Colora??o em grafos: uma experi?ncia no Ensino Fundamental
Autor(a) principal: | |
---|---|
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 |