The Different “Personalities” of the Rational Number Approached through Problem-solving
Autor(a) principal: | |
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Data de Publicação: | 2008 |
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Tipo de documento: | Artigo |
Idioma: | por |
Título da fonte: | Bolema: Boletim de Educação Matemática |
Texto Completo: | https://www.periodicos.rc.biblioteca.unesp.br/index.php/bolema/article/view/2106 |
Resumo: | We address the different “personalities” of the rational number and the concept of proportionality, analyzing the possibilities for using the Mathematics Teaching and Learning through Problem-solving Method. This method is based on the principle that knowledge can be constructed through the use of problems that generate new concepts and new contents. The different meanings of rational number – rational point, quotient, fraction, ratio, and operator – are constructs that depend on mathematical theories in which they are imbedded and the situations that evoke them in problem-solving. Some data will be presented from continuing education courses for teachers, aiming to contribute to understanding regarding the different “personalities” of the rational number. In general, these “personalities” are not easily identified by teachers and students, which is the reason for the many difficulties encountered during problem-solving involving rational numbers. One of these “personalities”, the ratio, provides the basis for the concept of proportionality, which is relevant because it is a unifying idea in mathematics. Key-words: Rational Numbers and Proportionality. Problem Solving. Teacher Education. |
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The Different “Personalities” of the Rational Number Approached through Problem-solvingAs Diferentes “Personalidades” do Número Racional Trabalhadas através da Resolução de ProblemasWe address the different “personalities” of the rational number and the concept of proportionality, analyzing the possibilities for using the Mathematics Teaching and Learning through Problem-solving Method. This method is based on the principle that knowledge can be constructed through the use of problems that generate new concepts and new contents. The different meanings of rational number – rational point, quotient, fraction, ratio, and operator – are constructs that depend on mathematical theories in which they are imbedded and the situations that evoke them in problem-solving. Some data will be presented from continuing education courses for teachers, aiming to contribute to understanding regarding the different “personalities” of the rational number. In general, these “personalities” are not easily identified by teachers and students, which is the reason for the many difficulties encountered during problem-solving involving rational numbers. One of these “personalities”, the ratio, provides the basis for the concept of proportionality, which is relevant because it is a unifying idea in mathematics. Key-words: Rational Numbers and Proportionality. Problem Solving. Teacher Education.Neste artigo, pretende-se abordar as diferentes “personalidades” do número racional e o conceito de proporcionalidade, analisando as possibilidades de utilizar a Metodologia de Ensino-Aprendizagem de Matemática através da Resolução de Problemas. Essa metodologia parte do princípio de que a construção do conhecimento pode ser realizada a partir de problemas geradores de novos conceitos e novos conteúdos. Os diferentes significados do número racional: ponto racional, quociente, fração, razão e operador são construtos que dependem das teorias matemáticas em que se inserem e das situações a que se referem na resolução de problemas. Serão apresentados alguns dados que foram desenvolvidos em cursos de formação continuada de professores visando à compreensão das diferentes “personalidades” do número racional. Em geral, essas “personalidades” não são facilmente identificadas, por professores e alunos, razão das grandes dificuldades encontradas durante a resolução de problemas envolvendo números racionais. Uma dessas “personalidades”, a razão, fundamenta o conceito de proporcionalidade, relevante por ser uma idéia unificadora na Matemática. Palavras-chave: Números Racionais e Proporcionalidade. Resolução de Problemas. Formação de Professores.UNESP - Campus de Rio Claro - Instituto de Geociências e Ciências Exatas2008-12-28info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://www.periodicos.rc.biblioteca.unesp.br/index.php/bolema/article/view/2106Bolema: Boletim de Educação Matemática; v. 21 n. 31 (2008); 79-1021980-44150103-636Xreponame:Bolema: Boletim de Educação Matemáticainstname:Universidade Estadual Paulista (UNESP)instacron:UNESPporhttps://www.periodicos.rc.biblioteca.unesp.br/index.php/bolema/article/view/2106/1831Onuchic, Lourdes de la RosaAllevato, Norma Suely Gomesinfo:eu-repo/semantics/openAccess2015-09-24T12:51:56Zoai:periodicos.rc.biblioteca.unesp.br:article/2106Revistahttps://www.periodicos.rc.biblioteca.unesp.br/index.php/bolema/PUBhttps://www.periodicos.rc.biblioteca.unesp.br/index.php/bolema/oaibolema.contato@gmail.com||romiarka@gmail.com1980-44150103-636Xopendoar:2015-09-24T12:51:56Bolema: Boletim de Educação Matemática - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
The Different “Personalities” of the Rational Number Approached through Problem-solving As Diferentes “Personalidades” do Número Racional Trabalhadas através da Resolução de Problemas |
title |
The Different “Personalities” of the Rational Number Approached through Problem-solving |
spellingShingle |
The Different “Personalities” of the Rational Number Approached through Problem-solving Onuchic, Lourdes de la Rosa |
title_short |
The Different “Personalities” of the Rational Number Approached through Problem-solving |
title_full |
The Different “Personalities” of the Rational Number Approached through Problem-solving |
title_fullStr |
The Different “Personalities” of the Rational Number Approached through Problem-solving |
title_full_unstemmed |
The Different “Personalities” of the Rational Number Approached through Problem-solving |
title_sort |
The Different “Personalities” of the Rational Number Approached through Problem-solving |
author |
Onuchic, Lourdes de la Rosa |
author_facet |
Onuchic, Lourdes de la Rosa Allevato, Norma Suely Gomes |
author_role |
author |
author2 |
Allevato, Norma Suely Gomes |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Onuchic, Lourdes de la Rosa Allevato, Norma Suely Gomes |
description |
We address the different “personalities” of the rational number and the concept of proportionality, analyzing the possibilities for using the Mathematics Teaching and Learning through Problem-solving Method. This method is based on the principle that knowledge can be constructed through the use of problems that generate new concepts and new contents. The different meanings of rational number – rational point, quotient, fraction, ratio, and operator – are constructs that depend on mathematical theories in which they are imbedded and the situations that evoke them in problem-solving. Some data will be presented from continuing education courses for teachers, aiming to contribute to understanding regarding the different “personalities” of the rational number. In general, these “personalities” are not easily identified by teachers and students, which is the reason for the many difficulties encountered during problem-solving involving rational numbers. One of these “personalities”, the ratio, provides the basis for the concept of proportionality, which is relevant because it is a unifying idea in mathematics. Key-words: Rational Numbers and Proportionality. Problem Solving. Teacher Education. |
publishDate |
2008 |
dc.date.none.fl_str_mv |
2008-12-28 |
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://www.periodicos.rc.biblioteca.unesp.br/index.php/bolema/article/view/2106 |
url |
https://www.periodicos.rc.biblioteca.unesp.br/index.php/bolema/article/view/2106 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.none.fl_str_mv |
https://www.periodicos.rc.biblioteca.unesp.br/index.php/bolema/article/view/2106/1831 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
UNESP - Campus de Rio Claro - Instituto de Geociências e Ciências Exatas |
publisher.none.fl_str_mv |
UNESP - Campus de Rio Claro - Instituto de Geociências e Ciências Exatas |
dc.source.none.fl_str_mv |
Bolema: Boletim de Educação Matemática; v. 21 n. 31 (2008); 79-102 1980-4415 0103-636X reponame:Bolema: Boletim de Educação Matemática instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Bolema: Boletim de Educação Matemática |
collection |
Bolema: Boletim de Educação Matemática |
repository.name.fl_str_mv |
Bolema: Boletim de Educação Matemática - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
bolema.contato@gmail.com||romiarka@gmail.com |
_version_ |
1800215873530626048 |