication has been used for many centuries, it was, however, only demonstrated for the first time in the year of 1867 by Hankel. From a mathematical point of view the issue regarding this theory is completely solved, but some difficulties in teaching and learning it still persists nowadays. The commercial model for relative numbers is still an important model in teaching relative numbers and often turns into its own conception. In the present study this model will be strongly criticized based on Duval’s semantic concept of coherence and an alternative will be presented taking as a basis the extension principle. A study involving students of the 7th grade of Junior High indicates not only a new possibility for teaching negative numbers, but also some obstacles created when the teaching of such numbers bases on the commercial model.
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spelling The commercial model: a persistent obstacle to learning the rule of signsO modelo comercial: um entrave persistente à aprendizagem da regra de sinaisNúmeros NegativosRegra de SinaisModelo comercialPrincípio de ExtensãoCongruência SemânticaNegative numbersRule os signsCommercial modelExtension principleSemantic coherenceThe rule of signs theory for multiplication has been used for many centuries, it was, however, only demonstrated for the first time in the year of 1867 by Hankel. From a mathematical point of view the issue regarding this theory is completely solved, but some difficulties in teaching and learning it still persists nowadays. The commercial model for relative numbers is still an important model in teaching relative numbers and often turns into its own conception. In the present study this model will be strongly criticized based on Duval’s semantic concept of coherence and an alternative will be presented taking as a basis the extension principle. A study involving students of the 7th grade of Junior High indicates not only a new possibility for teaching negative numbers, but also some obstacles created when the teaching of such numbers bases on the commercial model.A regra de sinais para a multiplicação, mesmo tendo sido utilizada por vários séculos, só foi demonstrada em 1867 por Hankel. Do ponto de vista matemático, a questão está resolvida completamente, mas dificuldades no ensino e na aprendizagem dessa regra ainda persistem hoje. O modelo comercial para os números relativos é ainda um modelo importante no ensino dos números relativos e que, muitas vezes, se transforma na sua própria concepção. Neste trabalho, criticamos de forma contundente esse modelo, analisando-o do ponto de vista da noção de congruência semântica desenvolvida por Duval e apresentamos uma alternativa que toma por base o princípio de extensão. Um estudo com alunos do 7o ano do ensino fundamental aponta uma possibilidade de ensino para os negativos e obstáculos que se estabelecem quando esses números são ensinados e a metáfora comercial é adotada. Editora Cruzeiro do Sul2013-07-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://revistapos.cruzeirodosul.edu.br/rencima/article/view/82410.26843/rencima.v4i2.824Revista de Ensino de Ciências e Matemática; v. 4 n. 2 (2013): jul./dez.; 37-562179-426X10.26843/rencima.v4i2reponame:Revista de Ensino de Ciências e Matemática - REnCiMainstname:Universidade de Caxias do Sul (UCS)instacron:UCSporhttps://revistapos.cruzeirodosul.edu.br/rencima/article/view/824/694https://creativecommons.org/licenses/by-nc-sa/4.0/deed.pt_BRinfo:eu-repo/semantics/openAccessHillesheim, Selma FelisbinoMoretti, Méricles Thadeu2023-04-20T21:25:35Zoai:ojs.pkp.sfu.ca:article/824Revistahttps://revistapos.cruzeirodosul.edu.br/index.php/rencima/indexPRIhttps://revistapos.cruzeirodosul.edu.br/index.php/rencima/oai||rencima@cruzeirodosul.edu.br2179-426X2179-426Xopendoar:2023-04-20T21:25:35Revista de Ensino de Ciências e Matemática - REnCiMa - Universidade de Caxias do Sul (UCS)false
dc.title.none.fl_str_mv The commercial model: a persistent obstacle to learning the rule of signs
O modelo comercial: um entrave persistente à aprendizagem da regra de sinais
title The commercial model: a persistent obstacle to learning the rule of signs
spellingShingle The commercial model: a persistent obstacle to learning the rule of signs
Hillesheim, Selma Felisbino
Números Negativos
Regra de Sinais
Modelo comercial
Princípio de Extensão
Congruência Semântica
Negative numbers
Rule os signs
Commercial model
Extension principle
Semantic coherence
title_short The commercial model: a persistent obstacle to learning the rule of signs
title_full The commercial model: a persistent obstacle to learning the rule of signs
title_fullStr The commercial model: a persistent obstacle to learning the rule of signs
title_full_unstemmed The commercial model: a persistent obstacle to learning the rule of signs
title_sort The commercial model: a persistent obstacle to learning the rule of signs
author Hillesheim, Selma Felisbino
author_facet Hillesheim, Selma Felisbino
Moretti, Méricles Thadeu
author_role author
author2 Moretti, Méricles Thadeu
author2_role author
dc.contributor.author.fl_str_mv Hillesheim, Selma Felisbino
Moretti, Méricles Thadeu
dc.subject.por.fl_str_mv Números Negativos
Regra de Sinais
Modelo comercial
Princípio de Extensão
Congruência Semântica
Negative numbers
Rule os signs
Commercial model
Extension principle
Semantic coherence
topic Números Negativos
Regra de Sinais
Modelo comercial
Princípio de Extensão
Congruência Semântica
Negative numbers
Rule os signs
Commercial model
Extension principle
Semantic coherence
description The rule of signs theory for multiplication has been used for many centuries, it was, however, only demonstrated for the first time in the year of 1867 by Hankel. From a mathematical point of view the issue regarding this theory is completely solved, but some difficulties in teaching and learning it still persists nowadays. The commercial model for relative numbers is still an important model in teaching relative numbers and often turns into its own conception. In the present study this model will be strongly criticized based on Duval’s semantic concept of coherence and an alternative will be presented taking as a basis the extension principle. A study involving students of the 7th grade of Junior High indicates not only a new possibility for teaching negative numbers, but also some obstacles created when the teaching of such numbers bases on the commercial model.
publishDate 2013
dc.date.none.fl_str_mv 2013-07-01
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/824
10.26843/rencima.v4i2.824
url https://revistapos.cruzeirodosul.edu.br/rencima/article/view/824
identifier_str_mv 10.26843/rencima.v4i2.824
dc.language.iso.fl_str_mv por
language por
dc.relation.none.fl_str_mv https://revistapos.cruzeirodosul.edu.br/rencima/article/view/824/694
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. 4 n. 2 (2013): jul./dez.; 37-56
2179-426X
10.26843/rencima.v4i2
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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