Teorema de Pick e aplicação em jogos geométricos
Autor(a) principal: | |
---|---|
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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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 |
format |
masterThesis |
status_str |
publishedVersion |
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 |
dc.source.none.fl_str_mv |
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UFG |
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Repositório Institucional da UFG |
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