Epistemology and rationality of intuition and imagination in the field of mathematics

Detalhes bibliográficos
Autor(a) principal: Cifuentes, José Carlos
Data de Publicação: 2020
Outros Autores: Gusmão, Lucimar Donizete
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Revista Pesquisa Qualitativa (Online)
Texto Completo: https://editora.sepq.org.br/rpq/article/view/342
Resumo: This paper aims to contribute to the clarification of the role of mathematical intuition and imagination in the constitution of mathematical knowledge, evidencing its epistemological and procedural characteristics. For that, an "epistemology of intuition and imagination" in the field of mathematics is outlined (suggested) emphasizing the need to adopt a dynamic conception of mathematics. In this context, intuition and imagination present themselves as forms of mathematical experience that give access, through paths that are not purely logical, to mathematical knowledge. Its epistemological and rationality characteristics, a rational of a non-logical nature, are highlighted by several examples, resources for moving the ideas involved. The epistemological study of intuition and imagination also allows highlighting its ontology, constituted of more relations than objects. From the pedagogical point of view, we discuss the formative character of philosophical studies involving intuition and imagination, mainly related to creativity in mathematics. Keywords: Mathematical knowledge; Mathematical experience; Epistemology of intuition and imagination; Creativity in mathematics.
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spelling Epistemology and rationality of intuition and imagination in the field of mathematicsEpistemologia e racionalidade da intuição e da imaginação no campo da matemáticaThis paper aims to contribute to the clarification of the role of mathematical intuition and imagination in the constitution of mathematical knowledge, evidencing its epistemological and procedural characteristics. For that, an "epistemology of intuition and imagination" in the field of mathematics is outlined (suggested) emphasizing the need to adopt a dynamic conception of mathematics. In this context, intuition and imagination present themselves as forms of mathematical experience that give access, through paths that are not purely logical, to mathematical knowledge. Its epistemological and rationality characteristics, a rational of a non-logical nature, are highlighted by several examples, resources for moving the ideas involved. The epistemological study of intuition and imagination also allows highlighting its ontology, constituted of more relations than objects. From the pedagogical point of view, we discuss the formative character of philosophical studies involving intuition and imagination, mainly related to creativity in mathematics. Keywords: Mathematical knowledge; Mathematical experience; Epistemology of intuition and imagination; Creativity in mathematics.Este artigo visa contribuir ao esclarecimento do papel da intuição e da imaginação matemáticas na constituição do conhecimento matemático, evidenciando suas características epistemológicas e procedimentais. Para tanto, uma “epistemologia da intuição e da imaginação” no campo da matemática é esboçada (sugerida) enfatizando a necessidade de adotar uma concepção dinâmica de matemática. Nesse contexto, a intuição e a imaginação são apresentadas como formas de experiência matemática que dão acesso, através de caminhos não puramente lógicos, ao conhecimento matemático. Suas características epistemológicas e de racionalidade, um racional de natureza não lógica, são evidenciadas por meio de diversos exemplos, fontes que movimentam as ideias envolvidas. O estudo epistemológico da intuição e da imaginação permite também evidenciar sua ontologia, constituída esta mais de relações do que de objetos. Do ponto de vista pedagógico, discutimos o caráter formativo dos estudos filosóficos, envolvendo intuição e imaginação, principalmente relacionado com a criatividade em matemática. Palavras-chave: Conhecimento matemático; Experiência matemática; Epistemologia da intuição e da imaginação; Criatividade em matemática.Sociedade de Estudos e Pesquisas Qualitativos - SE&PQ2020-10-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://editora.sepq.org.br/rpq/article/view/34210.33361/RPQ.2020.v.8.n.18.342Qualitative Research Journal ; Vol. 8 No. 18 (2020): Special Number: Philosophy of Mathematics; 503-523Revista Pesquisa Qualitativa; v. 8 n. 18 (2020): Edição Especial: Filosofia da Matemática; 503-5232525-82221809-025710.33361/RPQ.v.8.n.18reponame:Revista Pesquisa Qualitativa (Online)instname:Sociedade Brasileira de Estudos e Pesquisa Qualitativos (SE&PQ)instacron:SE&PQenghttps://editora.sepq.org.br/rpq/article/view/342/216Copyright (c) 2020 Revista Pesquisa Qualitativahttps://creativecommons.org/licenses/by/4.0info:eu-repo/semantics/openAccessCifuentes, José Carlos Gusmão, Lucimar Donizete 2022-01-29T23:21:45Zoai:editora.sepq.org.br:article/342Revistahttps://editora.sepq.org.br/index.php/rpq/indexONGhttps://editora.sepq.org.br/index.php/rpq/oai||revista.rpq@gmail.com2525-82221809-0257opendoar:2022-01-29T23:21:45Revista Pesquisa Qualitativa (Online) - Sociedade Brasileira de Estudos e Pesquisa Qualitativos (SE&PQ)false
dc.title.none.fl_str_mv Epistemology and rationality of intuition and imagination in the field of mathematics
Epistemologia e racionalidade da intuição e da imaginação no campo da matemática
title Epistemology and rationality of intuition and imagination in the field of mathematics
spellingShingle Epistemology and rationality of intuition and imagination in the field of mathematics
Cifuentes, José Carlos
title_short Epistemology and rationality of intuition and imagination in the field of mathematics
title_full Epistemology and rationality of intuition and imagination in the field of mathematics
title_fullStr Epistemology and rationality of intuition and imagination in the field of mathematics
title_full_unstemmed Epistemology and rationality of intuition and imagination in the field of mathematics
title_sort Epistemology and rationality of intuition and imagination in the field of mathematics
author Cifuentes, José Carlos
author_facet Cifuentes, José Carlos
Gusmão, Lucimar Donizete
author_role author
author2 Gusmão, Lucimar Donizete
author2_role author
dc.contributor.author.fl_str_mv Cifuentes, José Carlos
Gusmão, Lucimar Donizete
description This paper aims to contribute to the clarification of the role of mathematical intuition and imagination in the constitution of mathematical knowledge, evidencing its epistemological and procedural characteristics. For that, an "epistemology of intuition and imagination" in the field of mathematics is outlined (suggested) emphasizing the need to adopt a dynamic conception of mathematics. In this context, intuition and imagination present themselves as forms of mathematical experience that give access, through paths that are not purely logical, to mathematical knowledge. Its epistemological and rationality characteristics, a rational of a non-logical nature, are highlighted by several examples, resources for moving the ideas involved. The epistemological study of intuition and imagination also allows highlighting its ontology, constituted of more relations than objects. From the pedagogical point of view, we discuss the formative character of philosophical studies involving intuition and imagination, mainly related to creativity in mathematics. Keywords: Mathematical knowledge; Mathematical experience; Epistemology of intuition and imagination; Creativity in mathematics.
publishDate 2020
dc.date.none.fl_str_mv 2020-10-07
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
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status_str publishedVersion
dc.identifier.uri.fl_str_mv https://editora.sepq.org.br/rpq/article/view/342
10.33361/RPQ.2020.v.8.n.18.342
url https://editora.sepq.org.br/rpq/article/view/342
identifier_str_mv 10.33361/RPQ.2020.v.8.n.18.342
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv https://editora.sepq.org.br/rpq/article/view/342/216
dc.rights.driver.fl_str_mv Copyright (c) 2020 Revista Pesquisa Qualitativa
https://creativecommons.org/licenses/by/4.0
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Copyright (c) 2020 Revista Pesquisa Qualitativa
https://creativecommons.org/licenses/by/4.0
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Sociedade de Estudos e Pesquisas Qualitativos - SE&PQ
publisher.none.fl_str_mv Sociedade de Estudos e Pesquisas Qualitativos - SE&PQ
dc.source.none.fl_str_mv Qualitative Research Journal ; Vol. 8 No. 18 (2020): Special Number: Philosophy of Mathematics; 503-523
Revista Pesquisa Qualitativa; v. 8 n. 18 (2020): Edição Especial: Filosofia da Matemática; 503-523
2525-8222
1809-0257
10.33361/RPQ.v.8.n.18
reponame:Revista Pesquisa Qualitativa (Online)
instname:Sociedade Brasileira de Estudos e Pesquisa Qualitativos (SE&PQ)
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instname_str Sociedade Brasileira de Estudos e Pesquisa Qualitativos (SE&PQ)
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reponame_str Revista Pesquisa Qualitativa (Online)
collection Revista Pesquisa Qualitativa (Online)
repository.name.fl_str_mv Revista Pesquisa Qualitativa (Online) - Sociedade Brasileira de Estudos e Pesquisa Qualitativos (SE&PQ)
repository.mail.fl_str_mv ||revista.rpq@gmail.com
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