Lady Welby, Charles Peirce e a relação entre linguagem e matemática
Autor(a) principal: | |
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Data de Publicação: | 2021 |
Tipo de documento: | Tese |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFMT |
Texto Completo: | http://ri.ufmt.br/handle/1/3543 |
Resumo: | When relating Mathematics and Language, we had as main challenge to understand whether Mathematics is a Language or not. This debate is millenary and, throughout history, it has found great thinkers with consistent theories, some defending that it does, others defending that it does not. However, in the 21st century, after so many discoveries and advances, both in Mathematics and in Language, which side should we, teachers of Mathematics, conduct learning? For such reflection, we base the theoretical foundation of the evolution of Language and Mathematics on the Significant and Semiotic theories of the philosophers Welby and Peirce, respectively, today considered the parents of Modern Semiotics. The research methodology for the development of this thesis was Peirce's Semiotics and the Complementarity Principle in Otte's Mathematics Education. The objective of this study was to investigate, from an epistemological and semiotic point of view, what mathematical objects are, what reality they belong to and how language and mathematics have been related over time. In an eagerness to always seek to contextualize the facts, we present our protagonists, their personalities, their works, their desires and how much they still contribute significantly to science; we show that the meanings of objects, including mathematical objects, oscillated according to the beliefs of each era; we point out the factors that promoted the changes in the meanings of things; we highlight the similarities and differences between the semiotic theories of Peirce and Welby, proving that Language and Mathematics are two (important and different) references of Mathematical Education; we demonstrate that interpretation is the same as representation and it is the relationships that define objects and transform them into signs. We argue that the teacher, when understanding the relationship and the difference between Language and Mathematics, will realize that knowledge depends on concepts and intuitions, as Kant defended, and, interpreting this in terms of complementarity, as taught by Peirce and Otte, we conclude that Mathematics is not a language but an activity that involves thoughts, concepts, abstractions, representations, which are always in tune, or would need to be, because the object of Mathematics ceases to be the sign itself to assume semiotic behavior, that is, it would not be possible to work with signs without having access to them, as signs can serve both to think about objects and mathematical representations and to represent the result of an analysis. Through Modern Semiotics, we had the opportunity to understand, for example, that both Pure Mathematics and Applied Mathematics are essential, although distinct, and the complementarity makes them even greater, as well as Mathematics and Language. In this way, the human being only knows the world because, in some way, he represents it and only interprets that representation in another representation. For this reason, a sign is something whose knowledge depends on what is represented by it and, then, it will make sense for the study of Mathematics if we finally consider that science develops linked to the culture, customs, economics and needs of each society. |
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Lady Welby, Charles Peirce e a relação entre linguagem e matemáticaLady WelbyCharles PeirceLinguagemEducação matemáticaSemióticaComplementaridadeCNPQ::CIENCIAS HUMANAS::EDUCACAOLady WelbyCharles PeirceLanguageMathematics educationSemioticsComplementarityWhen relating Mathematics and Language, we had as main challenge to understand whether Mathematics is a Language or not. This debate is millenary and, throughout history, it has found great thinkers with consistent theories, some defending that it does, others defending that it does not. However, in the 21st century, after so many discoveries and advances, both in Mathematics and in Language, which side should we, teachers of Mathematics, conduct learning? For such reflection, we base the theoretical foundation of the evolution of Language and Mathematics on the Significant and Semiotic theories of the philosophers Welby and Peirce, respectively, today considered the parents of Modern Semiotics. The research methodology for the development of this thesis was Peirce's Semiotics and the Complementarity Principle in Otte's Mathematics Education. The objective of this study was to investigate, from an epistemological and semiotic point of view, what mathematical objects are, what reality they belong to and how language and mathematics have been related over time. In an eagerness to always seek to contextualize the facts, we present our protagonists, their personalities, their works, their desires and how much they still contribute significantly to science; we show that the meanings of objects, including mathematical objects, oscillated according to the beliefs of each era; we point out the factors that promoted the changes in the meanings of things; we highlight the similarities and differences between the semiotic theories of Peirce and Welby, proving that Language and Mathematics are two (important and different) references of Mathematical Education; we demonstrate that interpretation is the same as representation and it is the relationships that define objects and transform them into signs. We argue that the teacher, when understanding the relationship and the difference between Language and Mathematics, will realize that knowledge depends on concepts and intuitions, as Kant defended, and, interpreting this in terms of complementarity, as taught by Peirce and Otte, we conclude that Mathematics is not a language but an activity that involves thoughts, concepts, abstractions, representations, which are always in tune, or would need to be, because the object of Mathematics ceases to be the sign itself to assume semiotic behavior, that is, it would not be possible to work with signs without having access to them, as signs can serve both to think about objects and mathematical representations and to represent the result of an analysis. Through Modern Semiotics, we had the opportunity to understand, for example, that both Pure Mathematics and Applied Mathematics are essential, although distinct, and the complementarity makes them even greater, as well as Mathematics and Language. In this way, the human being only knows the world because, in some way, he represents it and only interprets that representation in another representation. For this reason, a sign is something whose knowledge depends on what is represented by it and, then, it will make sense for the study of Mathematics if we finally consider that science develops linked to the culture, customs, economics and needs of each society.Ao relacionar Matemática e Linguagem, tivemos como principal desafio compreender se a Matemática é, ou não, uma Linguagem. Esse debate é milenar e, ao longo da história, encontrou grandes pensadores com teorias consistentes, alguns defendendo que sim, outros defendendo que não. Entretanto, no século XXI, depois de tantas descobertas e avanços, tanto na Matemática quanto na Linguagem, de qual lado, nós, professores de Matemática, devemos conduzir a aprendizagem? Para tal reflexão, calcamos a fundamentação teórica das evoluções da Linguagem e da Matemática nas teorias Significs e Semiótica dos filósofos Welby e Peirce, respectivamente, hoje considerados os pais da Semiótica Moderna. As metodologias de pesquisa para o desenvolvimento desta tese foram a Semiótica de Peirce e o Princípio da Complementaridade na Educação Matemática de Otte. Investigar, do ponto de vista semiótico, o que são objetos matemáticos, a qual realidade eles pertencem e como a Linguagem e a Matemática vem se relacionando ao longo dos tempos, foi o objetivo deste estudo. Na ânsia de sempre buscar a contextualização dos fatos, apresentamos nossos protagonistas, suas personalidades, seus trabalhos, seus anseios e quanto ainda eles contribuem significativamente com a ciência; mostramos que os significados dos objetos, inclusive dos objetos matemáticos, foram oscilando de acordo com as crenças de cada época; apontamos os fatores que promoveram as mudanças dos significados das coisas; ressaltamos as semelhanças e diferenças entre as teorias semióticas de Peirce e de Welby, provando que Linguagem e Matemática são dois referenciais (importantes e diferentes) da Educação Matemática; demonstramos que interpretação é o mesmo que representação e são as relações que definem os objetos e os transformam em signos. Defendemos que o professor, ao compreender a relação e a diferença entre Linguagem e Matemática, perceberá que o conhecimento depende dos conceitos e das intuições, como defendia Kant, e, interpretando isso em termos de complementaridade, conforme nos ensina Peirce e Otte, concluímos que a Matemática não é uma linguagem e sim uma atividade que envolve pensamentos, conceitos, abstrações, representações, que estão sempre em sintonia, ou precisariam estar, porque o objeto da Matemática deixa de ser o próprio signo para assumir o comportamento semiótico, ou seja, não seria possível trabalhar com signos sem ter acesso a eles, pois os signos podem servir tanto para pensar sobre os objetos e as representações matemáticas como para representar o resultado de uma análise. Por meio da Semiótica Moderna, tivemos a oportunidade de compreender, por exemplo, que tanto a Matemática Pura quanto a Matemática Aplicada são essenciais, apesar de distintas, e a complementaridade as tornam maiores ainda, assim como a Matemática e a Linguagem. Dessa forma, o ser humano só conhece o mundo porque, de alguma forma, o representa e só interpreta essa representação numa outra representação. Por isso, signo é uma coisa de cujo conhecimento depende daquilo que é representado por ele e, então, haverá sentido para o estudo da Matemática se finalmente considerarmos que a ciência se desenvolve atrelada à cultura, aos costumes, à economia e às necessidades de cada sociedade.Universidade Federal de Mato GrossoBrasilInstituto de Educação (IE)UFMT CUC - CuiabáPrograma de Pós-Graduação em EducaçãoOtte, Michael Friedrichhttp://lattes.cnpq.br/1670481682966837Otte, Michael Friedrich190.244.267-71http://lattes.cnpq.br/1670481682966837Wielewski, Gladys Denise502.478.161-91http://lattes.cnpq.br/4154014326253864190.244.267-71Mansilla, Débora Eriléia Pedrotti569.620.701-44http://lattes.cnpq.br/7018286591963865Campos, Tânia Maria Mendonça044.859.558-34http://lattes.cnpq.br/1392227308859320Pietropaolo, Ruy César301.395.548-15http://lattes.cnpq.br/2747970094543043Alonso, Kátia Morosov654.466.741-20http://lattes.cnpq.br/3326858103129656Paula, Luciene de2022-10-06T17:07:18Z2021-03-042022-10-06T17:07:18Z2021-03-02info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisPAULA, Luciene de. Lady Welby, Charles Peirce e a relação entre linguagem e matemática. 2021. 284 f. Tese (Doutorado em Educação) - Universidade Federal de Mato Grosso, Instituto de Educação, Cuiabá, 2021.http://ri.ufmt.br/handle/1/3543porinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFMTinstname:Universidade Federal de Mato Grosso (UFMT)instacron:UFMT2022-10-07T07:03:08Zoai:localhost:1/3543Repositório InstitucionalPUBhttp://ri.ufmt.br/oai/requestjordanbiblio@gmail.comopendoar:2022-10-07T07:03:08Repositório Institucional da UFMT - Universidade Federal de Mato Grosso (UFMT)false |
dc.title.none.fl_str_mv |
Lady Welby, Charles Peirce e a relação entre linguagem e matemática |
title |
Lady Welby, Charles Peirce e a relação entre linguagem e matemática |
spellingShingle |
Lady Welby, Charles Peirce e a relação entre linguagem e matemática Paula, Luciene de Lady Welby Charles Peirce Linguagem Educação matemática Semiótica Complementaridade CNPQ::CIENCIAS HUMANAS::EDUCACAO Lady Welby Charles Peirce Language Mathematics education Semiotics Complementarity |
title_short |
Lady Welby, Charles Peirce e a relação entre linguagem e matemática |
title_full |
Lady Welby, Charles Peirce e a relação entre linguagem e matemática |
title_fullStr |
Lady Welby, Charles Peirce e a relação entre linguagem e matemática |
title_full_unstemmed |
Lady Welby, Charles Peirce e a relação entre linguagem e matemática |
title_sort |
Lady Welby, Charles Peirce e a relação entre linguagem e matemática |
author |
Paula, Luciene de |
author_facet |
Paula, Luciene de |
author_role |
author |
dc.contributor.none.fl_str_mv |
Otte, Michael Friedrich http://lattes.cnpq.br/1670481682966837 Otte, Michael Friedrich 190.244.267-71 http://lattes.cnpq.br/1670481682966837 Wielewski, Gladys Denise 502.478.161-91 http://lattes.cnpq.br/4154014326253864 190.244.267-71 Mansilla, Débora Eriléia Pedrotti 569.620.701-44 http://lattes.cnpq.br/7018286591963865 Campos, Tânia Maria Mendonça 044.859.558-34 http://lattes.cnpq.br/1392227308859320 Pietropaolo, Ruy César 301.395.548-15 http://lattes.cnpq.br/2747970094543043 Alonso, Kátia Morosov 654.466.741-20 http://lattes.cnpq.br/3326858103129656 |
dc.contributor.author.fl_str_mv |
Paula, Luciene de |
dc.subject.por.fl_str_mv |
Lady Welby Charles Peirce Linguagem Educação matemática Semiótica Complementaridade CNPQ::CIENCIAS HUMANAS::EDUCACAO Lady Welby Charles Peirce Language Mathematics education Semiotics Complementarity |
topic |
Lady Welby Charles Peirce Linguagem Educação matemática Semiótica Complementaridade CNPQ::CIENCIAS HUMANAS::EDUCACAO Lady Welby Charles Peirce Language Mathematics education Semiotics Complementarity |
description |
When relating Mathematics and Language, we had as main challenge to understand whether Mathematics is a Language or not. This debate is millenary and, throughout history, it has found great thinkers with consistent theories, some defending that it does, others defending that it does not. However, in the 21st century, after so many discoveries and advances, both in Mathematics and in Language, which side should we, teachers of Mathematics, conduct learning? For such reflection, we base the theoretical foundation of the evolution of Language and Mathematics on the Significant and Semiotic theories of the philosophers Welby and Peirce, respectively, today considered the parents of Modern Semiotics. The research methodology for the development of this thesis was Peirce's Semiotics and the Complementarity Principle in Otte's Mathematics Education. The objective of this study was to investigate, from an epistemological and semiotic point of view, what mathematical objects are, what reality they belong to and how language and mathematics have been related over time. In an eagerness to always seek to contextualize the facts, we present our protagonists, their personalities, their works, their desires and how much they still contribute significantly to science; we show that the meanings of objects, including mathematical objects, oscillated according to the beliefs of each era; we point out the factors that promoted the changes in the meanings of things; we highlight the similarities and differences between the semiotic theories of Peirce and Welby, proving that Language and Mathematics are two (important and different) references of Mathematical Education; we demonstrate that interpretation is the same as representation and it is the relationships that define objects and transform them into signs. We argue that the teacher, when understanding the relationship and the difference between Language and Mathematics, will realize that knowledge depends on concepts and intuitions, as Kant defended, and, interpreting this in terms of complementarity, as taught by Peirce and Otte, we conclude that Mathematics is not a language but an activity that involves thoughts, concepts, abstractions, representations, which are always in tune, or would need to be, because the object of Mathematics ceases to be the sign itself to assume semiotic behavior, that is, it would not be possible to work with signs without having access to them, as signs can serve both to think about objects and mathematical representations and to represent the result of an analysis. Through Modern Semiotics, we had the opportunity to understand, for example, that both Pure Mathematics and Applied Mathematics are essential, although distinct, and the complementarity makes them even greater, as well as Mathematics and Language. In this way, the human being only knows the world because, in some way, he represents it and only interprets that representation in another representation. For this reason, a sign is something whose knowledge depends on what is represented by it and, then, it will make sense for the study of Mathematics if we finally consider that science develops linked to the culture, customs, economics and needs of each society. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-03-04 2021-03-02 2022-10-06T17:07:18Z 2022-10-06T17:07:18Z |
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info:eu-repo/semantics/publishedVersion |
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info:eu-repo/semantics/doctoralThesis |
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doctoralThesis |
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publishedVersion |
dc.identifier.uri.fl_str_mv |
PAULA, Luciene de. Lady Welby, Charles Peirce e a relação entre linguagem e matemática. 2021. 284 f. Tese (Doutorado em Educação) - Universidade Federal de Mato Grosso, Instituto de Educação, Cuiabá, 2021. http://ri.ufmt.br/handle/1/3543 |
identifier_str_mv |
PAULA, Luciene de. Lady Welby, Charles Peirce e a relação entre linguagem e matemática. 2021. 284 f. Tese (Doutorado em Educação) - Universidade Federal de Mato Grosso, Instituto de Educação, Cuiabá, 2021. |
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http://ri.ufmt.br/handle/1/3543 |
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Universidade Federal de Mato Grosso Brasil Instituto de Educação (IE) UFMT CUC - Cuiabá Programa de Pós-Graduação em Educação |
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Universidade Federal de Mato Grosso Brasil Instituto de Educação (IE) UFMT CUC - Cuiabá Programa de Pós-Graduação em Educação |
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