The residual class of the Z7 ring and the seven musical notes with its agreements: A mathematical teaching and learning process in basic education

Detalhes bibliográficos
Autor(a) principal: Pontes, Edel Alexandre Silva
Data de Publicação: 2021
Outros Autores: Coelho, Elis Lima, Silva, Bruno Henrique Macêdo dos Santos, Moura, Helloyne Roberta Eloi, Batista, Igor Santana
Tipo de documento: Artigo
Idioma: por
Título da fonte: Research, Society and Development
Texto Completo: https://rsdjournal.org/index.php/rsd/article/view/15548
Resumo: Number Theory is one of the areas of mathematics that has considerable applications in basic education, especially in the final years of elementary school, and in order to vigorously understand these innumerable practices, it is necessary to understand the basic concepts of Modular Arithmetic. This work aimed to present the basic concepts of Modular Arithmetic and to relate in a playful way the concept of entire modules 7 through the seven musical notes. The research recommends exposing a methodological suggestion, through the ring (Z7, +, x), in the process of teaching and learning mathematics for students in the final years of elementary school. It is evident to remember that developing methodological procedures that can strongly assist the teaching and learning of mathematics are fundamental criteria for improving the popularization process of this science, often reneged, but of extreme importance for scientific and technological evolution. It is expected that our projections for understanding mathematical models will be debated, with the aim of fully strengthening the teaching of mathematics.
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spelling The residual class of the Z7 ring and the seven musical notes with its agreements: A mathematical teaching and learning process in basic educationLa clase residual del anillo Z7 y las siete notas musicales con sus acordes: Un proceso de enseñanza y aprendizaje de las matemáticas en la educación básicaA classe de resíduos do anel Z7 e as sete notas musicais com seus acordes: Um processo de ensino e aprendizagem de matemática na educação básicaEnseñanza y aprendizaje de las matemáticasAritmética modularNotas musicales.Ensino e aprendizagem de matemáticaAritmética ModularAs notas musicais. Teaching and learning of mathematicsModular ArithmeticMusical notes.Number Theory is one of the areas of mathematics that has considerable applications in basic education, especially in the final years of elementary school, and in order to vigorously understand these innumerable practices, it is necessary to understand the basic concepts of Modular Arithmetic. This work aimed to present the basic concepts of Modular Arithmetic and to relate in a playful way the concept of entire modules 7 through the seven musical notes. The research recommends exposing a methodological suggestion, through the ring (Z7, +, x), in the process of teaching and learning mathematics for students in the final years of elementary school. It is evident to remember that developing methodological procedures that can strongly assist the teaching and learning of mathematics are fundamental criteria for improving the popularization process of this science, often reneged, but of extreme importance for scientific and technological evolution. It is expected that our projections for understanding mathematical models will be debated, with the aim of fully strengthening the teaching of mathematics.La Teoría de Números es una de las áreas de la matemática que tiene aplicaciones apreciables en la educación básica, especialmente en los últimos años de la escuela primaria, y para comprender con vigor estas innumerables prácticas, es necesario comprender los conceptos básicos de la Aritmética Modular. Este trabajo tuvo como objetivo presentar los conceptos básicos de la Aritmética Modular y relacionar de manera lúdica el concepto de módulos completos 7 a través de las siete notas musicales. La investigación recomienda exponer una sugerencia metodológica, a través del anillo (Z7, +, x), en el proceso de enseñanza y aprendizaje de las matemáticas para los estudiantes de los últimos años de la escuela primaria. Es evidente recordar que desarrollar procedimientos metodológicos que puedan ayudar fuertemente a la enseñanza y el aprendizaje de las matemáticas son criterios fundamentales para mejorar el proceso de divulgación de esta ciencia, muchas veces renegada, pero de extrema importancia para la evolución científica y tecnológica. Se espera que se debatan nuestras proyecciones para la comprensión de modelos matemáticos, con el objetivo de fortalecer plenamente la enseñanza de las matemáticas.A Teoria dos Números é uma das áreas da matemática que possui apreciáveis aplicações na educação básica, principalmente nos anos finais do ensino fundamental, e para compreendermos com vigor essas inumeráveis práticas, faz-se necessário o entendimento dos conceitos básicos da Aritmética Modular. Este trabalho objetivou apresentar os conceitos básicos de Aritmética Modular e relacionar de forma lúdica o conceito de inteiros módulos 7 por intermédio das sete notas musicais. A pesquisa recomenda expor uma sugestão metodológica, por meio do anel (Z7, +, x), no processo de ensino e aprendizagem de matemática para alunos dos anos finais do ensino fundamental. É evidente lembrar que desenvolver procedimentos metodológicos que possam auxiliar fortemente o ensino e aprendizagem de matemática são critérios fundamentais para aprimorar o processo de popularização desta ciência, muitas vezes renegada, porém de extrema importância para a evolução cientifica e tecnológica. Espera-se que nossas projeções para compreensão de modelos matemáticos sejam debatidas, no desígnio de fortalecer inteiramente o ensino de matemática.Research, Society and Development2021-05-21info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://rsdjournal.org/index.php/rsd/article/view/1554810.33448/rsd-v10i6.15548Research, Society and Development; Vol. 10 No. 6; e6210615548Research, Society and Development; Vol. 10 Núm. 6; e6210615548Research, Society and Development; v. 10 n. 6; e62106155482525-3409reponame:Research, Society and Developmentinstname:Universidade Federal de Itajubá (UNIFEI)instacron:UNIFEIporhttps://rsdjournal.org/index.php/rsd/article/view/15548/13861Copyright (c) 2021 Edel Alexandre Silva Pontes; Elis Lima Coelho; Bruno Henrique Macêdo dos Santos Silva; Helloyne Roberta Eloi Moura; Igor Santana Batistahttps://creativecommons.org/licenses/by/4.0info:eu-repo/semantics/openAccessPontes, Edel Alexandre SilvaCoelho, Elis Lima Silva, Bruno Henrique Macêdo dos Santos Moura, Helloyne Roberta Eloi Batista, Igor Santana2021-06-10T22:51:46Zoai:ojs.pkp.sfu.ca:article/15548Revistahttps://rsdjournal.org/index.php/rsd/indexPUBhttps://rsdjournal.org/index.php/rsd/oairsd.articles@gmail.com2525-34092525-3409opendoar:2024-01-17T09:36:20.988957Research, Society and Development - Universidade Federal de Itajubá (UNIFEI)false
dc.title.none.fl_str_mv The residual class of the Z7 ring and the seven musical notes with its agreements: A mathematical teaching and learning process in basic education
La clase residual del anillo Z7 y las siete notas musicales con sus acordes: Un proceso de enseñanza y aprendizaje de las matemáticas en la educación básica
A classe de resíduos do anel Z7 e as sete notas musicais com seus acordes: Um processo de ensino e aprendizagem de matemática na educação básica
title The residual class of the Z7 ring and the seven musical notes with its agreements: A mathematical teaching and learning process in basic education
spellingShingle The residual class of the Z7 ring and the seven musical notes with its agreements: A mathematical teaching and learning process in basic education
Pontes, Edel Alexandre Silva
Enseñanza y aprendizaje de las matemáticas
Aritmética modular
Notas musicales.
Ensino e aprendizagem de matemática
Aritmética Modular
As notas musicais.
Teaching and learning of mathematics
Modular Arithmetic
Musical notes.
title_short The residual class of the Z7 ring and the seven musical notes with its agreements: A mathematical teaching and learning process in basic education
title_full The residual class of the Z7 ring and the seven musical notes with its agreements: A mathematical teaching and learning process in basic education
title_fullStr The residual class of the Z7 ring and the seven musical notes with its agreements: A mathematical teaching and learning process in basic education
title_full_unstemmed The residual class of the Z7 ring and the seven musical notes with its agreements: A mathematical teaching and learning process in basic education
title_sort The residual class of the Z7 ring and the seven musical notes with its agreements: A mathematical teaching and learning process in basic education
author Pontes, Edel Alexandre Silva
author_facet Pontes, Edel Alexandre Silva
Coelho, Elis Lima
Silva, Bruno Henrique Macêdo dos Santos
Moura, Helloyne Roberta Eloi
Batista, Igor Santana
author_role author
author2 Coelho, Elis Lima
Silva, Bruno Henrique Macêdo dos Santos
Moura, Helloyne Roberta Eloi
Batista, Igor Santana
author2_role author
author
author
author
dc.contributor.author.fl_str_mv Pontes, Edel Alexandre Silva
Coelho, Elis Lima
Silva, Bruno Henrique Macêdo dos Santos
Moura, Helloyne Roberta Eloi
Batista, Igor Santana
dc.subject.por.fl_str_mv Enseñanza y aprendizaje de las matemáticas
Aritmética modular
Notas musicales.
Ensino e aprendizagem de matemática
Aritmética Modular
As notas musicais.
Teaching and learning of mathematics
Modular Arithmetic
Musical notes.
topic Enseñanza y aprendizaje de las matemáticas
Aritmética modular
Notas musicales.
Ensino e aprendizagem de matemática
Aritmética Modular
As notas musicais.
Teaching and learning of mathematics
Modular Arithmetic
Musical notes.
description Number Theory is one of the areas of mathematics that has considerable applications in basic education, especially in the final years of elementary school, and in order to vigorously understand these innumerable practices, it is necessary to understand the basic concepts of Modular Arithmetic. This work aimed to present the basic concepts of Modular Arithmetic and to relate in a playful way the concept of entire modules 7 through the seven musical notes. The research recommends exposing a methodological suggestion, through the ring (Z7, +, x), in the process of teaching and learning mathematics for students in the final years of elementary school. It is evident to remember that developing methodological procedures that can strongly assist the teaching and learning of mathematics are fundamental criteria for improving the popularization process of this science, often reneged, but of extreme importance for scientific and technological evolution. It is expected that our projections for understanding mathematical models will be debated, with the aim of fully strengthening the teaching of mathematics.
publishDate 2021
dc.date.none.fl_str_mv 2021-05-21
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://rsdjournal.org/index.php/rsd/article/view/15548
10.33448/rsd-v10i6.15548
url https://rsdjournal.org/index.php/rsd/article/view/15548
identifier_str_mv 10.33448/rsd-v10i6.15548
dc.language.iso.fl_str_mv por
language por
dc.relation.none.fl_str_mv https://rsdjournal.org/index.php/rsd/article/view/15548/13861
dc.rights.driver.fl_str_mv https://creativecommons.org/licenses/by/4.0
info:eu-repo/semantics/openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/4.0
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Research, Society and Development
publisher.none.fl_str_mv Research, Society and Development
dc.source.none.fl_str_mv Research, Society and Development; Vol. 10 No. 6; e6210615548
Research, Society and Development; Vol. 10 Núm. 6; e6210615548
Research, Society and Development; v. 10 n. 6; e6210615548
2525-3409
reponame:Research, Society and Development
instname:Universidade Federal de Itajubá (UNIFEI)
instacron:UNIFEI
instname_str Universidade Federal de Itajubá (UNIFEI)
instacron_str UNIFEI
institution UNIFEI
reponame_str Research, Society and Development
collection Research, Society and Development
repository.name.fl_str_mv Research, Society and Development - Universidade Federal de Itajubá (UNIFEI)
repository.mail.fl_str_mv rsd.articles@gmail.com
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