Reta de Euler, circunferência dos nove pontos, sólidos platônicos e arquimedianos: aspectos teóricos, suas construções em GeoGebra e aplicações no ensino
Autor(a) principal: | |
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Data de Publicação: | 2019 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFG |
Texto Completo: | http://repositorio.bc.ufg.br/tede/handle/tede/10308 |
Resumo: | This study has as main theme the use of digital technologies to teach geometry. The objective is to show how a classroom approach can be favorable to the teaching of this discipline and for that reason the geometric constructions in the Geogebra program have been taken as object of study. Initially it was proposed a theoretical survey that would support the study, guiding the way in which the work would develop. After a brief presentation of the program Geogebra, was developed the construction of some geometric figures, detailing its main characteristics and results, also showing a guide for its construction in the program. The proposed figures were the notable points of a triangle (barycentre, orthocenter, incenter and circumcenter), Euler’s straight line, the nine-point circle, the platonic solids (tetrahedron, hexahedron or cube, octahedron, dodecahedron and icosahedron), and the archimedean solids (truncated tetrahedron, truncated dodecahedron, truncated icosahedron, snub cube, cuboctahedron, dodecahedron snub, icosidodecahedron, rombicuboctahedron, great rombicuboctahedron, rhombicosidodecahedron and large rhombicosidodecahedron). These constructions served for the final step of this work which was an experiment of teaching involving students of the 8th and 9th year of the private school system. The experiment consisted of three stages, the first being done in the classroom using paper, rubber, ruler, compass and protractor, the second using the program and the third comparing the previous two steps. During the experiment, the geometric construction and the teaching possibilities were emphasized and one of the main results obtained indicated that Geogebra was well accepted and that all the students expect to work with it again, because it makes the geometry more accessible until for those who say they have no affinity with this discipline. Another result observed is how to use this didactic resource in the classroom, since it was well accepted and showed positive results in teaching. |
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Lima, Thaynara Arielly dehttp://lattes.cnpq.br/3324489027928883Lima, Thaynara Arielly deVargas, Tiago MoreiraVasconcelos, José Eder Salvador dehttp://lattes.cnpq.br/2993359755750872Stival, Erick Gomes Pires2020-01-21T11:42:43Z2019-12-09STIVAL, E. G. P. Reta de Euler, circunferência dos nove pontos, sólidos platônicos e arquimedianos: aspectos teóricos, suas construções em GeoGebra e aplicações no ensino. 2019. 105 f. Dissertação (Mestrado em Matemática em Rede Nacional) - Universidade Federal de Goiás, Goiânia, 2019.http://repositorio.bc.ufg.br/tede/handle/tede/10308ark:/38995/0013000009p8pThis study has as main theme the use of digital technologies to teach geometry. The objective is to show how a classroom approach can be favorable to the teaching of this discipline and for that reason the geometric constructions in the Geogebra program have been taken as object of study. Initially it was proposed a theoretical survey that would support the study, guiding the way in which the work would develop. After a brief presentation of the program Geogebra, was developed the construction of some geometric figures, detailing its main characteristics and results, also showing a guide for its construction in the program. The proposed figures were the notable points of a triangle (barycentre, orthocenter, incenter and circumcenter), Euler’s straight line, the nine-point circle, the platonic solids (tetrahedron, hexahedron or cube, octahedron, dodecahedron and icosahedron), and the archimedean solids (truncated tetrahedron, truncated dodecahedron, truncated icosahedron, snub cube, cuboctahedron, dodecahedron snub, icosidodecahedron, rombicuboctahedron, great rombicuboctahedron, rhombicosidodecahedron and large rhombicosidodecahedron). These constructions served for the final step of this work which was an experiment of teaching involving students of the 8th and 9th year of the private school system. The experiment consisted of three stages, the first being done in the classroom using paper, rubber, ruler, compass and protractor, the second using the program and the third comparing the previous two steps. During the experiment, the geometric construction and the teaching possibilities were emphasized and one of the main results obtained indicated that Geogebra was well accepted and that all the students expect to work with it again, because it makes the geometry more accessible until for those who say they have no affinity with this discipline. Another result observed is how to use this didactic resource in the classroom, since it was well accepted and showed positive results in teaching.Este trabalho tem como principal temática o uso de tecnologias digitais para se ensinar geometria. O objetivo é mostrar como uma abordagem em sala de aula pode ser favorável ao ensino dessa disciplina e para tanto foi-se tomado por objeto de estudo as construções geométricas no programa Geogebra. Inicialmente foi proposto um levantamento teórico que embasasse o estudo, guiando a forma de como o trabalho se desenvolveria. Após uma breve apresentação do programa Geogebra foi desenvolvido a construção de algumas figuras geométricas, detalhando suas principais características e resultados, mostrando também um guia para sua construção no programa. As figuras propostas foram os pontos notáveis de um triângulo (baricentro, ortocentro, incentro e circuncentro), a reta de Euler, o círculo de nove pontos, os sólidos platônicos (tetraedro, hexaedro ou cubo, octaedro, dodecaedro e icosaedro), e os sólidos arquimedianos (tetraedro truncado, cubo truncado, octaedro truncado, dodecaedro truncado, icosaedro truncado, cubo snub, cuboctaedro, dodecaedro snub, icosidodecaedro, rombicuboctaedro, gran rombicuboctaedro, rombicosidodecaedro e gran rombicosidodecaedro). Essas construções serviram para o passo final deste trabalho que foi um experimento de ensino envolvendo estudantes do 8o e 9o ano da rede privada de ensino. O experimento consistiu em três etapas, sendo a primeira feita em sala de aula utilizando papel, borracha, régua, compasso e transferidor, a segunda utilizando o programa e a terceira comparando-se as duas etapas anteriores. Durante o experimento foi-se bastante enfatizado a construção geométrica e as possibilidades de ensino e assim um dos principais resultados obtidos apontou que o Geogebra foi bem aceito e que todos os alunos esperam trabalhar com ele novamente, pois o mesmo torna a geometria mais acessível até para aqueles que dizem não ter afinidade com esta disciplina. Outro resultado observado é sobre a forma de utilização desse recurso didático em sala de aula, visto que foi bem aceito e mostrou resultados positivos no ensino.Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2020-01-20T15:35:19Z No. of bitstreams: 2 Dissertação - Erick Gomes Pires Stival - 2019.pdf: 6716104 bytes, checksum: 05906d5f9dfde3f3a24c4d21c8269360 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2020-01-21T11:42:43Z (GMT) No. of bitstreams: 2 Dissertação - Erick Gomes Pires Stival - 2019.pdf: 6716104 bytes, checksum: 05906d5f9dfde3f3a24c4d21c8269360 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)Made available in DSpace on 2020-01-21T11:42:43Z (GMT). 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dc.title.eng.fl_str_mv |
Reta de Euler, circunferência dos nove pontos, sólidos platônicos e arquimedianos: aspectos teóricos, suas construções em GeoGebra e aplicações no ensino |
dc.title.alternative.eng.fl_str_mv |
Euler's line, nine point circumference, platonic and archimedean solids: theoretical aspects, their GeoGebra constructions, and teaching applications |
title |
Reta de Euler, circunferência dos nove pontos, sólidos platônicos e arquimedianos: aspectos teóricos, suas construções em GeoGebra e aplicações no ensino |
spellingShingle |
Reta de Euler, circunferência dos nove pontos, sólidos platônicos e arquimedianos: aspectos teóricos, suas construções em GeoGebra e aplicações no ensino Stival, Erick Gomes Pires Geometria Construção geométrica Software educacional Matemática Educação Geometry Geometric construction Educational software Mathematics Education CIENCIAS EXATAS E DA TERRA::MATEMATICA |
title_short |
Reta de Euler, circunferência dos nove pontos, sólidos platônicos e arquimedianos: aspectos teóricos, suas construções em GeoGebra e aplicações no ensino |
title_full |
Reta de Euler, circunferência dos nove pontos, sólidos platônicos e arquimedianos: aspectos teóricos, suas construções em GeoGebra e aplicações no ensino |
title_fullStr |
Reta de Euler, circunferência dos nove pontos, sólidos platônicos e arquimedianos: aspectos teóricos, suas construções em GeoGebra e aplicações no ensino |
title_full_unstemmed |
Reta de Euler, circunferência dos nove pontos, sólidos platônicos e arquimedianos: aspectos teóricos, suas construções em GeoGebra e aplicações no ensino |
title_sort |
Reta de Euler, circunferência dos nove pontos, sólidos platônicos e arquimedianos: aspectos teóricos, suas construções em GeoGebra e aplicações no ensino |
author |
Stival, Erick Gomes Pires |
author_facet |
Stival, Erick Gomes Pires |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Lima, Thaynara Arielly de |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/3324489027928883 |
dc.contributor.referee1.fl_str_mv |
Lima, Thaynara Arielly de |
dc.contributor.referee2.fl_str_mv |
Vargas, Tiago Moreira |
dc.contributor.referee3.fl_str_mv |
Vasconcelos, José Eder Salvador de |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/2993359755750872 |
dc.contributor.author.fl_str_mv |
Stival, Erick Gomes Pires |
contributor_str_mv |
Lima, Thaynara Arielly de Lima, Thaynara Arielly de Vargas, Tiago Moreira Vasconcelos, José Eder Salvador de |
dc.subject.por.fl_str_mv |
Geometria Construção geométrica Software educacional Matemática Educação |
topic |
Geometria Construção geométrica Software educacional Matemática Educação Geometry Geometric construction Educational software Mathematics Education CIENCIAS EXATAS E DA TERRA::MATEMATICA |
dc.subject.eng.fl_str_mv |
Geometry Geometric construction Educational software Mathematics Education |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::MATEMATICA |
description |
This study has as main theme the use of digital technologies to teach geometry. The objective is to show how a classroom approach can be favorable to the teaching of this discipline and for that reason the geometric constructions in the Geogebra program have been taken as object of study. Initially it was proposed a theoretical survey that would support the study, guiding the way in which the work would develop. After a brief presentation of the program Geogebra, was developed the construction of some geometric figures, detailing its main characteristics and results, also showing a guide for its construction in the program. The proposed figures were the notable points of a triangle (barycentre, orthocenter, incenter and circumcenter), Euler’s straight line, the nine-point circle, the platonic solids (tetrahedron, hexahedron or cube, octahedron, dodecahedron and icosahedron), and the archimedean solids (truncated tetrahedron, truncated dodecahedron, truncated icosahedron, snub cube, cuboctahedron, dodecahedron snub, icosidodecahedron, rombicuboctahedron, great rombicuboctahedron, rhombicosidodecahedron and large rhombicosidodecahedron). These constructions served for the final step of this work which was an experiment of teaching involving students of the 8th and 9th year of the private school system. The experiment consisted of three stages, the first being done in the classroom using paper, rubber, ruler, compass and protractor, the second using the program and the third comparing the previous two steps. During the experiment, the geometric construction and the teaching possibilities were emphasized and one of the main results obtained indicated that Geogebra was well accepted and that all the students expect to work with it again, because it makes the geometry more accessible until for those who say they have no affinity with this discipline. Another result observed is how to use this didactic resource in the classroom, since it was well accepted and showed positive results in teaching. |
publishDate |
2019 |
dc.date.issued.fl_str_mv |
2019-12-09 |
dc.date.accessioned.fl_str_mv |
2020-01-21T11:42:43Z |
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 |
STIVAL, E. G. P. Reta de Euler, circunferência dos nove pontos, sólidos platônicos e arquimedianos: aspectos teóricos, suas construções em GeoGebra e aplicações no ensino. 2019. 105 f. Dissertação (Mestrado em Matemática em Rede Nacional) - Universidade Federal de Goiás, Goiânia, 2019. |
dc.identifier.uri.fl_str_mv |
http://repositorio.bc.ufg.br/tede/handle/tede/10308 |
dc.identifier.dark.fl_str_mv |
ark:/38995/0013000009p8p |
identifier_str_mv |
STIVAL, E. G. P. Reta de Euler, circunferência dos nove pontos, sólidos platônicos e arquimedianos: aspectos teóricos, suas construções em GeoGebra e aplicações no ensino. 2019. 105 f. Dissertação (Mestrado em Matemática em Rede Nacional) - Universidade Federal de Goiás, Goiânia, 2019. ark:/38995/0013000009p8p |
url |
http://repositorio.bc.ufg.br/tede/handle/tede/10308 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.program.fl_str_mv |
4280721485626151024 |
dc.relation.confidence.fl_str_mv |
600 600 600 |
dc.relation.department.fl_str_mv |
-4268777512335152015 |
dc.relation.cnpq.fl_str_mv |
-7090823417984401694 |
dc.rights.driver.fl_str_mv |
http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess |
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http://creativecommons.org/licenses/by-nc-nd/4.0/ |
eu_rights_str_mv |
openAccess |
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dc.publisher.none.fl_str_mv |
Universidade Federal de Goiás |
dc.publisher.program.fl_str_mv |
PROFMAT - Programa de Pós-graduação em Matemática em Rede Nacional - Sociedade Brasileira de Matemática (IME) |
dc.publisher.initials.fl_str_mv |
UFG |
dc.publisher.country.fl_str_mv |
Brasil |
dc.publisher.department.fl_str_mv |
Instituto de Matemática e Estatística - IME (RG) |
publisher.none.fl_str_mv |
Universidade Federal de Goiás |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional da UFG instname:Universidade Federal de Goiás (UFG) instacron:UFG |
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UFG |
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Repositório Institucional da UFG |
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bitstream.checksum.fl_str_mv |
bd3efa91386c1718a7f26a329fdcb468 4afdbb8c545fd630ea7db775da747b2f d41d8cd98f00b204e9800998ecf8427e d41d8cd98f00b204e9800998ecf8427e 05906d5f9dfde3f3a24c4d21c8269360 |
bitstream.checksumAlgorithm.fl_str_mv |
MD5 MD5 MD5 MD5 MD5 |
repository.name.fl_str_mv |
Repositório Institucional da UFG - Universidade Federal de Goiás (UFG) |
repository.mail.fl_str_mv |
tasesdissertacoes.bc@ufg.br |
_version_ |
1811721471576244224 |