Uma proposta de ensino para a educação básica Usando o teorema de PICK
Autor(a) principal: | |
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Data de Publicação: | 2018 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Biblioteca Digital de Teses e Dissertações da UFMA |
Texto Completo: | https://tedebc.ufma.br/jspui/handle/tede/tede/2559 |
Resumo: | Considering that the students of Basic Education present difficulties to abstraction of the content of polygon area, at least as far as the traditional method is concerned, in this work we will present a proposal of study of this subject using the Pick Theorem in the Geoplane, which is the application of a simple formula in which it is done by the counting of points of the border and internal points of the polygon. It is a formula that can be objectively manipulated by a student of Elementary School II (6th to 9th grade). For that, Pick's Theorem is a didactic resource to be used by the teacher of the initial series to create figures and calculate their respective areas dynamically making the learning more concrete and lasting, as well as presenting the content in a more palpable way, the which facilitates the upcoming contents of High School. The demonstration of the formula is elementary, this is necessary to support examples of everyday life. Based on the recommendations of the Parametros Curriculares Nacionais, the method of cubing is presented, which is a way of calculating the area of regions used by peasants, a parallel of this method is made with the way used in the academic field, through the Educational Proposal, where the teacher following each step in teaching learning gives the student greater freedom and autonomy to debate and participate actively in the process of knowledge. |
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SILVA, João de Deus Mendes da571427933-68http://lattes.cnpq.br/3120123677696759RAPOSO JÚNIOR, Anselmo Baganha018242683-19http://lattes.cnpq.br/1897132155823007SILVA, João de Deus Mendes da571427933-68http://lattes.cnpq.br/3120123677696759RAPOSO JÚNIOR, Anselmo Baganha018242683-19http://lattes.cnpq.br/1897132155823007CARVALHO, Renata de Farias Limeirahttp://lattes.cnpq.br/3580580656850874MARÃO, José Antônio Pires Ferreirahttp://lattes.cnpq.br/4501761863997440784511833-87http://lattes.cnpq.br/6010120902733765FREITAS, Cled Veloso2019-03-01T12:48:29Z2018-11-26FREITAS, Cled Veloso. Uma proposta de ensino para a educação básica Usando o teorema de PICK. 2018. 72 f. Dissertação (Programa de Pós-Graduação em Rede - Matemática em Rede Nacional/CCET) - Universidade Federal do Maranhão, São Luís.https://tedebc.ufma.br/jspui/handle/tede/tede/2559Considering that the students of Basic Education present difficulties to abstraction of the content of polygon area, at least as far as the traditional method is concerned, in this work we will present a proposal of study of this subject using the Pick Theorem in the Geoplane, which is the application of a simple formula in which it is done by the counting of points of the border and internal points of the polygon. It is a formula that can be objectively manipulated by a student of Elementary School II (6th to 9th grade). For that, Pick's Theorem is a didactic resource to be used by the teacher of the initial series to create figures and calculate their respective areas dynamically making the learning more concrete and lasting, as well as presenting the content in a more palpable way, the which facilitates the upcoming contents of High School. The demonstration of the formula is elementary, this is necessary to support examples of everyday life. Based on the recommendations of the Parametros Curriculares Nacionais, the method of cubing is presented, which is a way of calculating the area of regions used by peasants, a parallel of this method is made with the way used in the academic field, through the Educational Proposal, where the teacher following each step in teaching learning gives the student greater freedom and autonomy to debate and participate actively in the process of knowledge.Considerando que os alunos da Educação Básica apresentam dificuldades para abstração do conteúdo de área de polígonos, pelo menos no que se refere ao método tradicional, neste trabalho apresentaremos uma proposta de estudo desse assunto utlizando o Teorema de Pick no Geoplano, que se trata da aplicação de uma fórmula simples em que se faz pela contagem de pontos da borda e pontos internos do polígono. _E uma fórmula que pode ser manipulada de forma objetiva por um aluno do Ensino Fundamental II (6o ao 9o ano). Para tanto, o Teorema de Pick é um recurso didático a ser usado pelo professor das séries iniciais para criar figuras e calcular suas respectivas áreas de forma dinâmica tornando o aprendizado mais concreto e duradouro, bem como apresentar o conteúdo de uma maneira mais palpável, o que facilita os conteúdos vindouros do Ensino Médio. A demonstração da fórmula é elementar, isso se faz necessário para embasar exemplos do cotidiano. Baseado no que recomendam os Parâmetros Curriculares Nacionais, apresenta-se o método de cubacão que _e uma maneira de calcular _área de regiões usada pelos campesinos, faz-se um paralelo deste método com a maneira usada no campo acadêmico, o que permite concluir que, por meio da Proposta Educacional, onde o docente seguindo cada etapa no ensino aprendizagem proporciona ao discente maior liberdade e autonomia para debater e participar ativamente no processo do conhecimento.Submitted by Daniella Santos (daniella.santos@ufma.br) on 2019-03-01T12:48:29Z No. of bitstreams: 1 CledFreitas.pdf: 1478608 bytes, checksum: f15aa169e95d3b721a34610a66d3c6fa (MD5)Made available in DSpace on 2019-03-01T12:48:29Z (GMT). No. of bitstreams: 1 CledFreitas.pdf: 1478608 bytes, checksum: f15aa169e95d3b721a34610a66d3c6fa (MD5) Previous issue date: 2018-11-26application/pdfporUniversidade Federal do MaranhãoPROGRAMA DE PÓS-GRADUAÇÃO EM REDE - MATEMÁTICA EM REDE NACIONAL/CCETUFMABrasilDEPARTAMENTO DE MATEMÁTICA/CCETÁreaGeometriaGeoplanoTeorema de PickAreaGeometryGeoplanePick TheoremMatemáticaEnsino-AprendizagemUma proposta de ensino para a educação básica Usando o teorema de PICKA teaching proposal for basic education Using the PICK theoreminfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/openAccessreponame:Biblioteca Digital de Teses e Dissertações da UFMAinstname:Universidade Federal do Maranhão (UFMA)instacron:UFMAORIGINALCledFreitas.pdfCledFreitas.pdfapplication/pdf1478608http://tedebc.ufma.br:8080/bitstream/tede/2559/2/CledFreitas.pdff15aa169e95d3b721a34610a66d3c6faMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-82255http://tedebc.ufma.br:8080/bitstream/tede/2559/1/license.txt97eeade1fce43278e63fe063657f8083MD51tede/25592019-03-01 09:48:29.765oai:tede2: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Biblioteca Digital de Teses e Dissertaçõeshttps://tedebc.ufma.br/jspui/PUBhttp://tedebc.ufma.br:8080/oai/requestrepositorio@ufma.br||repositorio@ufma.bropendoar:21312019-03-01T12:48:29Biblioteca Digital de Teses e Dissertações da UFMA - Universidade Federal do Maranhão (UFMA)false |
dc.title.por.fl_str_mv |
Uma proposta de ensino para a educação básica Usando o teorema de PICK |
dc.title.alternative.eng.fl_str_mv |
A teaching proposal for basic education Using the PICK theorem |
title |
Uma proposta de ensino para a educação básica Usando o teorema de PICK |
spellingShingle |
Uma proposta de ensino para a educação básica Usando o teorema de PICK FREITAS, Cled Veloso Área Geometria Geoplano Teorema de Pick Area Geometry Geoplane Pick Theorem Matemática Ensino-Aprendizagem |
title_short |
Uma proposta de ensino para a educação básica Usando o teorema de PICK |
title_full |
Uma proposta de ensino para a educação básica Usando o teorema de PICK |
title_fullStr |
Uma proposta de ensino para a educação básica Usando o teorema de PICK |
title_full_unstemmed |
Uma proposta de ensino para a educação básica Usando o teorema de PICK |
title_sort |
Uma proposta de ensino para a educação básica Usando o teorema de PICK |
author |
FREITAS, Cled Veloso |
author_facet |
FREITAS, Cled Veloso |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
SILVA, João de Deus Mendes da |
dc.contributor.advisor1ID.fl_str_mv |
571427933-68 |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/3120123677696759 |
dc.contributor.advisor-co1.fl_str_mv |
RAPOSO JÚNIOR, Anselmo Baganha |
dc.contributor.advisor-co1ID.fl_str_mv |
018242683-19 |
dc.contributor.advisor-co1Lattes.fl_str_mv |
http://lattes.cnpq.br/1897132155823007 |
dc.contributor.referee1.fl_str_mv |
SILVA, João de Deus Mendes da |
dc.contributor.referee1ID.fl_str_mv |
571427933-68 |
dc.contributor.referee1Lattes.fl_str_mv |
http://lattes.cnpq.br/3120123677696759 |
dc.contributor.referee2.fl_str_mv |
RAPOSO JÚNIOR, Anselmo Baganha |
dc.contributor.referee2ID.fl_str_mv |
018242683-19 |
dc.contributor.referee2Lattes.fl_str_mv |
http://lattes.cnpq.br/1897132155823007 |
dc.contributor.referee3.fl_str_mv |
CARVALHO, Renata de Farias Limeira |
dc.contributor.referee3Lattes.fl_str_mv |
http://lattes.cnpq.br/3580580656850874 |
dc.contributor.referee4.fl_str_mv |
MARÃO, José Antônio Pires Ferreira |
dc.contributor.referee4Lattes.fl_str_mv |
http://lattes.cnpq.br/4501761863997440 |
dc.contributor.authorID.fl_str_mv |
784511833-87 |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/6010120902733765 |
dc.contributor.author.fl_str_mv |
FREITAS, Cled Veloso |
contributor_str_mv |
SILVA, João de Deus Mendes da RAPOSO JÚNIOR, Anselmo Baganha SILVA, João de Deus Mendes da RAPOSO JÚNIOR, Anselmo Baganha CARVALHO, Renata de Farias Limeira MARÃO, José Antônio Pires Ferreira |
dc.subject.por.fl_str_mv |
Área Geometria Geoplano Teorema de Pick |
topic |
Área Geometria Geoplano Teorema de Pick Area Geometry Geoplane Pick Theorem Matemática Ensino-Aprendizagem |
dc.subject.eng.fl_str_mv |
Area Geometry Geoplane Pick Theorem |
dc.subject.cnpq.fl_str_mv |
Matemática Ensino-Aprendizagem |
description |
Considering that the students of Basic Education present difficulties to abstraction of the content of polygon area, at least as far as the traditional method is concerned, in this work we will present a proposal of study of this subject using the Pick Theorem in the Geoplane, which is the application of a simple formula in which it is done by the counting of points of the border and internal points of the polygon. It is a formula that can be objectively manipulated by a student of Elementary School II (6th to 9th grade). For that, Pick's Theorem is a didactic resource to be used by the teacher of the initial series to create figures and calculate their respective areas dynamically making the learning more concrete and lasting, as well as presenting the content in a more palpable way, the which facilitates the upcoming contents of High School. The demonstration of the formula is elementary, this is necessary to support examples of everyday life. Based on the recommendations of the Parametros Curriculares Nacionais, the method of cubing is presented, which is a way of calculating the area of regions used by peasants, a parallel of this method is made with the way used in the academic field, through the Educational Proposal, where the teacher following each step in teaching learning gives the student greater freedom and autonomy to debate and participate actively in the process of knowledge. |
publishDate |
2018 |
dc.date.issued.fl_str_mv |
2018-11-26 |
dc.date.accessioned.fl_str_mv |
2019-03-01T12:48:29Z |
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 |
FREITAS, Cled Veloso. Uma proposta de ensino para a educação básica Usando o teorema de PICK. 2018. 72 f. Dissertação (Programa de Pós-Graduação em Rede - Matemática em Rede Nacional/CCET) - Universidade Federal do Maranhão, São Luís. |
dc.identifier.uri.fl_str_mv |
https://tedebc.ufma.br/jspui/handle/tede/tede/2559 |
identifier_str_mv |
FREITAS, Cled Veloso. Uma proposta de ensino para a educação básica Usando o teorema de PICK. 2018. 72 f. Dissertação (Programa de Pós-Graduação em Rede - Matemática em Rede Nacional/CCET) - Universidade Federal do Maranhão, São Luís. |
url |
https://tedebc.ufma.br/jspui/handle/tede/tede/2559 |
dc.language.iso.fl_str_mv |
por |
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por |
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info:eu-repo/semantics/openAccess |
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Universidade Federal do Maranhão |
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PROGRAMA DE PÓS-GRADUAÇÃO EM REDE - MATEMÁTICA EM REDE NACIONAL/CCET |
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UFMA |
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Brasil |
dc.publisher.department.fl_str_mv |
DEPARTAMENTO DE MATEMÁTICA/CCET |
publisher.none.fl_str_mv |
Universidade Federal do Maranhão |
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