Relacionando as funções trigonométricas com música
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Biblioteca Digital de Teses e Dissertações da UFRPE |
Texto Completo: | http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/7890 |
Resumo: | This paper presents a research proposal about one aspect, among several possible, involving the intrinsic relation of mathematical studies with music, having as support point the following analytical tripod: sound waves, musical scales and trigonometric functions. The objective of this research is to investigate the relevance of the application and the use of tools for the construction of meaning in the teaching-learning of mathematics in the classes of the referred discipline. This study is modeled after an action research, developed based on the making of mathematical workshops held in a 3rd year high school class of a school of the state public network, in the municipality of Panelas-PE. As theoretical references of the research, we use, among others, mainly the postulates of Benson (2006), Kammeler (2000), Wright (2009) and Rousseau and Saint (2015), in order to promote and also revive a discussion about The relation involving the processes and / or thematic mechanisms of interaction mentioned above. Thus, the results of the research served to demonstrate that, through the application of mathematical workshops focused on the conjunction of mathematical procedures verified here, it is possible to bring the student closer to the teachings of mathematics. It was verified, therefore, that with the teacher-mediated contact for mathematical-musical congruence in the classroom, the student can be stimulated to have a better understanding of the interactions between trigonometric functions, sound waves, musical scales and, more specifically, the Fourier Series, thus experiencing and with satisfactory perceptions of practical usufruct, the development of a better mathematical awareness. |
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SANTOS, Marcelo Pedro dosGALVÃO, Eudes NaziazenoARAÚJO, Yane Lísley RamosCLEMENTE, Rodrigo GenuinoRODRIGUES, Michelangelo dos Santos2019-03-19T14:28:40Z2017-08-24RODRIGUES, Michelangelo dos Santos. Relacionando as funções trigonométricas com música. 2017. 90 f. Dissertação (Programa de Pós-Graduação em Matemática (PROFMAT)) - Universidade Federal Rural de Pernambuco, Recife.http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/7890This paper presents a research proposal about one aspect, among several possible, involving the intrinsic relation of mathematical studies with music, having as support point the following analytical tripod: sound waves, musical scales and trigonometric functions. The objective of this research is to investigate the relevance of the application and the use of tools for the construction of meaning in the teaching-learning of mathematics in the classes of the referred discipline. This study is modeled after an action research, developed based on the making of mathematical workshops held in a 3rd year high school class of a school of the state public network, in the municipality of Panelas-PE. As theoretical references of the research, we use, among others, mainly the postulates of Benson (2006), Kammeler (2000), Wright (2009) and Rousseau and Saint (2015), in order to promote and also revive a discussion about The relation involving the processes and / or thematic mechanisms of interaction mentioned above. Thus, the results of the research served to demonstrate that, through the application of mathematical workshops focused on the conjunction of mathematical procedures verified here, it is possible to bring the student closer to the teachings of mathematics. It was verified, therefore, that with the teacher-mediated contact for mathematical-musical congruence in the classroom, the student can be stimulated to have a better understanding of the interactions between trigonometric functions, sound waves, musical scales and, more specifically, the Fourier Series, thus experiencing and with satisfactory perceptions of practical usufruct, the development of a better mathematical awareness.Este trabalho apresenta uma proposta de investigação acerca de um aspecto, dentre vários possíveis, envolvendo a intrínseca relação dos estudos matemáticos com a música, tendo como ponto de apoio o seguinte tripé analítico: ondas sonoras, escalas musicais e funções trigonométricas. A pesquisa objetiva averiguar, por meio da utilização de um conjunto de atividades sequenciais, a relevância da aplicação e do uso de ferramentas de construção de sentido no âmbito do ensino-aprendizagem da matemática nas aulas da referenciada disciplina. Tal estudo envereda-se nos moldes de uma pesquisa-ação, desenvolvida tendo como base a confecção de oficinas de matemática realizadas numa turma de 3º ano do Ensino Médio de uma escola da rede pública estadual, no município de Panelas-PE. Como referenciais teóricos da pesquisa, utilizamos, entre outros, principalmente os postulados de Benson (2006), Kammeler (2000), Wright (2009) e Rousseau e Saint (2015), no intuito de promover e, também, de reavivar uma discussão sobre a relação envolvendo os processos e/ou mecanismos temáticos de interação supracitados. Assim sendo, os resultados da pesquisa serviram para demonstrar que, por meio da aplicação das oficinas de matemática focadas na conjunção dos procedimentos matemáticos aqui verificados, faz-se possível aproximar o aluno dos ensinamentos da matemática. Ficou constatado, portanto, que, com o contato mediado pelo professor tendo em vista a congruência matemáticomusical em sala de aula, o aluno pode ser estimulado a ter uma melhor compreensão acerca das interações existentes entre funções trigonométricas, ondas sonoras, escalas musicais e, mais especificamente, a Série de Fourier, vivenciando, assim, e com satisfatórias percepções de usufruto prático, o desenvolvimento de uma melhor consciência matemática.Submitted by Mario BC (mario@bc.ufrpe.br) on 2019-03-19T14:28:40Z No. of bitstreams: 1 Michelangelo dos Santos Rodrigues.pdf: 34231948 bytes, checksum: a34237b1b7ac5fa304cfb809d73d8749 (MD5)Made available in DSpace on 2019-03-19T14:28:40Z (GMT). No. of bitstreams: 1 Michelangelo dos Santos Rodrigues.pdf: 34231948 bytes, checksum: a34237b1b7ac5fa304cfb809d73d8749 (MD5) Previous issue date: 2017-08-24application/pdfporUniversidade Federal Rural de PernambucoPrograma de Pós-Graduação em Matemática (PROFMAT)UFRPEBrasilDepartamento de MatemáticaEnsino de matemáticaFunção trigonométricaMúsicaCIENCIAS EXATAS E DA TERRA::MATEMATICARelacionando as funções trigonométricas com músicainfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesis7256355350190039125600600600-6155401143231123537-7090823417984401694info:eu-repo/semantics/openAccessreponame:Biblioteca Digital de Teses e Dissertações da UFRPEinstname:Universidade Federal Rural de Pernambuco (UFRPE)instacron:UFRPEORIGINALMichelangelo dos Santos Rodrigues.pdfMichelangelo dos Santos Rodrigues.pdfapplication/pdf34231948http://www.tede2.ufrpe.br:8080/tede2/bitstream/tede2/7890/2/Michelangelo+dos+Santos+Rodrigues.pdfa34237b1b7ac5fa304cfb809d73d8749MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-82165http://www.tede2.ufrpe.br:8080/tede2/bitstream/tede2/7890/1/license.txtbd3efa91386c1718a7f26a329fdcb468MD51tede2/78902023-07-06 09:20:44.256oai:tede2: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Biblioteca Digital de Teses e Dissertaçõeshttp://www.tede2.ufrpe.br:8080/tede/PUBhttp://www.tede2.ufrpe.br:8080/oai/requestbdtd@ufrpe.br ||bdtd@ufrpe.bropendoar:2024-05-28T12:36:15.045151Biblioteca Digital de Teses e Dissertações da UFRPE - Universidade Federal Rural de Pernambuco (UFRPE)false |
dc.title.por.fl_str_mv |
Relacionando as funções trigonométricas com música |
title |
Relacionando as funções trigonométricas com música |
spellingShingle |
Relacionando as funções trigonométricas com música RODRIGUES, Michelangelo dos Santos Ensino de matemática Função trigonométrica Música CIENCIAS EXATAS E DA TERRA::MATEMATICA |
title_short |
Relacionando as funções trigonométricas com música |
title_full |
Relacionando as funções trigonométricas com música |
title_fullStr |
Relacionando as funções trigonométricas com música |
title_full_unstemmed |
Relacionando as funções trigonométricas com música |
title_sort |
Relacionando as funções trigonométricas com música |
author |
RODRIGUES, Michelangelo dos Santos |
author_facet |
RODRIGUES, Michelangelo dos Santos |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
SANTOS, Marcelo Pedro dos |
dc.contributor.referee1.fl_str_mv |
GALVÃO, Eudes Naziazeno |
dc.contributor.referee2.fl_str_mv |
ARAÚJO, Yane Lísley Ramos |
dc.contributor.referee3.fl_str_mv |
CLEMENTE, Rodrigo Genuino |
dc.contributor.author.fl_str_mv |
RODRIGUES, Michelangelo dos Santos |
contributor_str_mv |
SANTOS, Marcelo Pedro dos GALVÃO, Eudes Naziazeno ARAÚJO, Yane Lísley Ramos CLEMENTE, Rodrigo Genuino |
dc.subject.por.fl_str_mv |
Ensino de matemática Função trigonométrica Música |
topic |
Ensino de matemática Função trigonométrica Música CIENCIAS EXATAS E DA TERRA::MATEMATICA |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::MATEMATICA |
description |
This paper presents a research proposal about one aspect, among several possible, involving the intrinsic relation of mathematical studies with music, having as support point the following analytical tripod: sound waves, musical scales and trigonometric functions. The objective of this research is to investigate the relevance of the application and the use of tools for the construction of meaning in the teaching-learning of mathematics in the classes of the referred discipline. This study is modeled after an action research, developed based on the making of mathematical workshops held in a 3rd year high school class of a school of the state public network, in the municipality of Panelas-PE. As theoretical references of the research, we use, among others, mainly the postulates of Benson (2006), Kammeler (2000), Wright (2009) and Rousseau and Saint (2015), in order to promote and also revive a discussion about The relation involving the processes and / or thematic mechanisms of interaction mentioned above. Thus, the results of the research served to demonstrate that, through the application of mathematical workshops focused on the conjunction of mathematical procedures verified here, it is possible to bring the student closer to the teachings of mathematics. It was verified, therefore, that with the teacher-mediated contact for mathematical-musical congruence in the classroom, the student can be stimulated to have a better understanding of the interactions between trigonometric functions, sound waves, musical scales and, more specifically, the Fourier Series, thus experiencing and with satisfactory perceptions of practical usufruct, the development of a better mathematical awareness. |
publishDate |
2017 |
dc.date.issued.fl_str_mv |
2017-08-24 |
dc.date.accessioned.fl_str_mv |
2019-03-19T14:28:40Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
RODRIGUES, Michelangelo dos Santos. Relacionando as funções trigonométricas com música. 2017. 90 f. Dissertação (Programa de Pós-Graduação em Matemática (PROFMAT)) - Universidade Federal Rural de Pernambuco, Recife. |
dc.identifier.uri.fl_str_mv |
http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/7890 |
identifier_str_mv |
RODRIGUES, Michelangelo dos Santos. Relacionando as funções trigonométricas com música. 2017. 90 f. Dissertação (Programa de Pós-Graduação em Matemática (PROFMAT)) - Universidade Federal Rural de Pernambuco, Recife. |
url |
http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/7890 |
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Universidade Federal Rural de Pernambuco |
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UFRPE |
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