Teaching and learning of calculus: exploring the three worlds of Mathematics

Detalhes bibliográficos
Autor(a) principal: Bueno, Rafael Winícius da Silva
Data de Publicação: 2021
Outros Autores: Viali, Lori
Tipo de documento: Artigo
Idioma: por
Título da fonte: Olhar de Professor (Online)
Texto Completo: https://revistas.uepg.br/index.php/olhardeprofessor/article/view/16896
Resumo: This paper brings a theoretical investigation, in a qualitative perspective, understood as a bibliographic study, developed with the objective to describe the Three Worlds of Mathematics theory, proposed by David Tall, and connect it with relevant aspects to the teaching and learning of Calculus. In this sense a general view was built on the Conceptual Embodied, Operational Symbolic and Formal Axiomatic worlds and that are related specifically with this mathematical knowledge field were presented. The results led to the conclusion that in opposition to the mechanical and repetitive process used to calculate limits, derivatives and integrals that an alternative pedagogical approach can be built. In this regard, a suggestion is made for the introduction of the study of Calculus starting from met-before related to geometry, arithmetic and algebra, that belong to embodied and symbolic reality, perceived in the worlds inhabited by the students that are starting their path at the university.
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spelling Teaching and learning of calculus: exploring the three worlds of MathematicsEnseñanza y aprendizaje del cálculo: explorando los tres mundos de las MatemáticasEnsino e aprendizagem de cálculo: explorando os três mundos da Matemáticatrês mundos da matemáticaeducação superiorcálculo diferencial e integralThree worlds of mathematics. Higher education. Calculus.: Tres mundos de las matemáticas. Enseñanza superior. Cálculo.This paper brings a theoretical investigation, in a qualitative perspective, understood as a bibliographic study, developed with the objective to describe the Three Worlds of Mathematics theory, proposed by David Tall, and connect it with relevant aspects to the teaching and learning of Calculus. In this sense a general view was built on the Conceptual Embodied, Operational Symbolic and Formal Axiomatic worlds and that are related specifically with this mathematical knowledge field were presented. The results led to the conclusion that in opposition to the mechanical and repetitive process used to calculate limits, derivatives and integrals that an alternative pedagogical approach can be built. In this regard, a suggestion is made for the introduction of the study of Calculus starting from met-before related to geometry, arithmetic and algebra, that belong to embodied and symbolic reality, perceived in the worlds inhabited by the students that are starting their path at the university.El presente trabajo presenta una investigación teórica cualitativa, caracterizada como un estudio bibliográfico, realizada con el objetivo de describir la teoría de los Tres Mundos de las Matemáticas, propuesta por David Tall, y conectarla con aspectos relevantes para la enseñanza del Cálculo Diferencial e Integral. Con esa intención, se construyó una visión general de los mundos Conceptual Corporificado, Operativo Simbólico y Axiomático Formal. A continuación, se plantearon ideas inherentes a la teoría y centradas en el estudio de los conceptos fundamentales de este campo del conocimiento matemático. Se observó, en oposición a los procesos mecánicos e repetitivos, habituales en el cálculo de límites, derivadas e integrales de funciones reales, que se puede construir un enfoque pedagógico alternativo. Por ello, se sugiere introducir el estudio del Cálculo a partir de geometría, aritmética y álgebra, que pertenecen a la realidad corpórea y simbólica, vislumbradas en los mundos habitualmente habitados por estudiantes que ingresan a la educación superior.Este artigo traz uma pesquisa teórica, de cunho qualitativo, caracterizada como um estudo bibliográfico, realizada com o objetivo de descrever a teoria dos Três Mundos da Matemática, proposta por David Tall, e conectá-la com aspectos relevantes para o ensino e a aprendizagem de Cálculo. Nesse sentido, foi construído um panorama geral sobre os mundos Conceitual Corporificado, Operacional Simbólico e Formal Axiomático e foram trazidas ideias inerentes à teoria e voltadas para o estudo de conceitos desse campo do conhecimento. Percebeu-se, em oposição aos usuais processos mecânicos e repetitivos usados para o cálculo de limites, derivadas e integrais, que uma abordagem pedagógica alternativa pode ser construída. Dessa forma, sugere-se introduzir o estudo do Cálculo a partir de já-encontrados da geometria, da aritmética e da álgebra, que pertencem à realidade corpórea e simbólica, vislumbrada nos mundos habitados pelos acadêmicos que ingressam no Ensino Superior.Editora UEPG2021-06-26info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionPDF TextTexto PDFTexto PDFapplication/pdftext/xmlapplication/ziphttps://revistas.uepg.br/index.php/olhardeprofessor/article/view/1689610.5212/OlharProfr.v.24.16896.068Olhar de Professor; Bd. 24 (2021): Publicação Contínua; 1-20Olhar de Professor; Vol. 24 (2021): Continuous Publishing; 1-20Olhar de Professor; Vol. 24 (2021): Publicación Continua; 1-20Olhar de Professor; Vol. 24 (2021): Publicação Contínua; 1-20Olhar de Professor; v. 24 (2021): Publicação Contínua; 1-201984-01871518-5648reponame:Olhar de Professor (Online)instname:Universidade Estadual de Ponta Grossa (UEPG)instacron:UEPGporhttps://revistas.uepg.br/index.php/olhardeprofessor/article/view/16896/209209214441https://revistas.uepg.br/index.php/olhardeprofessor/article/view/16896/209209215759https://revistas.uepg.br/index.php/olhardeprofessor/article/view/16896/209209215783Copyright (c) 2021 Rafael Winícius da Silva Bueno, Lori Vialiinfo:eu-repo/semantics/openAccessBueno, Rafael Winícius da SilvaViali, Lori2022-03-10T19:53:58Zoai:uepg.br:article/16896Revistahttps://revistas2.uepg.br/index.php/olhardeprofessor/indexPUBhttps://revistas2.uepg.br/index.php/olhardeprofessor/oaiolhardeprofessor@uepg.br||1984-01871518-5648opendoar:2022-03-10T19:53:58Olhar de Professor (Online) - Universidade Estadual de Ponta Grossa (UEPG)false
dc.title.none.fl_str_mv Teaching and learning of calculus: exploring the three worlds of Mathematics
Enseñanza y aprendizaje del cálculo: explorando los tres mundos de las Matemáticas
Ensino e aprendizagem de cálculo: explorando os três mundos da Matemática
title Teaching and learning of calculus: exploring the three worlds of Mathematics
spellingShingle Teaching and learning of calculus: exploring the three worlds of Mathematics
Bueno, Rafael Winícius da Silva
três mundos da matemática
educação superior
cálculo diferencial e integral
Three worlds of mathematics. Higher education. Calculus.
: Tres mundos de las matemáticas. Enseñanza superior. Cálculo.
title_short Teaching and learning of calculus: exploring the three worlds of Mathematics
title_full Teaching and learning of calculus: exploring the three worlds of Mathematics
title_fullStr Teaching and learning of calculus: exploring the three worlds of Mathematics
title_full_unstemmed Teaching and learning of calculus: exploring the three worlds of Mathematics
title_sort Teaching and learning of calculus: exploring the three worlds of Mathematics
author Bueno, Rafael Winícius da Silva
author_facet Bueno, Rafael Winícius da Silva
Viali, Lori
author_role author
author2 Viali, Lori
author2_role author
dc.contributor.author.fl_str_mv Bueno, Rafael Winícius da Silva
Viali, Lori
dc.subject.por.fl_str_mv três mundos da matemática
educação superior
cálculo diferencial e integral
Three worlds of mathematics. Higher education. Calculus.
: Tres mundos de las matemáticas. Enseñanza superior. Cálculo.
topic três mundos da matemática
educação superior
cálculo diferencial e integral
Three worlds of mathematics. Higher education. Calculus.
: Tres mundos de las matemáticas. Enseñanza superior. Cálculo.
description This paper brings a theoretical investigation, in a qualitative perspective, understood as a bibliographic study, developed with the objective to describe the Three Worlds of Mathematics theory, proposed by David Tall, and connect it with relevant aspects to the teaching and learning of Calculus. In this sense a general view was built on the Conceptual Embodied, Operational Symbolic and Formal Axiomatic worlds and that are related specifically with this mathematical knowledge field were presented. The results led to the conclusion that in opposition to the mechanical and repetitive process used to calculate limits, derivatives and integrals that an alternative pedagogical approach can be built. In this regard, a suggestion is made for the introduction of the study of Calculus starting from met-before related to geometry, arithmetic and algebra, that belong to embodied and symbolic reality, perceived in the worlds inhabited by the students that are starting their path at the university.
publishDate 2021
dc.date.none.fl_str_mv 2021-06-26
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
PDF Text
Texto PDF
Texto PDF
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://revistas.uepg.br/index.php/olhardeprofessor/article/view/16896
10.5212/OlharProfr.v.24.16896.068
url https://revistas.uepg.br/index.php/olhardeprofessor/article/view/16896
identifier_str_mv 10.5212/OlharProfr.v.24.16896.068
dc.language.iso.fl_str_mv por
language por
dc.relation.none.fl_str_mv https://revistas.uepg.br/index.php/olhardeprofessor/article/view/16896/209209214441
https://revistas.uepg.br/index.php/olhardeprofessor/article/view/16896/209209215759
https://revistas.uepg.br/index.php/olhardeprofessor/article/view/16896/209209215783
dc.rights.driver.fl_str_mv Copyright (c) 2021 Rafael Winícius da Silva Bueno, Lori Viali
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Copyright (c) 2021 Rafael Winícius da Silva Bueno, Lori Viali
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
text/xml
application/zip
dc.publisher.none.fl_str_mv Editora UEPG
publisher.none.fl_str_mv Editora UEPG
dc.source.none.fl_str_mv Olhar de Professor; Bd. 24 (2021): Publicação Contínua; 1-20
Olhar de Professor; Vol. 24 (2021): Continuous Publishing; 1-20
Olhar de Professor; Vol. 24 (2021): Publicación Continua; 1-20
Olhar de Professor; Vol. 24 (2021): Publicação Contínua; 1-20
Olhar de Professor; v. 24 (2021): Publicação Contínua; 1-20
1984-0187
1518-5648
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reponame_str Olhar de Professor (Online)
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repository.mail.fl_str_mv olhardeprofessor@uepg.br||
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