Os aspectos matemáticos relacionados à média geométrica que emergem a partir da manipulação da escala dos números (1623) elaborada por Edmund Gunter com licenciandos em Matemática
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| Autor principal: | |
|---|---|
| Data de publicació: | 2022 |
| Format: | Master thesis |
| Idioma: | por |
| Font: | Repositório Comum do Brasil - Deposita |
| Download full: | https://deposita.ibict.br/handle/deposita/658 |
Sumari: | In view of the studies carried out in order to combine history with the teaching of mathematics through an interface, an updated perspective of historical writing was chosen that uses a historical source to seek resources that can serve as a basis for the development of activities. Aiming to contribute to studies that combine history and teaching in this approach, we chose to investigate a mathematical instrument described in Edmund Gunter's treatise (1581-1626), entitled The description and vse of the Sector, the Crosse-staffe, and other instruments, for such as are studious of Mathematicall practise, in such a way as to appropriate the scale of numbers inscribed in the Cross-staff instrument to didactically explore the notion of geometric mean. Thus, this study has the general objective of knowing the mathematical processes involving the geometric mean that permeated the formation of undergraduates in Mathematics from the handling of the scale of numbers. In this way, the research is characterized as qualitative with a bibliographic and documentary nature, in which a survey was carried out on the themes related to this study, as well as a treatment of the chosen historical source. As for the development of the activity, the support of the Theory of Objectification was used. The contextual sphere was mobilized from the study of the treaty in which the context of the elaboration of Gunter's work was presented. A study was also carried out in the epistemological scope directed to the scale of numbers. The historiographical sphere, on the other hand, permeates the two previous moments. Training was applied with a degree in Mathematics for the perception of mathematical knowledge related to the geometric mean, resulting in the mobilization of knowledge such as logarithm, analytical geometric and algebra associated with the geometric mean. In this way, it contributes to the training of mathematics teachers with the use of resources from history, especially with the scale of numbers for the teaching of geometric mean from articulations with other areas of mathematics. |
| _version_ | 1872168162369208320 |
|---|---|
| author | Santos, Andressa Gomes dos |
| author_browse | Santos, Andressa Gomes dos |
| author_facet | Santos, Andressa Gomes dos |
| author_role | author |
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| collection | Repositório Comum do Brasil - Deposita |
| contributor_str_mv | Pereira, Ana Carolina Costa |
| dc.contributor.advisor1.fl_str_mv | Pereira, Ana Carolina Costa |
| dc.contributor.author.fl_str_mv | Santos, Andressa Gomes dos |
| dc.contributor.authorLattes.fl_str_mv | https://lattes.cnpq.br/2241206887027621 |
| dc.date.accessioned.fl_str_mv | 2024-09-10T19:12:32Z |
| dc.date.issued.fl_str_mv | 2022 |
| dc.format.none.fl_str_mv | application/pdf application/pdf |
| dc.identifier.uri.fl_str_mv | https://deposita.ibict.br/handle/deposita/658 |
| dc.language.iso.fl_str_mv | por |
| dc.publisher.country.fl_str_mv | Brasil |
| dc.publisher.department.fl_str_mv | Instituto Federal de Educação, Ciência e Tecnologia do Ceará |
| dc.publisher.none.fl_str_mv | Fundação Cearense de Apoio ao Desenvolvimento Científico e Tecnológico |
| dc.publisher.program.fl_str_mv | Programa de Pós-Graduação em Ensino de Ciências e Matemática |
| dc.rights.driver.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.source.none.fl_str_mv | reponame:Repositório Comum do Brasil - Deposita instname:Instituto Brasileiro de Informação em Ciência e Tecnologia (Ibict) instacron:IBICT |
| dc.subject.cnpq.fl_str_mv | Ciências Exatas e da Terra |
| dc.subject.por.fl_str_mv | Média geométrica Interface entre história e ensino Formação de professores de Matemática |
| dc.title.por.fl_str_mv | Os aspectos matemáticos relacionados à média geométrica que emergem a partir da manipulação da escala dos números (1623) elaborada por Edmund Gunter com licenciandos em Matemática |
| dc.type.driver.fl_str_mv | info:eu-repo/semantics/masterThesis |
| dc.type.status.fl_str_mv | info:eu-repo/semantics/publishedVersion |
| description | In view of the studies carried out in order to combine history with the teaching of mathematics through an interface, an updated perspective of historical writing was chosen that uses a historical source to seek resources that can serve as a basis for the development of activities. Aiming to contribute to studies that combine history and teaching in this approach, we chose to investigate a mathematical instrument described in Edmund Gunter's treatise (1581-1626), entitled The description and vse of the Sector, the Crosse-staffe, and other instruments, for such as are studious of Mathematicall practise, in such a way as to appropriate the scale of numbers inscribed in the Cross-staff instrument to didactically explore the notion of geometric mean. Thus, this study has the general objective of knowing the mathematical processes involving the geometric mean that permeated the formation of undergraduates in Mathematics from the handling of the scale of numbers. In this way, the research is characterized as qualitative with a bibliographic and documentary nature, in which a survey was carried out on the themes related to this study, as well as a treatment of the chosen historical source. As for the development of the activity, the support of the Theory of Objectification was used. The contextual sphere was mobilized from the study of the treaty in which the context of the elaboration of Gunter's work was presented. A study was also carried out in the epistemological scope directed to the scale of numbers. The historiographical sphere, on the other hand, permeates the two previous moments. Training was applied with a degree in Mathematics for the perception of mathematical knowledge related to the geometric mean, resulting in the mobilization of knowledge such as logarithm, analytical geometric and algebra associated with the geometric mean. In this way, it contributes to the training of mathematics teachers with the use of resources from history, especially with the scale of numbers for the teaching of geometric mean from articulations with other areas of mathematics. |
| eu_rights_str_mv | openAccess |
| format | masterThesis |
| id | IBICT-1_64973d219c2f8d9c862879e7f5bd2b3d |
| instacron_str | IBICT |
| institution | IBICT |
| instname_str | Instituto Brasileiro de Informação em Ciência e Tecnologia (Ibict) |
| language | por |
| network_acronym_str | IBICT-1 |
| network_name_str | Repositório Comum do Brasil - Deposita |
| oai_identifier_str | oai:deposita.ibict.br:deposita/658 |
| publishDate | 2022 |
| publishDateSort | 2022 |
| publisher.none.fl_str_mv | Fundação Cearense de Apoio ao Desenvolvimento Científico e Tecnológico |
| reponame_str | Repositório Comum do Brasil - Deposita |
| repository.mail.fl_str_mv | deposita@ibict.br |
| repository.name.fl_str_mv | Repositório Comum do Brasil - Deposita - Instituto Brasileiro de Informação em Ciência e Tecnologia (Ibict) |
| repository_id_str | 4658 |
| spelling | Pereira, Ana Carolina Costahttps://lattes.cnpq.br/2241206887027621Santos, Andressa Gomes dos2024-09-10T19:12:32Z2022https://deposita.ibict.br/handle/deposita/658In view of the studies carried out in order to combine history with the teaching of mathematics through an interface, an updated perspective of historical writing was chosen that uses a historical source to seek resources that can serve as a basis for the development of activities. Aiming to contribute to studies that combine history and teaching in this approach, we chose to investigate a mathematical instrument described in Edmund Gunter's treatise (1581-1626), entitled The description and vse of the Sector, the Crosse-staffe, and other instruments, for such as are studious of Mathematicall practise, in such a way as to appropriate the scale of numbers inscribed in the Cross-staff instrument to didactically explore the notion of geometric mean. Thus, this study has the general objective of knowing the mathematical processes involving the geometric mean that permeated the formation of undergraduates in Mathematics from the handling of the scale of numbers. In this way, the research is characterized as qualitative with a bibliographic and documentary nature, in which a survey was carried out on the themes related to this study, as well as a treatment of the chosen historical source. As for the development of the activity, the support of the Theory of Objectification was used. The contextual sphere was mobilized from the study of the treaty in which the context of the elaboration of Gunter's work was presented. A study was also carried out in the epistemological scope directed to the scale of numbers. The historiographical sphere, on the other hand, permeates the two previous moments. Training was applied with a degree in Mathematics for the perception of mathematical knowledge related to the geometric mean, resulting in the mobilization of knowledge such as logarithm, analytical geometric and algebra associated with the geometric mean. In this way, it contributes to the training of mathematics teachers with the use of resources from history, especially with the scale of numbers for the teaching of geometric mean from articulations with other areas of mathematics.Diante dos estudos realizados, com o intuito de aliar a história ao ensino de Matemática, por meio de uma interface, optou-se por uma perspectiva atualizada da escrita histórica, que utiliza uma fonte histórica para, nela, buscar recursos que possam servir como base para o desenvolvimento de atividades. Almejando contribuir com os estudos que aliam história e ensino nessa abordagem, escolheu-se investigar um instrumento matemático descrito no tratado de Edmund Gunter (1581-1626), intitulado The description and vse of the Sector, the Crossestaffe, and other instruments, for such as are studious of Mathematicall practise, de modo a se apropriar da escala dos números inscrita no instrumento Cross-staff, para explorar didaticamente a noção de média geométrica. Assim, este estudo tem como objetivo geral conhecer os processos matemáticos envolvendo a média geométrica, que permearam a formação de licenciandos em Matemática a partir do manuseio da escala dos números. Dessa maneira, a pesquisa se caracteriza como qualitativa, de cunho bibliográfico e documental, em que se realizou um levantamento sobre as temáticas relacionadas a este estudo, bem como um tratamento da fonte histórica escolhida. Para o desenvolvimento da atividade, utilizou-se o suporte da Teoria da Objetivação. A esfera contextual foi mobilizada por meio do estudo do tratado, em que se apresentou o contexto de elaboração da obra de Gunter. Também foi realizado um estudo, no âmbito epistemológico, direcionado para a escala dos números. Já a esfera historiográfica perpassa pelos dois momentos anteriores. Foi aplicada uma formação com licenciandos em Matemática para a percepção de saberes matemáticos relacionados à média geométrica, obtendo-se como resultado a mobilização de saberes como logaritmo, geométrica analítica e álgebra, associados à média geométrica. Portanto, contribui-se para a formação de professores de Matemática, com a utilização de recursos provenientes da história, em especial, com a escala dos números para o ensino de média geométrica a partir de articulações com outros âmbitos da Matemática.FUNCAPNordeste-1application/pdfapplication/pdfporFundação Cearense de Apoio ao Desenvolvimento Científico e TecnológicoPrograma de Pós-Graduação em Ensino de Ciências e MatemáticaBrasilInstituto Federal de Educação, Ciência e Tecnologia do CearáMédia geométricaInterface entre história e ensinoFormação de professores de MatemáticaCiências Exatas e da TerraOs aspectos matemáticos relacionados à média geométrica que emergem a partir da manipulação da escala dos números (1623) elaborada por Edmund Gunter com licenciandos em Matemáticainfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/openAccessreponame:Repositório Comum do Brasil - Depositainstname:Instituto Brasileiro de Informação em Ciência e Tecnologia (Ibict)instacron:IBICTTEXTAndressa Gomes dos Santos.pdf.txtWritten by FormatFilter org.dspace.app.mediafilter.TikaTextExtractionFilter on 2025-06-06T20:17:46Z (GMT).Extracted texttext/plain102780https://deposita.ibict.br/bitstreams/efedad2a-52eb-4407-adc6-4bec0f74c3c1/download64e985a44d206e52ae11636ea8a31c2dMD53falseAnonymousREADTHUMBNAILAndressa Gomes dos Santos.pdf.jpgWritten by FormatFilter org.dspace.app.mediafilter.PDFBoxThumbnail on 2025-06-06T20:17:46Z (GMT).Generated Thumbnailimage/jpeg3113https://deposita.ibict.br/bitstreams/aabfe5d5-d950-4fbf-a77a-92fed32b26ea/downloadbca74a21af0a7a92b984f4cb878b128eMD54falseAnonymousREADLICENSElicense.txtWritten by org.dspace.content.LicenseUtilstext/plain; charset=utf-81867https://deposita.ibict.br/bitstreams/a85cb2f9-2152-43e6-8b42-ade4d7f1f96b/downloada7c148eec59885ba1ba6d14692be8465MD51falseAnonymousREADORIGINALAndressa Gomes dos Santos.pdf/dspace/deposita/upload/Andressa Gomes dos Santos.pdfDocumento principalapplication/pdf6832550https://deposita.ibict.br/bitstreams/2745657f-6ff3-4526-95e1-a4462cc0a062/download67c7de4c21b9f1506f0f0b793850da86MD52trueAnonymousREADdeposita/6582026-03-20T17:40:54.050977Zopen.accessoai:deposita.ibict.br:deposita/658https://deposita.ibict.brRepositório ComumPUBhttp://deposita.ibict.br/oai/requestdeposita@ibict.bropendoar:46582026-03-20T17:40:54Repositório Comum do Brasil - Deposita - Instituto Brasileiro de Informação em Ciência e Tecnologia (Ibict)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 |
| spellingShingle | Os aspectos matemáticos relacionados à média geométrica que emergem a partir da manipulação da escala dos números (1623) elaborada por Edmund Gunter com licenciandos em Matemática Santos, Andressa Gomes dos Média geométrica Interface entre história e ensino Formação de professores de Matemática Ciências Exatas e da Terra |
| status_str | publishedVersion |
| title | Os aspectos matemáticos relacionados à média geométrica que emergem a partir da manipulação da escala dos números (1623) elaborada por Edmund Gunter com licenciandos em Matemática |
| title_full | Os aspectos matemáticos relacionados à média geométrica que emergem a partir da manipulação da escala dos números (1623) elaborada por Edmund Gunter com licenciandos em Matemática |
| title_fullStr | Os aspectos matemáticos relacionados à média geométrica que emergem a partir da manipulação da escala dos números (1623) elaborada por Edmund Gunter com licenciandos em Matemática |
| title_full_unstemmed | Os aspectos matemáticos relacionados à média geométrica que emergem a partir da manipulação da escala dos números (1623) elaborada por Edmund Gunter com licenciandos em Matemática |
| title_short | Os aspectos matemáticos relacionados à média geométrica que emergem a partir da manipulação da escala dos números (1623) elaborada por Edmund Gunter com licenciandos em Matemática |
| title_sort | Os aspectos matemáticos relacionados à média geométrica que emergem a partir da manipulação da escala dos números (1623) elaborada por Edmund Gunter com licenciandos em Matemática |
| topic | Média geométrica Interface entre história e ensino Formação de professores de Matemática Ciências Exatas e da Terra |
| url | https://deposita.ibict.br/handle/deposita/658 |