Descobrindo o número PI

Detalhes bibliográficos
Autor(a) principal: Keller, Flávia Adolf Lutz
Data de Publicação: 2013
Tipo de documento: Dissertação
Idioma: por
Título da fonte: Repositório Institucional da UFSCAR
Texto Completo: https://repositorio.ufscar.br/handle/ufscar/5950
Resumo: The value of the circumference s length divided by its diameter has a result a constant named PI; This value is known since ancient times by the Greeks and Egyptians, but only in current history this constant has been recognized as an irrational number. This study has as objective to explore the relationship of the circle by II elementary school students and extension of numerical sets from this constant. Making sense of this value by checking its regularity in all circles through practical experiments and also exploring the technological resources available in the school, making the students to follow the steps for determining of the numerical value and to participate in the construction and discovery process of new knowledge. The teaching sequence proposed was based on Engineering teaching as research methodology, conducting in the end a posteriori analysis which demonstrates that learning from manipulable objects, together with technological resources available provides to students with a greater assimilation of mathematical content, one becoming a remarkable experience for elementary school students and being an important tool which complements the lessons and makes them more participative. It is hoped that this work support math teachers to reflect the usage of manipulative materials, educational software and all available resources which provide greater assimilation and approach the student with the mathematical concepts.
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spelling Keller, Flávia Adolf LutzMoura, Renato José dehttp://lattes.cnpq.br/5227908949297904893b6c1d-87e6-4bc0-bd9a-11024725f5b82016-06-02T20:29:24Z2013-10-112016-06-02T20:29:24Z2013-08-24KELLER, Flávia Adolf Lutz. Descobrindo o número π. 2013. 66 f. Dissertação (Mestrado em Ciências Exatas e da Terra) - Universidade Federal de São Carlos, São Carlos, 2013.https://repositorio.ufscar.br/handle/ufscar/5950The value of the circumference s length divided by its diameter has a result a constant named PI; This value is known since ancient times by the Greeks and Egyptians, but only in current history this constant has been recognized as an irrational number. This study has as objective to explore the relationship of the circle by II elementary school students and extension of numerical sets from this constant. Making sense of this value by checking its regularity in all circles through practical experiments and also exploring the technological resources available in the school, making the students to follow the steps for determining of the numerical value and to participate in the construction and discovery process of new knowledge. The teaching sequence proposed was based on Engineering teaching as research methodology, conducting in the end a posteriori analysis which demonstrates that learning from manipulable objects, together with technological resources available provides to students with a greater assimilation of mathematical content, one becoming a remarkable experience for elementary school students and being an important tool which complements the lessons and makes them more participative. It is hoped that this work support math teachers to reflect the usage of manipulative materials, educational software and all available resources which provide greater assimilation and approach the student with the mathematical concepts.O valor do comprimento de uma circunferência dividido pelo seu diâmetro tem como resultado um valor constante. Tal constante é denominada PI. Este valor é conhecido desde a antiguidade, por egípcios e gregos, mas somente na história mais recente esta constante foi reconhecida como sendo um número irracional. O objetivo deste trabalho foi explorar essa relação do círculo por alunos do Ensino Fundamental II e ampliação dos conjuntos numéricos a partir desta constante. Determinar este valor, verificando sua regularidade em todos os círculos através de experimentos práticos e também explorando os recursos tecnológicos disponíveis na escola, fazendo com que os alunos calculem o valor numérico de π , fazendo-os participar do processo de construção e descoberta deste novo conhecimento. A sequência didática proposta foi baseada na Engenharia didática como metodologia de investigação, realizando-se ao final, uma análise a posteriori que demonstra que o aprendizado a partir de objetos manipuláveis, aliados aos recursos tecnológicos disponíveis, proporciona aos alunos uma maior assimilação do conteúdo matemático, tornando-se uma experiência marcante para os alunos do Ensino Fundamental e sendo uma importante ferramenta que completa as aulas e as tornam mais participativas. Espera-se que este trabalho auxilie os professores de matemática a refletirem que o uso de materiais manipulativos, software educacionais e todos os recursos disponíveis proporcionam maior assimilação e aproximação do aluno com os conceitos matemáticos.Financiadora de Estudos e Projetosapplication/pdfporUniversidade Federal de São CarlosPrograma de Mestrado Profissional em Matemática em Rede Nacional - PROFMATUFSCarBRCírculoNúmeros irracionaisValor de PIMateriais manipulativosSoftware educacionalCircleValue of PIIrrationalManipulative materialsEducational softwareCIENCIAS EXATAS E DA TERRA::MATEMATICADescobrindo o número PIinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesis-1-1010df237-e099-433b-8b5a-3e17e31a2311info:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFSCARinstname:Universidade Federal de São Carlos (UFSCAR)instacron:UFSCARORIGINAL5498.pdfapplication/pdf2689266https://repositorio.ufscar.br/bitstream/ufscar/5950/1/5498.pdf8ae3a0b585aa8d0bb8ddfb21f15b47d9MD51TEXT5498.pdf.txt5498.pdf.txtExtracted texttext/plain0https://repositorio.ufscar.br/bitstream/ufscar/5950/2/5498.pdf.txtd41d8cd98f00b204e9800998ecf8427eMD52THUMBNAIL5498.pdf.jpg5498.pdf.jpgIM Thumbnailimage/jpeg5433https://repositorio.ufscar.br/bitstream/ufscar/5950/3/5498.pdf.jpg419e8ea28a904dbc80e0bcdc3e7d8795MD53ufscar/59502023-09-18 18:31:48.572oai:repositorio.ufscar.br:ufscar/5950Repositório InstitucionalPUBhttps://repositorio.ufscar.br/oai/requestopendoar:43222023-09-18T18:31:48Repositório Institucional da UFSCAR - Universidade Federal de São Carlos (UFSCAR)false
dc.title.por.fl_str_mv Descobrindo o número PI
title Descobrindo o número PI
spellingShingle Descobrindo o número PI
Keller, Flávia Adolf Lutz
Círculo
Números irracionais
Valor de PI
Materiais manipulativos
Software educacional
Circle
Value of PI
Irrational
Manipulative materials
Educational software
CIENCIAS EXATAS E DA TERRA::MATEMATICA
title_short Descobrindo o número PI
title_full Descobrindo o número PI
title_fullStr Descobrindo o número PI
title_full_unstemmed Descobrindo o número PI
title_sort Descobrindo o número PI
author Keller, Flávia Adolf Lutz
author_facet Keller, Flávia Adolf Lutz
author_role author
dc.contributor.author.fl_str_mv Keller, Flávia Adolf Lutz
dc.contributor.advisor1.fl_str_mv Moura, Renato José de
dc.contributor.advisor1Lattes.fl_str_mv http://lattes.cnpq.br/5227908949297904
dc.contributor.authorID.fl_str_mv 893b6c1d-87e6-4bc0-bd9a-11024725f5b8
contributor_str_mv Moura, Renato José de
dc.subject.por.fl_str_mv Círculo
Números irracionais
Valor de PI
Materiais manipulativos
Software educacional
topic Círculo
Números irracionais
Valor de PI
Materiais manipulativos
Software educacional
Circle
Value of PI
Irrational
Manipulative materials
Educational software
CIENCIAS EXATAS E DA TERRA::MATEMATICA
dc.subject.eng.fl_str_mv Circle
Value of PI
Irrational
Manipulative materials
Educational software
dc.subject.cnpq.fl_str_mv CIENCIAS EXATAS E DA TERRA::MATEMATICA
description The value of the circumference s length divided by its diameter has a result a constant named PI; This value is known since ancient times by the Greeks and Egyptians, but only in current history this constant has been recognized as an irrational number. This study has as objective to explore the relationship of the circle by II elementary school students and extension of numerical sets from this constant. Making sense of this value by checking its regularity in all circles through practical experiments and also exploring the technological resources available in the school, making the students to follow the steps for determining of the numerical value and to participate in the construction and discovery process of new knowledge. The teaching sequence proposed was based on Engineering teaching as research methodology, conducting in the end a posteriori analysis which demonstrates that learning from manipulable objects, together with technological resources available provides to students with a greater assimilation of mathematical content, one becoming a remarkable experience for elementary school students and being an important tool which complements the lessons and makes them more participative. It is hoped that this work support math teachers to reflect the usage of manipulative materials, educational software and all available resources which provide greater assimilation and approach the student with the mathematical concepts.
publishDate 2013
dc.date.available.fl_str_mv 2013-10-11
2016-06-02T20:29:24Z
dc.date.issued.fl_str_mv 2013-08-24
dc.date.accessioned.fl_str_mv 2016-06-02T20:29:24Z
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dc.identifier.citation.fl_str_mv KELLER, Flávia Adolf Lutz. Descobrindo o número π. 2013. 66 f. Dissertação (Mestrado em Ciências Exatas e da Terra) - Universidade Federal de São Carlos, São Carlos, 2013.
dc.identifier.uri.fl_str_mv https://repositorio.ufscar.br/handle/ufscar/5950
identifier_str_mv KELLER, Flávia Adolf Lutz. Descobrindo o número π. 2013. 66 f. Dissertação (Mestrado em Ciências Exatas e da Terra) - Universidade Federal de São Carlos, São Carlos, 2013.
url https://repositorio.ufscar.br/handle/ufscar/5950
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