Um estudo do tratado das fluxões de Colin Maclaurin e suasconexões com o ensino de cálculo diferencial e integral
In this paper we present our reflections on a two-volume study of Colin Maclaurin's A Treatise of Fluxions and its connections to the teaching of differential and integral calculus, published in 1742. It is intended to support the thesis that the conceptual approaches present in these books by...
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Colin Maclaurin Tratado das fluxões História do cálculo diferencial e integral CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
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Colin Maclaurin Tratado das fluxões História do cálculo diferencial e integral CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA Soares, Evanildo Costa Um estudo do tratado das fluxões de Colin Maclaurin e suasconexões com o ensino de cálculo diferencial e integral |
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In this paper we present our reflections on a two-volume study of Colin Maclaurin's A Treatise of Fluxions and its connections to the teaching of differential and integral calculus, published in 1742. It is intended to support the thesis that the conceptual approaches present in these books by Maclaurin can subsidize the organization of historical sequences associated with the calculus content, to be connected as a complementary approach to the textbooks, in the restructuring of the ways of processing the teaching of differential calculus and fulltime in undergraduate courses in Mathematics. To develop the historical investigation, we
examined the work, in the various aspects related to the construction of the history of differential and integral calculus, focusing our attention on the logical foundations of the fluxional method idealized by Isaac Newton and, later, improved and expanded by Colin Maclaurin. The epistemological analysis involved the concept of fluxion and its implications in the consolidation of the derived idea, properties, rules and demonstrations, which became known as the direct method of fluxion. From this approach on the study of derivatives through the
fluxional method, aspects emerged concerning the formalization of the study on the notion
of integral, its methods, rules and properties, known as the inverse method. At the end of the
research, we concluded that the potentialization and conceptual identity of calculus based
on the study of the fluxional method can serve as subsidies for the conceptual training of
future Mathematics teachers, to achieve a comprehensive learning of this subject, which
later can unfold in the improvement of the teaching and learning process of differential and
integral calculus, in order to re-signify and complement the conceptual approach present in
calculus books, and thus strengthen the understanding of the concepts necessary for learning analysis, in the study of differential calculus and integral part of undergraduate courses
in Mathematics. |
| author2 |
Mendes, Iran Abreu |
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Mendes, Iran Abreu Soares, Evanildo Costa |
| format |
doctoralThesis |
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Soares, Evanildo Costa |
| author_sort |
Soares, Evanildo Costa |
| title |
Um estudo do tratado das fluxões de Colin Maclaurin e suasconexões com o ensino de cálculo diferencial e integral |
| title_short |
Um estudo do tratado das fluxões de Colin Maclaurin e suasconexões com o ensino de cálculo diferencial e integral |
| title_full |
Um estudo do tratado das fluxões de Colin Maclaurin e suasconexões com o ensino de cálculo diferencial e integral |
| title_fullStr |
Um estudo do tratado das fluxões de Colin Maclaurin e suasconexões com o ensino de cálculo diferencial e integral |
| title_full_unstemmed |
Um estudo do tratado das fluxões de Colin Maclaurin e suasconexões com o ensino de cálculo diferencial e integral |
| title_sort |
um estudo do tratado das fluxões de colin maclaurin e suasconexões com o ensino de cálculo diferencial e integral |
| publisher |
Universidade Federal do Rio Grande do Norte |
| publishDate |
2024 |
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https://repositorio.ufrn.br/handle/123456789/57419 |
| work_keys_str_mv |
AT soaresevanildocosta umestudodotratadodasfluxoesdecolinmaclaurinesuasconexoescomoensinodecalculodiferencialeintegral |
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ri-123456789-574192024-01-25T17:53:46Z Um estudo do tratado das fluxões de Colin Maclaurin e suasconexões com o ensino de cálculo diferencial e integral Soares, Evanildo Costa Mendes, Iran Abreu https://orcid.org/0000-0002-3366-8774 http://lattes.cnpq.br/4341477189320182 Morey, Bernadete Barbosa https://orcid.org/0000-0003-3253-0383 http://lattes.cnpq.br/7554818862651491 Sousa, Giselle Costa de https://orcid.org/0000-0003-0213-4179 http://lattes.cnpq.br/1300121866958282 Fossa, John Andrew Pires, Maria Auxiliadora Lisboa Moreno Colin Maclaurin Tratado das fluxões História do cálculo diferencial e integral CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA In this paper we present our reflections on a two-volume study of Colin Maclaurin's A Treatise of Fluxions and its connections to the teaching of differential and integral calculus, published in 1742. It is intended to support the thesis that the conceptual approaches present in these books by Maclaurin can subsidize the organization of historical sequences associated with the calculus content, to be connected as a complementary approach to the textbooks, in the restructuring of the ways of processing the teaching of differential calculus and fulltime in undergraduate courses in Mathematics. To develop the historical investigation, we examined the work, in the various aspects related to the construction of the history of differential and integral calculus, focusing our attention on the logical foundations of the fluxional method idealized by Isaac Newton and, later, improved and expanded by Colin Maclaurin. The epistemological analysis involved the concept of fluxion and its implications in the consolidation of the derived idea, properties, rules and demonstrations, which became known as the direct method of fluxion. From this approach on the study of derivatives through the fluxional method, aspects emerged concerning the formalization of the study on the notion of integral, its methods, rules and properties, known as the inverse method. At the end of the research, we concluded that the potentialization and conceptual identity of calculus based on the study of the fluxional method can serve as subsidies for the conceptual training of future Mathematics teachers, to achieve a comprehensive learning of this subject, which later can unfold in the improvement of the teaching and learning process of differential and integral calculus, in order to re-signify and complement the conceptual approach present in calculus books, and thus strengthen the understanding of the concepts necessary for learning analysis, in the study of differential calculus and integral part of undergraduate courses in Mathematics. Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES Neste trabalho, apresentamos nossas reflexões acerca de um estudo dos dois volumes do Tratado das Fluxões (A Treatise of Fluxions) de Colin Maclaurin e suas conexões com o ensino de cálculo diferencial e integral, publicada em 1742. Pretende-se sustentar a tese de que as abordagens conceituais presentes nesses livros de Maclaurin (1698-1746) podem subsidiar a organização de sequenciais históricos associados ao conteúdo de cálculo, para serem conectados como abordagem complementar aos livros didáticos, na reestruturação das maneiras de processar o ensino de cálculo diferencial e integral em cursos de licenciatura em Matemática. Para desenvolver a investigação histórica, examinamos a obra relacionada ao tratado das fluxões, nos diversos aspectos relacionados a construção da história do cálculo diferencial e integral, centrando nossa atenção nos fundamentos lógicos do método fluxional idealizado por Isaac Newton e, posteriormente, aprimorado e ampliado por Colin Maclaurin. A análise epistemológica envolveu o conceito de fluxão e suas implicações na consolidação da ideia derivada, propriedades, regras e demonstrações, que ficou conhecido como método direto da fluxão. Dessa abordagem sobre o estudo das derivadas por meio do método fluxional surgiram aspectos concernentes à formalização do estudo sobre a noção de integral, seus métodos, regras e propriedades, conhecido como método inverso. Ao final da pesquisa, concluímos que a potencialização e a identidade conceitual do cálculo a partir do estudo sobre o método fluxional poderão servir de subsídios para a formação conceitual de futuros professores de Matemática, para o alcance de uma aprendizagem compreensiva deste assunto, o que posteriormente poderá se desdobrar no aperfeiçoamento do processo de ensino e aprendizagem do cálculo diferencial e integral, de modo a ressignificar e complementar a abordagem conceitual dos conteúdos sobre derivada e integral presente nos livros de cálculo, e assim fortalecer a compreensão dos conceito necessários à aprendizagem da análise, no estudo do cálculo diferencial e integral nos cursos de licenciatura em Matemática. 2024-01-25T17:52:58Z 2024-01-25T17:52:58Z 2023-09-15 doctoralThesis SOARES, Evanildo Costa. Um estudo do tratado das fluxões de Colin Maclaurin e suasconexões com o ensino de cálculo diferencial e integral. Orientador: Dr. Iran Abreu Mendes. 2023. 187f. Tese (Doutorado em Ensino de Ciências e Matemática) - Centro de Ciências Exatas e da Terra, Universidade Federal do Rio Grande do Norte, Natal, 2023. https://repositorio.ufrn.br/handle/123456789/57419 pt_BR Acesso Aberto application/pdf Universidade Federal do Rio Grande do Norte Brasil UFRN PROGRAMA DE PÓS-GRADUAÇÃO EM ENSINO DE CIÊNCIAS E MATEMÁTICA |