Estratégias de cálculo mental com números racionais: um olhar sobre a expertise profissional de Cecilia Parra

Detalhes bibliográficos
Ano de defesa: 2024
Autor(a) principal: Cosme, Ruth Edite
Orientador(a): Não Informado pela instituição
Banca de defesa: Não Informado pela instituição
Tipo de documento: Tese
Tipo de acesso: Acesso aberto
Idioma: por
Instituição de defesa: Não Informado pela instituição
Programa de Pós-Graduação: Não Informado pela instituição
Departamento: Não Informado pela instituição
País: Não Informado pela instituição
Palavras-chave em Português:
Cálculo mental
Cecilia Parra
Expertise
História da educação matemática
Números racionais
Link de acesso: https://repositorio.ufsc.br/handle/123456789/261163
Resumo: Dissertação apresentada ao Programa de PósGraduação em Educação em Ciências, Educação Matemática e Tecnologias Educativas, Universidade Federal do Paraná, Setor Palotina, como requisito parcial à obtenção do título de Mestre em Ensino de Matemática. Linha de pesquisa: Filosofia, História e Sociologia da Educação em Ciências e Educação Matemática Orientador(a): Prof(a). Dr(a). Danilene Gullich Donin Berticelli.
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spelling Cosme, Ruth Edite2024-11-25T19:42:59Z2024-11-25T19:42:59Z2024COSME, Ruth Edite. Estratégias de cálculo mental com números racionais: um olhar sobre a expertise profissional de Cecilia Parra. Dissertação (Mestrado). Universidade Federal do Paraná. Setor Palotina, PR, Programa de Pós-Graduação em Educação em Ciências, Educação Matemática e Tecnologias Educativas. Palotina, PR, 2024.https://repositorio.ufsc.br/handle/123456789/261163Dissertação apresentada ao Programa de PósGraduação em Educação em Ciências, Educação Matemática e Tecnologias Educativas, Universidade Federal do Paraná, Setor Palotina, como requisito parcial à obtenção do título de Mestre em Ensino de Matemática. Linha de pesquisa: Filosofia, História e Sociologia da Educação em Ciências e Educação Matemática Orientador(a): Prof(a). Dr(a). Danilene Gullich Donin Berticelli.Esta pesquisa traz como objetivo central compreender a expertise profissional de Cecilia Parra, autora argentina, referência na didática da matemática sobre cálculo mental com números racionais, convidada pelo Governo da Cidade de Buenos Aires para trabalhar em documentos curriculares, no final do século XX e início do século XXI. Para tal, utilizamo-nos da história cultural, com os autores Burke (2016); Certeau (1985); Chartier (2002, 2011); Chervel (1990); Julia (2001); Pinto (2007, 2014); Valente (2020), trazendo contribuições da mesma para analisar documentos curriculares argentinos (Buenos Aires, 2004, 2006). Estes foram elaborados por Cecilia Parra, onde são apresentadas atividades e orientações para docentes. Trilhamos uma parte da trajetória desta pesquisa pelos bastidores da elaboração curricular brasileira, para perscrutar de que forma o cálculo mental com números naturais e racionais foi articulado na época analisada, que corresponde do ano de 2004 a 2010. Para melhor compreender os saberes presentes no material, fizemos uma discussão sobre o cálculo mental na educação básica entre os autores Berticelli (2017); Berticelli e Zancan (2017); Conceição (2021); Frana (2023), Berticelli e Novaes (2023); Parra (1996), Thompson (2010), em um paralelo com pesquisas realizadas dentro desta temática, sobre o cálculo mental no ensino de números naturais e destes articulados aos racionais. Com a intenção de entender alguns conceitos destes últimos, utilizamos Walle (2019, Romanatto (1997), Boyer (1974), Gomes (2010) e Bertoni (2009). Além disso, apresentamos uma entrevista realizada com Cecilia Parra, que nos abriu novas perspectivas, relacionadas às teorias de Guy Brousseau (2008) e Gérard Vergnaud (1996, 2007, 2009), presentes nos materiais argentinos. Os autores Hofstetter, Schneuwly e Freymond (2017); Morais (2019); Morais, Bertini e Valente (2021); Morais e Valente (2020) foram basilares na compreensão da expertise de Parra analisada nestes materiais. Concluímos que a autora é uma expert neste quesito, visto que cumpriu uma demanda do estado, trabalhando na elaboração do documento curricular, concomitante ao manual analisado, sendo estes ricos em conhecimentos e estratégias de cálculo mental no ensino de números racionais.porCálculo mentalCecilia ParraExpertiseHistória da educação matemáticaNúmeros racionaisEstratégias de cálculo mental com números racionais: um olhar sobre a expertise profissional de Cecilia Parrainfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisreponame:Repositório Institucional da UFSCinstname:Universidade Federal de Santa Catarina (UFSC)instacron:UFSCinfo:eu-repo/semantics/openAccessLICENSElicense.txtlicense.txttext/plain; charset=utf-817508https://repositorio.ufsc.br/bitstream/123456789/261163/2/license.txtc0bc68be64da770871e46b24415ba2e2MD52ORIGINALR - D - RUTH EDITE COSME.pdfR - D - RUTH EDITE COSME.pdfDissertação Ruthapplication/pdf4376839https://repositorio.ufsc.br/bitstream/123456789/261163/1/R%20-%20D%20-%20RUTH%20EDITE%20COSME.pdf1b9d4b2a23be036d888cb81c0addfd06MD51123456789/2611632024-11-25 16:46:25.702oai:repositorio.ufsc.br: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dc.title.pt_BR.fl_str_mv Estratégias de cálculo mental com números racionais: um olhar sobre a expertise profissional de Cecilia Parra
title Estratégias de cálculo mental com números racionais: um olhar sobre a expertise profissional de Cecilia Parra
spellingShingle Estratégias de cálculo mental com números racionais: um olhar sobre a expertise profissional de Cecilia Parra
Cosme, Ruth Edite
Cálculo mental
Cecilia Parra
Expertise
História da educação matemática
Números racionais
title_short Estratégias de cálculo mental com números racionais: um olhar sobre a expertise profissional de Cecilia Parra
title_full Estratégias de cálculo mental com números racionais: um olhar sobre a expertise profissional de Cecilia Parra
title_fullStr Estratégias de cálculo mental com números racionais: um olhar sobre a expertise profissional de Cecilia Parra
title_full_unstemmed Estratégias de cálculo mental com números racionais: um olhar sobre a expertise profissional de Cecilia Parra
title_sort Estratégias de cálculo mental com números racionais: um olhar sobre a expertise profissional de Cecilia Parra
author Cosme, Ruth Edite
author_facet Cosme, Ruth Edite
author_role author
dc.contributor.author.fl_str_mv Cosme, Ruth Edite
dc.subject.por.fl_str_mv Cálculo mental
Cecilia Parra
Expertise
História da educação matemática
Números racionais
topic Cálculo mental
Cecilia Parra
Expertise
História da educação matemática
Números racionais
description Dissertação apresentada ao Programa de PósGraduação em Educação em Ciências, Educação Matemática e Tecnologias Educativas, Universidade Federal do Paraná, Setor Palotina, como requisito parcial à obtenção do título de Mestre em Ensino de Matemática. Linha de pesquisa: Filosofia, História e Sociologia da Educação em Ciências e Educação Matemática Orientador(a): Prof(a). Dr(a). Danilene Gullich Donin Berticelli.
publishDate 2024
dc.date.accessioned.fl_str_mv 2024-11-25T19:42:59Z
dc.date.available.fl_str_mv 2024-11-25T19:42:59Z
dc.date.issued.fl_str_mv 2024
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/doctoralThesis
format doctoralThesis
status_str publishedVersion
dc.identifier.citation.fl_str_mv COSME, Ruth Edite. Estratégias de cálculo mental com números racionais: um olhar sobre a expertise profissional de Cecilia Parra. Dissertação (Mestrado). Universidade Federal do Paraná. Setor Palotina, PR, Programa de Pós-Graduação em Educação em Ciências, Educação Matemática e Tecnologias Educativas. Palotina, PR, 2024.
dc.identifier.uri.fl_str_mv https://repositorio.ufsc.br/handle/123456789/261163
identifier_str_mv COSME, Ruth Edite. Estratégias de cálculo mental com números racionais: um olhar sobre a expertise profissional de Cecilia Parra. Dissertação (Mestrado). Universidade Federal do Paraná. Setor Palotina, PR, Programa de Pós-Graduação em Educação em Ciências, Educação Matemática e Tecnologias Educativas. Palotina, PR, 2024.
url https://repositorio.ufsc.br/handle/123456789/261163
dc.language.iso.fl_str_mv por
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dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFSC
instname:Universidade Federal de Santa Catarina (UFSC)
instacron:UFSC
instname_str Universidade Federal de Santa Catarina (UFSC)
instacron_str UFSC
institution UFSC
reponame_str Repositório Institucional da UFSC
collection Repositório Institucional da UFSC
bitstream.url.fl_str_mv https://repositorio.ufsc.br/bitstream/123456789/261163/2/license.txt
https://repositorio.ufsc.br/bitstream/123456789/261163/1/R%20-%20D%20-%20RUTH%20EDITE%20COSME.pdf
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repository.name.fl_str_mv Repositório Institucional da UFSC - Universidade Federal de Santa Catarina (UFSC)
repository.mail.fl_str_mv sandra.sobrera@ufsc.br
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