Colora??o em grafos: uma experi?ncia no Ensino Fundamental

Detalhes bibliográficos
Autor(a) principal: Costa, F?bio da Rocha
Data de Publicação: 2017
Tipo de documento: Dissertação
Idioma: por
Título da fonte: Biblioteca Digital de Teses e Dissertações da UFRRJ
Texto Completo: https://tede.ufrrj.br/jspui/handle/jspui/2570
Resumo: The main goal of this work is to analyze, within a Case Study, an experiment with Graph Coloring problems that involves 40 students of the 9th grade of Elementary School from the Educand?rio Monteiro Lobato, in Campo Grande/RJ. To carry out the experiment we did 8 lessons of 50 minutes. In the first classes, a motivational questionnaire (adapted from Questionnaire of Gontijo) and a test involving questions of logical reasoning (Test 1) was applied, which students can solve with the regular curriculum. Such questions are solved easily with techniques from Graph Coloring, but at this stage the students obviously still do not know them. After the tests, some classes were dedicated to teaching basic concepts of graphs and simple coloring techniques. In the final classes was applied Test 2 (in the form of Test 1), where students can already choose to use techniques of Coloring to solve the questions, and then a Final Questionnaire, to evaluate what they found in the classes. After the study, results showed a significant improvement in the development of the activities that use the idea of Graph Theory - Coloring, by the students. Their participation and motivation was one of the positive aspects of this research, as well as the different solutions found to solve the activities proposed during the study.
id UFRRJ-1_68d03cb15e79d1e8b2a55df37f6fe335
oai_identifier_str oai:localhost:jspui/2570
network_acronym_str UFRRJ-1
network_name_str Biblioteca Digital de Teses e Dissertações da UFRRJ
repository_id_str
spelling Oliveira J?nior, Montauban Moreira de053.670.767-77Oliveira J?nior, Montauban Moreira dePereira, Andr? Luiz MartinsMattos, Jos? Roberto Linhares de099.935.267-97http://lattes.cnpq.br/1896979181547566Costa, F?bio da Rocha2019-01-09T15:16:54Z2017-05-29COSTA, F?bio da Rocha. Colora??o em grafos: uma experi?ncia no Ensino Fundamental. 2017.129 f. Disserta??o (Mestrado Profissional em Matem?tica em Rede Nacional - PROFMAT) - Instituto de Ci?ncias Exatas, Departamento de Matem?tica, Universidade Federal Rural do Rio de Janeiro, Serop?dica - RJ, 2017.https://tede.ufrrj.br/jspui/handle/jspui/2570The main goal of this work is to analyze, within a Case Study, an experiment with Graph Coloring problems that involves 40 students of the 9th grade of Elementary School from the Educand?rio Monteiro Lobato, in Campo Grande/RJ. To carry out the experiment we did 8 lessons of 50 minutes. In the first classes, a motivational questionnaire (adapted from Questionnaire of Gontijo) and a test involving questions of logical reasoning (Test 1) was applied, which students can solve with the regular curriculum. Such questions are solved easily with techniques from Graph Coloring, but at this stage the students obviously still do not know them. After the tests, some classes were dedicated to teaching basic concepts of graphs and simple coloring techniques. In the final classes was applied Test 2 (in the form of Test 1), where students can already choose to use techniques of Coloring to solve the questions, and then a Final Questionnaire, to evaluate what they found in the classes. After the study, results showed a significant improvement in the development of the activities that use the idea of Graph Theory - Coloring, by the students. Their participation and motivation was one of the positive aspects of this research, as well as the different solutions found to solve the activities proposed during the study.O principal objetivo deste trabalho ? analisar, atrav?s de um estudo de caso, uma experi?ncia com problemas de Colora??o de V?rtices em Grafos envolvendo 40 alunos do 9? ano do Ensino Fundamental do Educand?rio Monteiro Lobato, em Campo Grande/RJ, da rede particular de ensino. Para realizar a experi?ncia foram utilizadas 8 aulas de Matem?tica (Teoria dos Grafos ? Colora??o) de 50 minutos. Nas primeiras aulas foram aplicados um question?rio motivacional inicial (adaptado do Question?rio adaptado de Gontijo) e um teste envolvendo quest?es de racioc?nio l?gico (Teste 1), que os alunos conseguem resolver com base no curr?culo regular. Tais quest?es s?o resolvidas atrav?s de t?cnicas de Colora??o em Grafos, mas os alunos obviamente ainda n?o as conhecem nesta etapa. Ap?s os testes, algumas aulas foram dedicadas ao ensino de conceitos b?sicos de Grafos e t?cnicas simples de resolu??o de problemas por Colora??o. Nas aulas finais foram aplicados o Teste 2 (nos moldes do Teste 1), onde os alunos j? podem optar por usar t?cnicas de Colora??o para resolver as quest?es, e em seguida um Question?rio Final, para avaliar o que eles acharam das aulas. Com o estudo elaborado e aplicado, foram alcan?ados resultados que mostraram uma melhora significativa no desenvolvimento das atividades que se utilizam da ideia de Teoria dos Grafos ? Colora??o, por parte dos alunos. A participa??o e a motiva??o deles foi um dos pontos positivos desta pesquisa, bem como as diversas solu??es encontradas para resolver as atividades propostas durante o estudo.Submitted by Jorge Silva (jorgelmsilva@ufrrj.br) on 2019-01-09T15:16:54Z No. of bitstreams: 1 2017 - F?bio da Rocha Costa.pdf: 3990732 bytes, checksum: 8834cfe0018989e8b34965b2af740f5c (MD5)Made available in DSpace on 2019-01-09T15:16:54Z (GMT). No. of bitstreams: 1 2017 - F?bio da Rocha Costa.pdf: 3990732 bytes, checksum: 8834cfe0018989e8b34965b2af740f5c (MD5) Previous issue date: 2017-05-29CNPqapplication/pdfhttps://tede.ufrrj.br/retrieve/9194/2017%20-%20F%c3%a1bio%20da%20Rocha%20Costa.pdf.jpghttps://tede.ufrrj.br/retrieve/15744/2017%20-%20F%c3%a1bio%20da%20Rocha%20Costa.pdf.jpghttps://tede.ufrrj.br/retrieve/22056/2017%20-%20F%c3%a1bio%20da%20Rocha%20Costa.pdf.jpghttps://tede.ufrrj.br/retrieve/28440/2017%20-%20F%c3%a1bio%20da%20Rocha%20Costa.pdf.jpghttps://tede.ufrrj.br/retrieve/34854/2017%20-%20F%c3%a1bio%20da%20Rocha%20Costa.pdf.jpghttps://tede.ufrrj.br/retrieve/41250/2017%20-%20F%c3%a1bio%20da%20Rocha%20Costa.pdf.jpghttps://tede.ufrrj.br/retrieve/47652/2017%20-%20F%c3%a1bio%20da%20Rocha%20Costa.pdf.jpghttps://tede.ufrrj.br/retrieve/54088/2017%20-%20F%c3%a1bio%20da%20Rocha%20Costa.pdf.jpgporUniversidade Federal Rural do Rio de JaneiroPrograma de P?s-Gradua??o em Matem?tica em Rede NacionalUFRRJBrasilInstituto de Ci?ncias ExatasColora??o em grafosEnsino fundamentalMatem?ticaGraph coloringElementary schoolMathematicsMatem?ticaColora??o em grafos: uma experi?ncia no Ensino FundamentalGraph coloring: an experience in Elementary Schoolinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/openAccessreponame:Biblioteca Digital de Teses e Dissertações da UFRRJinstname:Universidade Federal Rural do Rio de Janeiro (UFRRJ)instacron:UFRRJTHUMBNAIL2017 - F?bio da Rocha Costa.pdf.jpg2017 - F?bio da Rocha Costa.pdf.jpgimage/jpeg1959http://localhost:8080/tede/bitstream/jspui/2570/18/2017+-+F%C3%A1bio+da+Rocha+Costa.pdf.jpgd9ed6fb6f64deb0fe39ffba9dabdede2MD518TEXT2017 - F?bio da Rocha Costa.pdf.txt2017 - F?bio da Rocha Costa.pdf.txttext/plain137049http://localhost:8080/tede/bitstream/jspui/2570/17/2017+-+F%C3%A1bio+da+Rocha+Costa.pdf.txtface56d875464083f549d7bfb03dc554MD517ORIGINAL2017 - F?bio da Rocha Costa.pdf2017 - F?bio da Rocha Costa.pdfapplication/pdf3990732http://localhost:8080/tede/bitstream/jspui/2570/2/2017+-+F%C3%A1bio+da+Rocha+Costa.pdf8834cfe0018989e8b34965b2af740f5cMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-82089http://localhost:8080/tede/bitstream/jspui/2570/1/license.txt7b5ba3d2445355f386edab96125d42b7MD51jspui/25702021-05-27 14:28:38.947oai:localhost: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Biblioteca Digital de Teses e Dissertaçõeshttps://tede.ufrrj.br/PUBhttps://tede.ufrrj.br/oai/requestbibliot@ufrrj.br||bibliot@ufrrj.bropendoar:2021-05-27T17:28:38Biblioteca Digital de Teses e Dissertações da UFRRJ - Universidade Federal Rural do Rio de Janeiro (UFRRJ)false
dc.title.por.fl_str_mv Colora??o em grafos: uma experi?ncia no Ensino Fundamental
dc.title.alternative.eng.fl_str_mv Graph coloring: an experience in Elementary School
title Colora??o em grafos: uma experi?ncia no Ensino Fundamental
spellingShingle Colora??o em grafos: uma experi?ncia no Ensino Fundamental
Costa, F?bio da Rocha
Colora??o em grafos
Ensino fundamental
Matem?tica
Graph coloring
Elementary school
Mathematics
Matem?tica
title_short Colora??o em grafos: uma experi?ncia no Ensino Fundamental
title_full Colora??o em grafos: uma experi?ncia no Ensino Fundamental
title_fullStr Colora??o em grafos: uma experi?ncia no Ensino Fundamental
title_full_unstemmed Colora??o em grafos: uma experi?ncia no Ensino Fundamental
title_sort Colora??o em grafos: uma experi?ncia no Ensino Fundamental
author Costa, F?bio da Rocha
author_facet Costa, F?bio da Rocha
author_role author
dc.contributor.advisor1.fl_str_mv Oliveira J?nior, Montauban Moreira de
dc.contributor.advisor1ID.fl_str_mv 053.670.767-77
dc.contributor.referee1.fl_str_mv Oliveira J?nior, Montauban Moreira de
dc.contributor.referee2.fl_str_mv Pereira, Andr? Luiz Martins
dc.contributor.referee3.fl_str_mv Mattos, Jos? Roberto Linhares de
dc.contributor.authorID.fl_str_mv 099.935.267-97
dc.contributor.authorLattes.fl_str_mv http://lattes.cnpq.br/1896979181547566
dc.contributor.author.fl_str_mv Costa, F?bio da Rocha
contributor_str_mv Oliveira J?nior, Montauban Moreira de
Oliveira J?nior, Montauban Moreira de
Pereira, Andr? Luiz Martins
Mattos, Jos? Roberto Linhares de
dc.subject.por.fl_str_mv Colora??o em grafos
Ensino fundamental
Matem?tica
topic Colora??o em grafos
Ensino fundamental
Matem?tica
Graph coloring
Elementary school
Mathematics
Matem?tica
dc.subject.eng.fl_str_mv Graph coloring
Elementary school
Mathematics
dc.subject.cnpq.fl_str_mv Matem?tica
description The main goal of this work is to analyze, within a Case Study, an experiment with Graph Coloring problems that involves 40 students of the 9th grade of Elementary School from the Educand?rio Monteiro Lobato, in Campo Grande/RJ. To carry out the experiment we did 8 lessons of 50 minutes. In the first classes, a motivational questionnaire (adapted from Questionnaire of Gontijo) and a test involving questions of logical reasoning (Test 1) was applied, which students can solve with the regular curriculum. Such questions are solved easily with techniques from Graph Coloring, but at this stage the students obviously still do not know them. After the tests, some classes were dedicated to teaching basic concepts of graphs and simple coloring techniques. In the final classes was applied Test 2 (in the form of Test 1), where students can already choose to use techniques of Coloring to solve the questions, and then a Final Questionnaire, to evaluate what they found in the classes. After the study, results showed a significant improvement in the development of the activities that use the idea of Graph Theory - Coloring, by the students. Their participation and motivation was one of the positive aspects of this research, as well as the different solutions found to solve the activities proposed during the study.
publishDate 2017
dc.date.issued.fl_str_mv 2017-05-29
dc.date.accessioned.fl_str_mv 2019-01-09T15:16:54Z
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 COSTA, F?bio da Rocha. Colora??o em grafos: uma experi?ncia no Ensino Fundamental. 2017.129 f. Disserta??o (Mestrado Profissional em Matem?tica em Rede Nacional - PROFMAT) - Instituto de Ci?ncias Exatas, Departamento de Matem?tica, Universidade Federal Rural do Rio de Janeiro, Serop?dica - RJ, 2017.
dc.identifier.uri.fl_str_mv https://tede.ufrrj.br/jspui/handle/jspui/2570
identifier_str_mv COSTA, F?bio da Rocha. Colora??o em grafos: uma experi?ncia no Ensino Fundamental. 2017.129 f. Disserta??o (Mestrado Profissional em Matem?tica em Rede Nacional - PROFMAT) - Instituto de Ci?ncias Exatas, Departamento de Matem?tica, Universidade Federal Rural do Rio de Janeiro, Serop?dica - RJ, 2017.
url https://tede.ufrrj.br/jspui/handle/jspui/2570
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.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universidade Federal Rural do Rio de Janeiro
dc.publisher.program.fl_str_mv Programa de P?s-Gradua??o em Matem?tica em Rede Nacional
dc.publisher.initials.fl_str_mv UFRRJ
dc.publisher.country.fl_str_mv Brasil
dc.publisher.department.fl_str_mv Instituto de Ci?ncias Exatas
publisher.none.fl_str_mv Universidade Federal Rural do Rio de Janeiro
dc.source.none.fl_str_mv reponame:Biblioteca Digital de Teses e Dissertações da UFRRJ
instname:Universidade Federal Rural do Rio de Janeiro (UFRRJ)
instacron:UFRRJ
instname_str Universidade Federal Rural do Rio de Janeiro (UFRRJ)
instacron_str UFRRJ
institution UFRRJ
reponame_str Biblioteca Digital de Teses e Dissertações da UFRRJ
collection Biblioteca Digital de Teses e Dissertações da UFRRJ
bitstream.url.fl_str_mv http://localhost:8080/tede/bitstream/jspui/2570/18/2017+-+F%C3%A1bio+da+Rocha+Costa.pdf.jpg
http://localhost:8080/tede/bitstream/jspui/2570/17/2017+-+F%C3%A1bio+da+Rocha+Costa.pdf.txt
http://localhost:8080/tede/bitstream/jspui/2570/2/2017+-+F%C3%A1bio+da+Rocha+Costa.pdf
http://localhost:8080/tede/bitstream/jspui/2570/1/license.txt
bitstream.checksum.fl_str_mv d9ed6fb6f64deb0fe39ffba9dabdede2
face56d875464083f549d7bfb03dc554
8834cfe0018989e8b34965b2af740f5c
7b5ba3d2445355f386edab96125d42b7
bitstream.checksumAlgorithm.fl_str_mv MD5
MD5
MD5
MD5
repository.name.fl_str_mv Biblioteca Digital de Teses e Dissertações da UFRRJ - Universidade Federal Rural do Rio de Janeiro (UFRRJ)
repository.mail.fl_str_mv bibliot@ufrrj.br||bibliot@ufrrj.br
_version_ 1800313485406502912