Sólidos geométricos: uma abordagem histórica, conceitual e aplicada sobre volumes

Detalhes bibliográficos
Autor(a) principal: Santos, Robson Francisco dos
Data de Publicação: 2023
Tipo de documento: Dissertação
Idioma: por
Título da fonte: Repositório Institucional da UFS
Texto Completo: https://ri.ufs.br/jspui/handle/riufs/18490
Resumo: In this work, the concept of volume of the main geometric solids studied in high school is alluded to – the teaching modality for which it is intended. In this approach, priority was given to calculating the volume of the Prism, the Pyramid, the Cylinder, the Cone, and the Sphere, in two aspects: Cavalieri’s principle - a method very present in textbooks of the last stage of basic education and the use of the process of integration as an alternative method in the deduction of the volume formulas of the solids studied here. It is also versed on the application of the concept of volume addressed in some external evaluations–OBMEP and ENEM; in addition to portraying the historical importance of spatial geometry, its teaching and learning both in the students’ school life and in their social life. Considering that a field study was carried out showing the application of knowledge acquired in the classroom on the concept of volume, whether empirical or cognitive, and the impact of this learning on the decision-making of a citizen who aims to improve his production of inputs food products for cattle raising, without losing sight of the cost/benefit of this whole process.
id UFS-2_3c499bebcfabd06843b134678332e924
oai_identifier_str oai:ufs.br:riufs/18490
network_acronym_str UFS-2
network_name_str Repositório Institucional da UFS
repository_id_str
spelling Santos, Robson Francisco dosAraujo, Gerson Cruz2023-10-10T22:30:55Z2023-10-10T22:30:55Z2023-08-30SANTOS, Robson Francisco dos. Sólidos geométricos: uma abordagem histórica, conceitual e aplicada sobre volumes. 2023. 107 f. Dissertação (Mestrado Profissional em Matemática) - Universidade Federal de Sergipe, São Cristóvão, 2023.https://ri.ufs.br/jspui/handle/riufs/18490In this work, the concept of volume of the main geometric solids studied in high school is alluded to – the teaching modality for which it is intended. In this approach, priority was given to calculating the volume of the Prism, the Pyramid, the Cylinder, the Cone, and the Sphere, in two aspects: Cavalieri’s principle - a method very present in textbooks of the last stage of basic education and the use of the process of integration as an alternative method in the deduction of the volume formulas of the solids studied here. It is also versed on the application of the concept of volume addressed in some external evaluations–OBMEP and ENEM; in addition to portraying the historical importance of spatial geometry, its teaching and learning both in the students’ school life and in their social life. Considering that a field study was carried out showing the application of knowledge acquired in the classroom on the concept of volume, whether empirical or cognitive, and the impact of this learning on the decision-making of a citizen who aims to improve his production of inputs food products for cattle raising, without losing sight of the cost/benefit of this whole process.Neste trabalho é aludido o conceito de volume dos principais sólidos geométricos estudados no ensino médio – modalidade de ensino a qual ele se destina. Nessa abordagem, priorizou-se o cálculo de volume do Prisma, da Pirâmide, do Cilindro, do Cone e da Esfera, em duas vertentes: princípio de Cavalieri – método muito presente nos livros didáticos da última etapa da educação básica e o uso do processo de integração como método alternativo nas deduções das fórmulas de volume dos sólidos aqui estudados. Também é versado sobre a aplicação do conceito de volume abordado em algumas avaliações externas–OBMEP e ENEM; além de retratar a importância histórica da geometria espacial, seu ensino e sua aprendizagem tanto na vida escolar dos discentes quanto no seu convívio social. Haja vista que foi feito um estudo de campo mostrando a aplicação do conhecimento adquirido em sala de aula sobre o conceito de volume, seja ele empírico ou cognitivo, e o impacto desse aprendizado na tomada de decisão de um cidadão que visa melhorar sua produção de insumos alimentícios para criação de gado, sem perder de vista o custo/benefício de todo esse processo.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESSão CristóvãoporMatemáticaEnsino médioGeometria espacialSólidos geométricosVolumeAplicaçãoGeometric solidsApplicationCIENCIAS EXATAS E DA TERRA::MATEMATICASólidos geométricos: uma abordagem histórica, conceitual e aplicada sobre volumesinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisMestrado Profissional em MatemáticaUniversidade Federal de Sergipe (UFS)reponame:Repositório Institucional da UFSinstname:Universidade Federal de Sergipe (UFS)instacron:UFSinfo:eu-repo/semantics/openAccessLICENSElicense.txtlicense.txttext/plain; charset=utf-81475https://ri.ufs.br/jspui/bitstream/riufs/18490/1/license.txt098cbbf65c2c15e1fb2e49c5d306a44cMD51ORIGINALROBSON_FRANCISCO_SANTOS.pdfROBSON_FRANCISCO_SANTOS.pdfapplication/pdf10296226https://ri.ufs.br/jspui/bitstream/riufs/18490/2/ROBSON_FRANCISCO_SANTOS.pdf0d1015fffd032e750f6e777693713878MD52riufs/184902023-10-10 19:31:00.243oai:ufs.br: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Repositório InstitucionalPUBhttps://ri.ufs.br/oai/requestrepositorio@academico.ufs.bropendoar:2023-10-10T22:31Repositório Institucional da UFS - Universidade Federal de Sergipe (UFS)false
dc.title.pt_BR.fl_str_mv Sólidos geométricos: uma abordagem histórica, conceitual e aplicada sobre volumes
title Sólidos geométricos: uma abordagem histórica, conceitual e aplicada sobre volumes
spellingShingle Sólidos geométricos: uma abordagem histórica, conceitual e aplicada sobre volumes
Santos, Robson Francisco dos
Matemática
Ensino médio
Geometria espacial
Sólidos geométricos
Volume
Aplicação
Geometric solids
Application
CIENCIAS EXATAS E DA TERRA::MATEMATICA
title_short Sólidos geométricos: uma abordagem histórica, conceitual e aplicada sobre volumes
title_full Sólidos geométricos: uma abordagem histórica, conceitual e aplicada sobre volumes
title_fullStr Sólidos geométricos: uma abordagem histórica, conceitual e aplicada sobre volumes
title_full_unstemmed Sólidos geométricos: uma abordagem histórica, conceitual e aplicada sobre volumes
title_sort Sólidos geométricos: uma abordagem histórica, conceitual e aplicada sobre volumes
author Santos, Robson Francisco dos
author_facet Santos, Robson Francisco dos
author_role author
dc.contributor.author.fl_str_mv Santos, Robson Francisco dos
dc.contributor.advisor1.fl_str_mv Araujo, Gerson Cruz
contributor_str_mv Araujo, Gerson Cruz
dc.subject.por.fl_str_mv Matemática
Ensino médio
Geometria espacial
Sólidos geométricos
Volume
Aplicação
topic Matemática
Ensino médio
Geometria espacial
Sólidos geométricos
Volume
Aplicação
Geometric solids
Application
CIENCIAS EXATAS E DA TERRA::MATEMATICA
dc.subject.eng.fl_str_mv Geometric solids
Application
dc.subject.cnpq.fl_str_mv CIENCIAS EXATAS E DA TERRA::MATEMATICA
description In this work, the concept of volume of the main geometric solids studied in high school is alluded to – the teaching modality for which it is intended. In this approach, priority was given to calculating the volume of the Prism, the Pyramid, the Cylinder, the Cone, and the Sphere, in two aspects: Cavalieri’s principle - a method very present in textbooks of the last stage of basic education and the use of the process of integration as an alternative method in the deduction of the volume formulas of the solids studied here. It is also versed on the application of the concept of volume addressed in some external evaluations–OBMEP and ENEM; in addition to portraying the historical importance of spatial geometry, its teaching and learning both in the students’ school life and in their social life. Considering that a field study was carried out showing the application of knowledge acquired in the classroom on the concept of volume, whether empirical or cognitive, and the impact of this learning on the decision-making of a citizen who aims to improve his production of inputs food products for cattle raising, without losing sight of the cost/benefit of this whole process.
publishDate 2023
dc.date.accessioned.fl_str_mv 2023-10-10T22:30:55Z
dc.date.available.fl_str_mv 2023-10-10T22:30:55Z
dc.date.issued.fl_str_mv 2023-08-30
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 SANTOS, Robson Francisco dos. Sólidos geométricos: uma abordagem histórica, conceitual e aplicada sobre volumes. 2023. 107 f. Dissertação (Mestrado Profissional em Matemática) - Universidade Federal de Sergipe, São Cristóvão, 2023.
dc.identifier.uri.fl_str_mv https://ri.ufs.br/jspui/handle/riufs/18490
identifier_str_mv SANTOS, Robson Francisco dos. Sólidos geométricos: uma abordagem histórica, conceitual e aplicada sobre volumes. 2023. 107 f. Dissertação (Mestrado Profissional em Matemática) - Universidade Federal de Sergipe, São Cristóvão, 2023.
url https://ri.ufs.br/jspui/handle/riufs/18490
dc.language.iso.fl_str_mv por
language por
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.program.fl_str_mv Mestrado Profissional em Matemática
dc.publisher.initials.fl_str_mv Universidade Federal de Sergipe (UFS)
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFS
instname:Universidade Federal de Sergipe (UFS)
instacron:UFS
instname_str Universidade Federal de Sergipe (UFS)
instacron_str UFS
institution UFS
reponame_str Repositório Institucional da UFS
collection Repositório Institucional da UFS
bitstream.url.fl_str_mv https://ri.ufs.br/jspui/bitstream/riufs/18490/1/license.txt
https://ri.ufs.br/jspui/bitstream/riufs/18490/2/ROBSON_FRANCISCO_SANTOS.pdf
bitstream.checksum.fl_str_mv 098cbbf65c2c15e1fb2e49c5d306a44c
0d1015fffd032e750f6e777693713878
bitstream.checksumAlgorithm.fl_str_mv MD5
MD5
repository.name.fl_str_mv Repositório Institucional da UFS - Universidade Federal de Sergipe (UFS)
repository.mail.fl_str_mv repositorio@academico.ufs.br
_version_ 1802110643892912128