O Teorema do Casamento de Hall e aplicações no ensino básico

Detalhes bibliográficos
Ano de defesa: 2025
Autor(a) principal: Santana, Andréa de Melo Narciso
Orientador(a): Dória, André Vinicius Santos
Banca de defesa: Não Informado pela instituição
Tipo de documento: Dissertação
Tipo de acesso: Acesso aberto
Idioma: por
Instituição de defesa: Não Informado pela instituição
Programa de Pós-Graduação: Mestrado Profissional em Matemática
Departamento: Não Informado pela instituição
País: Não Informado pela instituição
Palavras-chave em Português:
Teoria dos grafos
Análise combinatória
Ensino médio
Teorema de Hall
Casamento
Combinatória
Palavras-chave em Inglês:
Hall’s theorem
Marriage
Combinatorics
High school
Área do conhecimento CNPq:
CIENCIAS EXATAS E DA TERRA::MATEMATICA
Link de acesso: https://ri.ufs.br/jspui/handle/riufs/22924
Resumo: The purpose of this dissertation is to present Hall’s Marriage Theorem, its variations and methodologies, aiming to combine theory and practice, stimulating students’ logical reasoning, critical thinking and creativity. In addition to the classic version of the theorem, two other reformulations were developed and related, distinguishing themselves from the usual theoretical framework. In order to contribute to the construction of a more inclusive, efficient, and motivating education, practical activities were proposed, and part of them was applied to second-year high school students. The practice, structured in three stages, allowed to observe the students’ progress in facing mathematical challenges. Despite the difficulties, the students’ engagement was remarkable, driven by the investigative approach and by the contextualization of Hall’s Marriage Theorem in practical and real situations.
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spelling Santana, Andréa de Melo NarcisoDória, André Vinicius Santos2025-08-15T20:01:39Z2025-08-15T20:01:39Z2025-07-22SANTANA, Andréa de Melo Narciso. O Teorema do Casamento de Hall e aplicações no ensino básico. 2025. 40 f. Dissertação (Mestrado Profissional em Matemática) — Universidade Federal de Sergipe, São Cristóvão, 2025.https://ri.ufs.br/jspui/handle/riufs/22924The purpose of this dissertation is to present Hall’s Marriage Theorem, its variations and methodologies, aiming to combine theory and practice, stimulating students’ logical reasoning, critical thinking and creativity. In addition to the classic version of the theorem, two other reformulations were developed and related, distinguishing themselves from the usual theoretical framework. In order to contribute to the construction of a more inclusive, efficient, and motivating education, practical activities were proposed, and part of them was applied to second-year high school students. The practice, structured in three stages, allowed to observe the students’ progress in facing mathematical challenges. Despite the difficulties, the students’ engagement was remarkable, driven by the investigative approach and by the contextualization of Hall’s Marriage Theorem in practical and real situations.O objetivo desta disserta¸c˜ao ´e apresentar o Teorema do Casamento de Hall, suas varia¸c˜oes e metodologias, buscando combinar teoria e pr´atica, estimulando o racioc´ınio l´ogico, o pensamento cr´ıtico e a criatividade dos alunos. Em complemento `a vers˜ao cl´assica do teorema, duas outras reformula¸c˜oes foram desenvolvidas e relacionadas, distinguindo-se do referencial te´orico usual. Com o intuito de contribuir na constru¸c˜ao de um ensino mais inclusivo, eficiente e motivador, atividades pr´aticas foram propostas e parte delas foi aplicada em alunos do segundo ano do ensino m´edio. A pr´atica, estruturada em trˆes etapas, permitiu observar o progresso dos estudantes diante dos desafios matem´aticos. Apesar das dificuldades, o engajamento dos alunos foi not´avel, impulsionado pela abordagem investigativa e pela contextualiza¸c˜ao do Teorema do Casamento de Hall em situa¸c˜oes pr´aticas e reais.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESSão CristóvãoporTeoria dos grafosAnálise combinatóriaEnsino médioTeorema de HallCasamentoCombinatóriaHall’s theoremMarriageCombinatoricsHigh schoolCIENCIAS EXATAS E DA TERRA::MATEMATICAO Teorema do Casamento de Hall e aplicações no ensino básicoinfo: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/22924/1/license.txt098cbbf65c2c15e1fb2e49c5d306a44cMD51ORIGINALANDREA_MELO_NARCISO_SANTANA.pdfANDREA_MELO_NARCISO_SANTANA.pdfapplication/pdf4263238https://ri.ufs.br/jspui/bitstream/riufs/22924/2/ANDREA_MELO_NARCISO_SANTANA.pdf481402e2b11905e0988887c6fa2ffc1eMD52riufs/229242025-08-15 17:01:45.607oai:oai:ri.ufs.br:repo_01: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Repositório InstitucionalPUBhttps://ri.ufs.br/oai/requestrepositorio@academico.ufs.bropendoar:2025-08-15T20:01:45Repositório Institucional da UFS - Universidade Federal de Sergipe (UFS)false
dc.title.pt_BR.fl_str_mv O Teorema do Casamento de Hall e aplicações no ensino básico
title O Teorema do Casamento de Hall e aplicações no ensino básico
spellingShingle O Teorema do Casamento de Hall e aplicações no ensino básico
Santana, Andréa de Melo Narciso
Teoria dos grafos
Análise combinatória
Ensino médio
Teorema de Hall
Casamento
Combinatória
Hall’s theorem
Marriage
Combinatorics
High school
CIENCIAS EXATAS E DA TERRA::MATEMATICA
title_short O Teorema do Casamento de Hall e aplicações no ensino básico
title_full O Teorema do Casamento de Hall e aplicações no ensino básico
title_fullStr O Teorema do Casamento de Hall e aplicações no ensino básico
title_full_unstemmed O Teorema do Casamento de Hall e aplicações no ensino básico
title_sort O Teorema do Casamento de Hall e aplicações no ensino básico
author Santana, Andréa de Melo Narciso
author_facet Santana, Andréa de Melo Narciso
author_role author
dc.contributor.author.fl_str_mv Santana, Andréa de Melo Narciso
dc.contributor.advisor1.fl_str_mv Dória, André Vinicius Santos
contributor_str_mv Dória, André Vinicius Santos
dc.subject.por.fl_str_mv Teoria dos grafos
Análise combinatória
Ensino médio
Teorema de Hall
Casamento
Combinatória
topic Teoria dos grafos
Análise combinatória
Ensino médio
Teorema de Hall
Casamento
Combinatória
Hall’s theorem
Marriage
Combinatorics
High school
CIENCIAS EXATAS E DA TERRA::MATEMATICA
dc.subject.eng.fl_str_mv Hall’s theorem
Marriage
Combinatorics
High school
dc.subject.cnpq.fl_str_mv CIENCIAS EXATAS E DA TERRA::MATEMATICA
description The purpose of this dissertation is to present Hall’s Marriage Theorem, its variations and methodologies, aiming to combine theory and practice, stimulating students’ logical reasoning, critical thinking and creativity. In addition to the classic version of the theorem, two other reformulations were developed and related, distinguishing themselves from the usual theoretical framework. In order to contribute to the construction of a more inclusive, efficient, and motivating education, practical activities were proposed, and part of them was applied to second-year high school students. The practice, structured in three stages, allowed to observe the students’ progress in facing mathematical challenges. Despite the difficulties, the students’ engagement was remarkable, driven by the investigative approach and by the contextualization of Hall’s Marriage Theorem in practical and real situations.
publishDate 2025
dc.date.accessioned.fl_str_mv 2025-08-15T20:01:39Z
dc.date.available.fl_str_mv 2025-08-15T20:01:39Z
dc.date.issued.fl_str_mv 2025-07-22
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 SANTANA, Andréa de Melo Narciso. O Teorema do Casamento de Hall e aplicações no ensino básico. 2025. 40 f. Dissertação (Mestrado Profissional em Matemática) — Universidade Federal de Sergipe, São Cristóvão, 2025.
dc.identifier.uri.fl_str_mv https://ri.ufs.br/jspui/handle/riufs/22924
identifier_str_mv SANTANA, Andréa de Melo Narciso. O Teorema do Casamento de Hall e aplicações no ensino básico. 2025. 40 f. Dissertação (Mestrado Profissional em Matemática) — Universidade Federal de Sergipe, São Cristóvão, 2025.
url https://ri.ufs.br/jspui/handle/riufs/22924
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)
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instacron_str UFS
institution UFS
reponame_str Repositório Institucional da UFS
collection Repositório Institucional da UFS
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https://ri.ufs.br/jspui/bitstream/riufs/22924/2/ANDREA_MELO_NARCISO_SANTANA.pdf
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