Teorema de Pick e aplicação em jogos geométricos

Detalhes bibliográficos
Autor(a) principal: Santos, Altierre Borges
Data de Publicação: 2024
Tipo de documento: Dissertação
Idioma: por
Título da fonte: Repositório Institucional da UFG
dARK ID: ark:/38995/001300000fdzm
Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/13619
Resumo: This research explores the potential of Pick’s Theorem and its extensions, applied at game developing for teaching mathematics. Advancing the development of games aimed at teaching, is an action of great relevance, as games, when used correctly, contribute to the improvement of students’ understanding of mathematical concepts as well as develops their reasoning skills, some of which are indicated in official documents such as the BNCC and DC-GOEM. With a view to contributing in this direction, we began our activities with a detailed study of Pick’s Theorem and some of its extensions. Pick’s Theorem presents a formula for calculating areas on a mesh in the plane. In this initial study, we identified promising possibilities for game creation. Moreover, we study in detail some games already proposed on this subject. The proposal of games for teaching must be supported by solid scientific evidence, so that, rather than being fun for the students, we obtain powerful tools contributing to the teaching and learning process. This concern led us to study current trends in games for teaching. We studied trends such as classical formalist, empirical-activist, modern formalist, technicist, constructivist and socio-ethnocultural. We used some elements of the empirical-activist and technicist trends combined to select some games and to design others. Didactic sequences for using games in the classroom are proposed. Both the games and the didactic sequences represented contributions to improve teaching and learning of mathematics
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spelling Santos, Ronaldo Antonio doshttp://lattes.cnpq.br/9663485072140551Santos, Ronaldo Antonio dosSmith, Ole PeterBatista, Marcos Robertohttp://lattes.cnpq.br/4297515694236656Santos, Altierre Borges2024-11-06T16:36:43Z2024-11-06T16:36:43Z2024-08-29SANTOS, A. B. Teorema de Pick e aplicação em jogos geométricos. 2024. 99 f. Dissertação (Mestrado em Matemática em Rede Nacional) - Instituto de Matemática e Estatística, Universidade Federal de Goiás, Goiânia, 2024.http://repositorio.bc.ufg.br/tede/handle/tede/13619ark:/38995/001300000fdzmThis research explores the potential of Pick’s Theorem and its extensions, applied at game developing for teaching mathematics. Advancing the development of games aimed at teaching, is an action of great relevance, as games, when used correctly, contribute to the improvement of students’ understanding of mathematical concepts as well as develops their reasoning skills, some of which are indicated in official documents such as the BNCC and DC-GOEM. With a view to contributing in this direction, we began our activities with a detailed study of Pick’s Theorem and some of its extensions. Pick’s Theorem presents a formula for calculating areas on a mesh in the plane. In this initial study, we identified promising possibilities for game creation. Moreover, we study in detail some games already proposed on this subject. The proposal of games for teaching must be supported by solid scientific evidence, so that, rather than being fun for the students, we obtain powerful tools contributing to the teaching and learning process. This concern led us to study current trends in games for teaching. We studied trends such as classical formalist, empirical-activist, modern formalist, technicist, constructivist and socio-ethnocultural. We used some elements of the empirical-activist and technicist trends combined to select some games and to design others. Didactic sequences for using games in the classroom are proposed. Both the games and the didactic sequences represented contributions to improve teaching and learning of mathematicsEsta dissertação explora o potencial do Teorema de Pick e suas extensões para o desenvolvimento de jogos voltados para o ensino de matemática, pois, os jogos, quando utilizados de maneira correta, contribuem para melhorar a compreensão dos alunos sobre conceitos matemáticos e também para desenvolver suas habilidades de raciocínio, algumas indicadas em documentos oficiais como a BNCC e a DC-GOEM. Com vistas a contribuir nessa direção, iniciamos nossas atividades com o estudo detalhado de Teorema de Pick e algumas de suas extensões. O Teorema de Pick apresenta uma fórmula para o cálculo de áreas sobre uma rede de pontos no plano. Nesse estudo inicial, identificamos possibilidades promissoras para a elaboração de jogos. Também estudamos em detalhes alguns jogos já propostos para o assunto. A proposta de jogos voltados para o ensino deve estar apoiada em sólidas evidências científicas, pois assim, mais que uma diversão para os estudantes, teremos uma poderosa ferramenta para contribuir no processo de ensino e aprendizagem. Essa preocupação nos levou ao estudo das tendências atuais para jogos no ensino. Estudamos tendências como a formalista-clássica, empírico-ativista, formalista moderna, tecnicista, construtivista e socioetnocultural .Usamos alguns elementos das tendências empírico-ativista e tecnicista combinados para selecionar e elaborar alguns jogos. Sequências didáticas para o uso dos jogos em sala são propostas. Tanto os jogos quanto as sequências didáticas representam contribuições significativas para a melhoria no ensino-aprendizagem de matemáticaporUniversidade Federal de GoiásPROFMAT - Programa de Pós-graduação em Matemática em Rede Nacional - Sociedade Brasileira de Matemática (IME)UFGBrasilInstituto de Matemática e Estatística - IME (RMG)Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessEnsinoGeoplanoJogosMatemáticaTeorema de PickGamesGeoboardMathematicsPick’s theoremTeachingCIENCIAS EXATAS E DA TERRA::MATEMATICATeorema de Pick e aplicação em jogos geométricosPick's theorem and its application to geometric gamesinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisreponame:Repositório Institucional da UFGinstname:Universidade Federal de Goiás (UFG)instacron:UFGLICENSElicense.txtlicense.txttext/plain; charset=utf-81748http://repositorio.bc.ufg.br/tede/bitstreams/571775dd-336b-4c6e-bf5c-5f78051575ac/download8a4605be74aa9ea9d79846c1fba20a33MD51ORIGINALDissertação - Altierre Borges Santos - 2024.pdfDissertação - Altierre Borges Santos - 2024.pdfapplication/pdf1115306http://repositorio.bc.ufg.br/tede/bitstreams/30f238f5-5495-4a73-ab5b-7ce20761c6c0/download0a2f255b2e12478b69ebda4725360e3eMD52CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805http://repositorio.bc.ufg.br/tede/bitstreams/50791835-2efe-4770-8426-05e1309b3f6d/download4460e5956bc1d1639be9ae6146a50347MD53tede/136192024-11-06 13:36:43.715http://creativecommons.org/licenses/by-nc-nd/4.0/Attribution-NonCommercial-NoDerivatives 4.0 Internationalopen.accessoai:repositorio.bc.ufg.br:tede/13619http://repositorio.bc.ufg.br/tedeRepositório InstitucionalPUBhttp://repositorio.bc.ufg.br/oai/requesttasesdissertacoes.bc@ufg.bropendoar:2024-11-06T16:36:43Repositório Institucional da UFG - Universidade Federal de Goiás (UFG)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
dc.title.none.fl_str_mv Teorema de Pick e aplicação em jogos geométricos
dc.title.alternative.eng.fl_str_mv Pick's theorem and its application to geometric games
title Teorema de Pick e aplicação em jogos geométricos
spellingShingle Teorema de Pick e aplicação em jogos geométricos
Santos, Altierre Borges
Ensino
Geoplano
Jogos
Matemática
Teorema de Pick
Games
Geoboard
Mathematics
Pick’s theorem
Teaching
CIENCIAS EXATAS E DA TERRA::MATEMATICA
title_short Teorema de Pick e aplicação em jogos geométricos
title_full Teorema de Pick e aplicação em jogos geométricos
title_fullStr Teorema de Pick e aplicação em jogos geométricos
title_full_unstemmed Teorema de Pick e aplicação em jogos geométricos
title_sort Teorema de Pick e aplicação em jogos geométricos
author Santos, Altierre Borges
author_facet Santos, Altierre Borges
author_role author
dc.contributor.advisor1.fl_str_mv Santos, Ronaldo Antonio dos
dc.contributor.advisor1Lattes.fl_str_mv http://lattes.cnpq.br/9663485072140551
dc.contributor.referee1.fl_str_mv Santos, Ronaldo Antonio dos
dc.contributor.referee2.fl_str_mv Smith, Ole Peter
dc.contributor.referee3.fl_str_mv Batista, Marcos Roberto
dc.contributor.authorLattes.fl_str_mv http://lattes.cnpq.br/4297515694236656
dc.contributor.author.fl_str_mv Santos, Altierre Borges
contributor_str_mv Santos, Ronaldo Antonio dos
Santos, Ronaldo Antonio dos
Smith, Ole Peter
Batista, Marcos Roberto
dc.subject.por.fl_str_mv Ensino
Geoplano
Jogos
Matemática
Teorema de Pick
topic Ensino
Geoplano
Jogos
Matemática
Teorema de Pick
Games
Geoboard
Mathematics
Pick’s theorem
Teaching
CIENCIAS EXATAS E DA TERRA::MATEMATICA
dc.subject.eng.fl_str_mv Games
Geoboard
Mathematics
Pick’s theorem
Teaching
dc.subject.cnpq.fl_str_mv CIENCIAS EXATAS E DA TERRA::MATEMATICA
description This research explores the potential of Pick’s Theorem and its extensions, applied at game developing for teaching mathematics. Advancing the development of games aimed at teaching, is an action of great relevance, as games, when used correctly, contribute to the improvement of students’ understanding of mathematical concepts as well as develops their reasoning skills, some of which are indicated in official documents such as the BNCC and DC-GOEM. With a view to contributing in this direction, we began our activities with a detailed study of Pick’s Theorem and some of its extensions. Pick’s Theorem presents a formula for calculating areas on a mesh in the plane. In this initial study, we identified promising possibilities for game creation. Moreover, we study in detail some games already proposed on this subject. The proposal of games for teaching must be supported by solid scientific evidence, so that, rather than being fun for the students, we obtain powerful tools contributing to the teaching and learning process. This concern led us to study current trends in games for teaching. We studied trends such as classical formalist, empirical-activist, modern formalist, technicist, constructivist and socio-ethnocultural. We used some elements of the empirical-activist and technicist trends combined to select some games and to design others. Didactic sequences for using games in the classroom are proposed. Both the games and the didactic sequences represented contributions to improve teaching and learning of mathematics
publishDate 2024
dc.date.accessioned.fl_str_mv 2024-11-06T16:36:43Z
dc.date.available.fl_str_mv 2024-11-06T16:36:43Z
dc.date.issued.fl_str_mv 2024-08-29
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
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dc.identifier.citation.fl_str_mv SANTOS, A. B. Teorema de Pick e aplicação em jogos geométricos. 2024. 99 f. Dissertação (Mestrado em Matemática em Rede Nacional) - Instituto de Matemática e Estatística, Universidade Federal de Goiás, Goiânia, 2024.
dc.identifier.uri.fl_str_mv http://repositorio.bc.ufg.br/tede/handle/tede/13619
dc.identifier.dark.fl_str_mv ark:/38995/001300000fdzm
identifier_str_mv SANTOS, A. B. Teorema de Pick e aplicação em jogos geométricos. 2024. 99 f. Dissertação (Mestrado em Matemática em Rede Nacional) - Instituto de Matemática e Estatística, Universidade Federal de Goiás, Goiânia, 2024.
ark:/38995/001300000fdzm
url http://repositorio.bc.ufg.br/tede/handle/tede/13619
dc.language.iso.fl_str_mv por
language por
dc.rights.driver.fl_str_mv Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
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 (RMG)
publisher.none.fl_str_mv Universidade Federal de Goiás
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