Rational Number with Meaning of Fraction: relational aspect, ordering, equivalence and representations
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Data de Publicação: | 2021 |
Tipo de documento: | Artigo |
Idioma: | por |
Título da fonte: | Revista de Educação Matemática (Online) |
Texto Completo: | https://www.revistasbemsp.com.br/index.php/REMat-SP/article/view/126 |
Resumo: | This article is about a research that aimed to analyze the process of teaching and learning the rational number, with the meaning of fractions, as well as their ordering and equivalence. 7th grade elementary school students, from a public school in São Paulo, who did not demonstrate understanding for any meaning of the rational number, experienced didactic-pedagogical activities, systematized to promote the development and coordination of competencies and skills associated with the rational number, such as: observe, perceive and understand. The activities were based on theoretical assumptions, considering the relational aspect for understanding a fraction and the role of semiotic representations in the development of mathematical concepts. The data of these activities were analyzed qualitatively in light of the theoretical framework of the research. According to the results, the use of the relational aspect for the concept of fraction and treatments and conversions between representations was fundamental for the elaboration of the meaning of the rational number as a fraction and for its ordering. However, for the concept of equivalence, the results presented by all students were diffuse, allowing inferring their non-consolidation given the conceptual non-permanence to the detriment of the fractions used and their representations. It is concluded that, for these students, the understanding of the rational number, with the meaning of the part-whole relationship and its ordering, was significantly elaborated considering the relational aspect and its representations. |
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Rational Number with Meaning of Fraction: relational aspect, ordering, equivalence and representationsNúmero Racional com Significado de Fracción: aspecto relacional, ordenamiento, equivalencias y representacionesNúmero Racional com o Significado de Fração: aspecto relacional, ordenação, equivalência e representaçõesEnsino e aprendizagemNúmero racionalFraçõesEnseñanza y aprendizajenúmero racionalfraccionesTeaching and LearningRational NumberFractionsThis article is about a research that aimed to analyze the process of teaching and learning the rational number, with the meaning of fractions, as well as their ordering and equivalence. 7th grade elementary school students, from a public school in São Paulo, who did not demonstrate understanding for any meaning of the rational number, experienced didactic-pedagogical activities, systematized to promote the development and coordination of competencies and skills associated with the rational number, such as: observe, perceive and understand. The activities were based on theoretical assumptions, considering the relational aspect for understanding a fraction and the role of semiotic representations in the development of mathematical concepts. The data of these activities were analyzed qualitatively in light of the theoretical framework of the research. According to the results, the use of the relational aspect for the concept of fraction and treatments and conversions between representations was fundamental for the elaboration of the meaning of the rational number as a fraction and for its ordering. However, for the concept of equivalence, the results presented by all students were diffuse, allowing inferring their non-consolidation given the conceptual non-permanence to the detriment of the fractions used and their representations. It is concluded that, for these students, the understanding of the rational number, with the meaning of the part-whole relationship and its ordering, was significantly elaborated considering the relational aspect and its representations.Este artículo trata sobre una investigación que tuvo como objetivo analizar el proceso de enseñanza y aprendizaje del número racional, con el significado de las fracciones, así como su ordenamiento y equivalencia. Alumnos de 7 ° grado de primaria, de una escuela pública de São Paulo, que no demostraron comprensión de ningún significado del número racional, experimentaron actividades didáctico-pedagógicas, sistematizadas para promover el desarrollo y coordinación de competencias y habilidades asociadas al número racional, tales como: observar, percibir y comprender. Las actividades se basaron en supuestos teóricos, considerando el aspecto relacional para la comprensión de una fracción y el papel de las representaciones semióticas en el desarrollo de conceptos matemáticos. Los datos de estas actividades fueron analizados cualitativamente a la luz del marco teórico de la investigación. Según los resultados, el uso del aspecto relacional para el concepto de fracción y los tratamientos y conversiones entre representaciones fue fundamental para la elaboración del significado del número racional como fracción y para su ordenamiento. Sin embargo, para el concepto de equivalencia, los resultados presentados por todos los estudiantes fueron difusos, lo que permitió inferir su no consolidación dada la no permanencia conceptual en detrimento de las fracciones utilizadas y sus representaciones. Se concluye que, para estos estudiantes, la comprensión del número racional, con el significado de la relación parte-todo y su ordenamiento, se elaboró significativamente considerando el aspecto relacional y sus representaciones.Este artigo é sobre uma pesquisa que objetivou analisar o processo de ensino e aprendizagem do número racional, com o significado de frações, bem como suas ordenações e equivalências. Alunos de 7º ano da Educação Básica, de uma escola pública paulista, que demonstraram nenhum entendimento para qualquer significado do número racional, vivenciaram atividades didático-pedagógicas, sistematizadas para promoverem o desenvolvimento e a coordenação de competências e habilidades associadas ao número racional, tais como: observar, realizar e compreender. As atividades basearam-se em pressupostos teóricos, considerando o aspecto relacional para o entendimento de uma fração e o papel das representações semióticas na elaboração de conceitos matemáticos. Dados dessas atividades foram qualitativamente analisados em função do referencial teórico da pesquisa. Conforme os resultados, a utilização do aspecto relacional para o conceito de fração e de tratamento e conversões entre representações, foi fundamental para a elaboração do significado do número racional como fração e para sua ordenação. No entanto, para o conceito de equivalência os resultados mostrados por todos os alunos foram difusos, permitindo inferir sua não consolidação dada a não permanência conceitual em detrimento das frações utilizadas e de suas representações. A conclusão é que, para esses alunos, a compreensão do número racional, com o significado de relação parte-todo e suas ordenações, foi significativamente elaborada tendo em vista o aspecto relacional e suas representações.Sociedade Brasileira de Educação Matemática (SBEM)2021-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/ziphttps://www.revistasbemsp.com.br/index.php/REMat-SP/article/view/12610.37001/remat25269062v18id521Revista de Educação Matemática; Vol. 18 (2021): Publicação contínua; e021025Revista de Educação Matemática; Vol. 18 (2021): Publicação contínua; e021025Revista de Educação Matemática; v. 18 (2021): Publicação contínua; e0210252526-9062reponame:Revista de Educação Matemática (Online)instname:Sociedade Brasileira de Educação Matemática, Brasília (SBEM-DF)instacron:SBEMporhttps://www.revistasbemsp.com.br/index.php/REMat-SP/article/view/126/140https://www.revistasbemsp.com.br/index.php/REMat-SP/article/view/126/439https://www.revistasbemsp.com.br/index.php/REMat-SP/article/view/126/455https://www.revistasbemsp.com.br/index.php/REMat-SP/article/view/126/471https://creativecommons.org/licenses/by-nc-nd/4.0info:eu-repo/semantics/openAccessOliveira, Raquel Gomes de2023-07-16T02:24:10Zoai:ojs2.www.revistasbemsp.com.br:article/126Revistahttps://www.revistasbemsp.com.br/index.php/REMat-SPONGhttps://www.revistasbemsp.com.br/index.php/REMat-SP/oaidouglas.tinti@unicid.edu.br2526-90621676-8868opendoar:2023-07-16T02:24:10Revista de Educação Matemática (Online) - Sociedade Brasileira de Educação Matemática, Brasília (SBEM-DF)false |
dc.title.none.fl_str_mv |
Rational Number with Meaning of Fraction: relational aspect, ordering, equivalence and representations Número Racional com Significado de Fracción: aspecto relacional, ordenamiento, equivalencias y representaciones Número Racional com o Significado de Fração: aspecto relacional, ordenação, equivalência e representações |
title |
Rational Number with Meaning of Fraction: relational aspect, ordering, equivalence and representations |
spellingShingle |
Rational Number with Meaning of Fraction: relational aspect, ordering, equivalence and representations Oliveira, Raquel Gomes de Ensino e aprendizagem Número racional Frações Enseñanza y aprendizaje número racional fracciones Teaching and Learning Rational Number Fractions |
title_short |
Rational Number with Meaning of Fraction: relational aspect, ordering, equivalence and representations |
title_full |
Rational Number with Meaning of Fraction: relational aspect, ordering, equivalence and representations |
title_fullStr |
Rational Number with Meaning of Fraction: relational aspect, ordering, equivalence and representations |
title_full_unstemmed |
Rational Number with Meaning of Fraction: relational aspect, ordering, equivalence and representations |
title_sort |
Rational Number with Meaning of Fraction: relational aspect, ordering, equivalence and representations |
author |
Oliveira, Raquel Gomes de |
author_facet |
Oliveira, Raquel Gomes de |
author_role |
author |
dc.contributor.author.fl_str_mv |
Oliveira, Raquel Gomes de |
dc.subject.por.fl_str_mv |
Ensino e aprendizagem Número racional Frações Enseñanza y aprendizaje número racional fracciones Teaching and Learning Rational Number Fractions |
topic |
Ensino e aprendizagem Número racional Frações Enseñanza y aprendizaje número racional fracciones Teaching and Learning Rational Number Fractions |
description |
This article is about a research that aimed to analyze the process of teaching and learning the rational number, with the meaning of fractions, as well as their ordering and equivalence. 7th grade elementary school students, from a public school in São Paulo, who did not demonstrate understanding for any meaning of the rational number, experienced didactic-pedagogical activities, systematized to promote the development and coordination of competencies and skills associated with the rational number, such as: observe, perceive and understand. The activities were based on theoretical assumptions, considering the relational aspect for understanding a fraction and the role of semiotic representations in the development of mathematical concepts. The data of these activities were analyzed qualitatively in light of the theoretical framework of the research. According to the results, the use of the relational aspect for the concept of fraction and treatments and conversions between representations was fundamental for the elaboration of the meaning of the rational number as a fraction and for its ordering. However, for the concept of equivalence, the results presented by all students were diffuse, allowing inferring their non-consolidation given the conceptual non-permanence to the detriment of the fractions used and their representations. It is concluded that, for these students, the understanding of the rational number, with the meaning of the part-whole relationship and its ordering, was significantly elaborated considering the relational aspect and its representations. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-01-01 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
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article |
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publishedVersion |
dc.identifier.uri.fl_str_mv |
https://www.revistasbemsp.com.br/index.php/REMat-SP/article/view/126 10.37001/remat25269062v18id521 |
url |
https://www.revistasbemsp.com.br/index.php/REMat-SP/article/view/126 |
identifier_str_mv |
10.37001/remat25269062v18id521 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.none.fl_str_mv |
https://www.revistasbemsp.com.br/index.php/REMat-SP/article/view/126/140 https://www.revistasbemsp.com.br/index.php/REMat-SP/article/view/126/439 https://www.revistasbemsp.com.br/index.php/REMat-SP/article/view/126/455 https://www.revistasbemsp.com.br/index.php/REMat-SP/article/view/126/471 |
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https://creativecommons.org/licenses/by-nc-nd/4.0 info:eu-repo/semantics/openAccess |
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https://creativecommons.org/licenses/by-nc-nd/4.0 |
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openAccess |
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application/pdf application/zip |
dc.publisher.none.fl_str_mv |
Sociedade Brasileira de Educação Matemática (SBEM) |
publisher.none.fl_str_mv |
Sociedade Brasileira de Educação Matemática (SBEM) |
dc.source.none.fl_str_mv |
Revista de Educação Matemática; Vol. 18 (2021): Publicação contínua; e021025 Revista de Educação Matemática; Vol. 18 (2021): Publicação contínua; e021025 Revista de Educação Matemática; v. 18 (2021): Publicação contínua; e021025 2526-9062 reponame:Revista de Educação Matemática (Online) instname:Sociedade Brasileira de Educação Matemática, Brasília (SBEM-DF) instacron:SBEM |
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Sociedade Brasileira de Educação Matemática, Brasília (SBEM-DF) |
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SBEM |
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SBEM |
reponame_str |
Revista de Educação Matemática (Online) |
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Revista de Educação Matemática (Online) |
repository.name.fl_str_mv |
Revista de Educação Matemática (Online) - Sociedade Brasileira de Educação Matemática, Brasília (SBEM-DF) |
repository.mail.fl_str_mv |
douglas.tinti@unicid.edu.br |
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