Uma terapia filosófica da Modelagem Matemática na Educação Matemática
Autor(a) principal: | |
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Data de Publicação: | 2023 |
Tipo de documento: | Tese |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFSCAR |
Texto Completo: | https://repositorio.ufscar.br/handle/ufscar/17499 |
Resumo: | Based on Ludwig Wittgenstein's therapeutic philosophy, the aim is to clarify conceptual confusions that exist in possible images related to what is described about Mathematical Modelling in Mathematics Education as found in dissertations and theses developed in Brazil. The research approach is qualitative, and it is classified as exploratory and bibliographic, when the uses of the linguistic expressions, mathematical modelling and mathematical model are explored in an empirical material constituted by forty-seven Brazilian dissertations and theses from the period 1976 to 2022. The interpretation of the use of these linguistic expressions occurred in the construction of three images: 1) in Modelling, the student discovers mathematics inserted in some extralinguistic reality; 2) the mathematical model is an underlying representation of empirical reality; 3) in Modelling, mathematical knowledge would originate in mental constructions. Inspired by Wittgenstein's therapy, possible clarifications of the conceptual confusions imbricated in these images were initiated. Concerning the first image, two conceptual confusions were verified, indicating that in Modelling the nature of mathematical statements is taken as equal in nature to the statements of the empirical sciences, and the conclusions of the students (rediscoveries or personal discoveries) in Modelling are of empirical nature. As a possible clarification, it is argued that mathematical statements are of a normative nature that enable the understanding of the empirical world. In this sense, the student will be able to do Modelling from the moment he knows the rules of mathematics and of Modelling itself and is able to act guided by these rules. As for the second image, the confusion is that there would be an isomorphism between the mathematical model and the empirical reality. To clarify, it is argued that, from a Wittgensteinian perspective, the mathematical model can be conceived as representation (Darstellung), such as a paradigm, a linguistic object that organizes and gives meaning to empirical experience. As for the third image, the conceptual confusion is that the mathematical knowledge constructed in the Modelling is mental representations (Vorstellungen) of mathematical concepts. It is made explicit that there can be a kind of construction of mathematical knowledge initiated by the various uses of mathematical rules presented to the student. Paying attention to the use of the linguistic expressions mathematical modelling and mathematical model in the empirical material of this research, it is pointed out that in Modelling there is an exclusive use of the referential conception of language related to the empiricist and intuitionist meanings of Mathematics. |
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Costa, Daniana deCaldeira, Ademir Donizetihttp://lattes.cnpq.br/8185048034258055http://lattes.cnpq.br/883818331385102437891bba-f106-49cf-8ef3-3baf4c50f4102023-03-15T11:48:39Z2023-03-15T11:48:39Z2023-02-27COSTA, Daniana de. Uma terapia filosófica da Modelagem Matemática na Educação Matemática. 2023. Tese (Doutorado em Educação) – Universidade Federal de São Carlos, São Carlos, 2023. Disponível em: https://repositorio.ufscar.br/handle/ufscar/17499.https://repositorio.ufscar.br/handle/ufscar/17499Based on Ludwig Wittgenstein's therapeutic philosophy, the aim is to clarify conceptual confusions that exist in possible images related to what is described about Mathematical Modelling in Mathematics Education as found in dissertations and theses developed in Brazil. The research approach is qualitative, and it is classified as exploratory and bibliographic, when the uses of the linguistic expressions, mathematical modelling and mathematical model are explored in an empirical material constituted by forty-seven Brazilian dissertations and theses from the period 1976 to 2022. The interpretation of the use of these linguistic expressions occurred in the construction of three images: 1) in Modelling, the student discovers mathematics inserted in some extralinguistic reality; 2) the mathematical model is an underlying representation of empirical reality; 3) in Modelling, mathematical knowledge would originate in mental constructions. Inspired by Wittgenstein's therapy, possible clarifications of the conceptual confusions imbricated in these images were initiated. Concerning the first image, two conceptual confusions were verified, indicating that in Modelling the nature of mathematical statements is taken as equal in nature to the statements of the empirical sciences, and the conclusions of the students (rediscoveries or personal discoveries) in Modelling are of empirical nature. As a possible clarification, it is argued that mathematical statements are of a normative nature that enable the understanding of the empirical world. In this sense, the student will be able to do Modelling from the moment he knows the rules of mathematics and of Modelling itself and is able to act guided by these rules. As for the second image, the confusion is that there would be an isomorphism between the mathematical model and the empirical reality. To clarify, it is argued that, from a Wittgensteinian perspective, the mathematical model can be conceived as representation (Darstellung), such as a paradigm, a linguistic object that organizes and gives meaning to empirical experience. As for the third image, the conceptual confusion is that the mathematical knowledge constructed in the Modelling is mental representations (Vorstellungen) of mathematical concepts. It is made explicit that there can be a kind of construction of mathematical knowledge initiated by the various uses of mathematical rules presented to the student. Paying attention to the use of the linguistic expressions mathematical modelling and mathematical model in the empirical material of this research, it is pointed out that in Modelling there is an exclusive use of the referential conception of language related to the empiricist and intuitionist meanings of Mathematics.Com base na filosofia terapêutica de Ludwig Wittgenstein, objetiva-se esclarecer confusões conceituais existentes em eventuais imagens vinculadas ao que é descrito sobre a Modelagem Matemática na Educação Matemática conforme encontrado em dissertações e teses desenvolvidas no Brasil. A abordagem da pesquisa é qualitativa e classifica-se como exploratória e bibliográfica, ao serem exploradas os usos das expressões linguísticas, modelagem matemática e modelo matemático em um material empírico constituído por quarenta e sete dissertações e teses brasileiras do período de 1976 a 2022. A interpretação dos usos dessas expressões linguísticas incorreu na construção de três imagens: 1) na Modelagem, o estudante descobre a Matemática inserida em alguma realidade extralinguística; 2) o modelo matemático é uma representação subjacente à realidade empírica; 3) na Modelagem, os conhecimentos matemáticos teriam origem em construções mentais. Sob inspiração da terapia wittgensteiniana, lançaram-se possíveis esclarecimentos sobre as confusões conceituais imbricadas nessas imagens. Quanto à primeira imagem, verificou-se duas confusões conceituais, indicando que, na Modelagem, a natureza dos enunciados matemáticos são tidos como de igual natureza aos enunciados das Ciências Empíricas e as conclusões dos estudantes (redescobertas ou descobertas pessoais) na Modelagem são de natureza empírica. Como possível esclarecimento, é discutido que os enunciados matemáticos são de natureza normativa que possibilitam a compreensão do mundo empírico. Nesse sentido, o estudante poderá fazer Modelagem, a partir do momento que conhecer as regras da Matemática e da própria Modelagem, podendo agir guiado por essas regras. Quanto à segunda imagem, a confusão é que haveria um isomorfismo entre o modelo matemático e a realidade empírica. Como esclarecimento, é argumentado que, considerando uma perspectiva wittgensteiniana, o modelo matemático pode ser concebido como uma representação (Darstellung), tal como um paradigma, um objeto linguístico que organiza, que dá sentido à experiência empírica. Quanto à terceira imagem, a confusão conceitual é que os conhecimentos matemáticos construídos na Modelagem são representações mentais (Vorstellungen) de conceitos matemáticos. É explicitado que pode haver um tipo de construção de conhecimentos matemáticos iniciada pelos diversos usos de regras matemáticas apresentadas ao estudante. Ao atentar para os usos das expressões linguísticas modelagem matemática e modelo matemático no material empírico desta pesquisa, salienta-se que na Modelagem existe um uso exclusivo da concepção referencial da linguagem relacionada às acepções empirista e intuicionista da Matemática na Modelagem.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)porUniversidade Federal de São CarlosCâmpus São CarlosPrograma de Pós-Graduação em Educação - PPGEUFSCarAttribution-NonCommercial-NoDerivs 3.0 Brazilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/openAccessModelagem MatemáticaTerapia filosófica de WittgensteinLinguagemRepresentaçãoConhecimento matemáticoMathematical ModellingWittgenstein's philosophical therapyLanguageRepresentationMathematical knowledgeCIENCIAS HUMANAS::EDUCACAOUma terapia filosófica da Modelagem Matemática na Educação MatemáticaA philosophical therapy of Mathematical Modelling in Mathematics Educationinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesis600600f422515f-1bba-44c8-a931-6b2954cb26e4reponame:Repositório Institucional da UFSCARinstname:Universidade Federal de São Carlos (UFSCAR)instacron:UFSCARORIGINALTese Daniana de Costa_versão revisada.pdfTese Daniana de Costa_versão revisada.pdfTese Daniana de Costaapplication/pdf3068133https://repositorio.ufscar.br/bitstream/ufscar/17499/1/Tese%20Daniana%20de%20Costa_vers%c3%a3o%20revisada.pdf92c21f7df1e78f07479d3cf9a198f752MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8810https://repositorio.ufscar.br/bitstream/ufscar/17499/2/license_rdff337d95da1fce0a22c77480e5e9a7aecMD52TEXTTese Daniana de Costa_versão revisada.pdf.txtTese Daniana de Costa_versão revisada.pdf.txtExtracted texttext/plain460154https://repositorio.ufscar.br/bitstream/ufscar/17499/3/Tese%20Daniana%20de%20Costa_vers%c3%a3o%20revisada.pdf.txtdcd816fd1a638f7a0288b2e76e1ee8feMD53THUMBNAILTese Daniana de Costa_versão revisada.pdf.jpgTese Daniana de Costa_versão revisada.pdf.jpgIM Thumbnailimage/jpeg7079https://repositorio.ufscar.br/bitstream/ufscar/17499/4/Tese%20Daniana%20de%20Costa_vers%c3%a3o%20revisada.pdf.jpga93babd1b63d6a3e6621ec4d369d884dMD54ufscar/174992023-09-18 18:32:33.14oai:repositorio.ufscar.br:ufscar/17499Repositório InstitucionalPUBhttps://repositorio.ufscar.br/oai/requestopendoar:43222023-09-18T18:32:33Repositório Institucional da UFSCAR - Universidade Federal de São Carlos (UFSCAR)false |
dc.title.por.fl_str_mv |
Uma terapia filosófica da Modelagem Matemática na Educação Matemática |
dc.title.alternative.eng.fl_str_mv |
A philosophical therapy of Mathematical Modelling in Mathematics Education |
title |
Uma terapia filosófica da Modelagem Matemática na Educação Matemática |
spellingShingle |
Uma terapia filosófica da Modelagem Matemática na Educação Matemática Costa, Daniana de Modelagem Matemática Terapia filosófica de Wittgenstein Linguagem Representação Conhecimento matemático Mathematical Modelling Wittgenstein's philosophical therapy Language Representation Mathematical knowledge CIENCIAS HUMANAS::EDUCACAO |
title_short |
Uma terapia filosófica da Modelagem Matemática na Educação Matemática |
title_full |
Uma terapia filosófica da Modelagem Matemática na Educação Matemática |
title_fullStr |
Uma terapia filosófica da Modelagem Matemática na Educação Matemática |
title_full_unstemmed |
Uma terapia filosófica da Modelagem Matemática na Educação Matemática |
title_sort |
Uma terapia filosófica da Modelagem Matemática na Educação Matemática |
author |
Costa, Daniana de |
author_facet |
Costa, Daniana de |
author_role |
author |
dc.contributor.authorlattes.por.fl_str_mv |
http://lattes.cnpq.br/8838183313851024 |
dc.contributor.author.fl_str_mv |
Costa, Daniana de |
dc.contributor.advisor1.fl_str_mv |
Caldeira, Ademir Donizeti |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/8185048034258055 |
dc.contributor.authorID.fl_str_mv |
37891bba-f106-49cf-8ef3-3baf4c50f410 |
contributor_str_mv |
Caldeira, Ademir Donizeti |
dc.subject.por.fl_str_mv |
Modelagem Matemática Terapia filosófica de Wittgenstein Linguagem Representação Conhecimento matemático |
topic |
Modelagem Matemática Terapia filosófica de Wittgenstein Linguagem Representação Conhecimento matemático Mathematical Modelling Wittgenstein's philosophical therapy Language Representation Mathematical knowledge CIENCIAS HUMANAS::EDUCACAO |
dc.subject.eng.fl_str_mv |
Mathematical Modelling Wittgenstein's philosophical therapy Language Representation Mathematical knowledge |
dc.subject.cnpq.fl_str_mv |
CIENCIAS HUMANAS::EDUCACAO |
description |
Based on Ludwig Wittgenstein's therapeutic philosophy, the aim is to clarify conceptual confusions that exist in possible images related to what is described about Mathematical Modelling in Mathematics Education as found in dissertations and theses developed in Brazil. The research approach is qualitative, and it is classified as exploratory and bibliographic, when the uses of the linguistic expressions, mathematical modelling and mathematical model are explored in an empirical material constituted by forty-seven Brazilian dissertations and theses from the period 1976 to 2022. The interpretation of the use of these linguistic expressions occurred in the construction of three images: 1) in Modelling, the student discovers mathematics inserted in some extralinguistic reality; 2) the mathematical model is an underlying representation of empirical reality; 3) in Modelling, mathematical knowledge would originate in mental constructions. Inspired by Wittgenstein's therapy, possible clarifications of the conceptual confusions imbricated in these images were initiated. Concerning the first image, two conceptual confusions were verified, indicating that in Modelling the nature of mathematical statements is taken as equal in nature to the statements of the empirical sciences, and the conclusions of the students (rediscoveries or personal discoveries) in Modelling are of empirical nature. As a possible clarification, it is argued that mathematical statements are of a normative nature that enable the understanding of the empirical world. In this sense, the student will be able to do Modelling from the moment he knows the rules of mathematics and of Modelling itself and is able to act guided by these rules. As for the second image, the confusion is that there would be an isomorphism between the mathematical model and the empirical reality. To clarify, it is argued that, from a Wittgensteinian perspective, the mathematical model can be conceived as representation (Darstellung), such as a paradigm, a linguistic object that organizes and gives meaning to empirical experience. As for the third image, the conceptual confusion is that the mathematical knowledge constructed in the Modelling is mental representations (Vorstellungen) of mathematical concepts. It is made explicit that there can be a kind of construction of mathematical knowledge initiated by the various uses of mathematical rules presented to the student. Paying attention to the use of the linguistic expressions mathematical modelling and mathematical model in the empirical material of this research, it is pointed out that in Modelling there is an exclusive use of the referential conception of language related to the empiricist and intuitionist meanings of Mathematics. |
publishDate |
2023 |
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2023-03-15T11:48:39Z |
dc.date.available.fl_str_mv |
2023-03-15T11:48:39Z |
dc.date.issued.fl_str_mv |
2023-02-27 |
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info:eu-repo/semantics/doctoralThesis |
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COSTA, Daniana de. Uma terapia filosófica da Modelagem Matemática na Educação Matemática. 2023. Tese (Doutorado em Educação) – Universidade Federal de São Carlos, São Carlos, 2023. Disponível em: https://repositorio.ufscar.br/handle/ufscar/17499. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufscar.br/handle/ufscar/17499 |
identifier_str_mv |
COSTA, Daniana de. Uma terapia filosófica da Modelagem Matemática na Educação Matemática. 2023. Tese (Doutorado em Educação) – Universidade Federal de São Carlos, São Carlos, 2023. Disponível em: https://repositorio.ufscar.br/handle/ufscar/17499. |
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