Sala de aula invertida e história da Matemática: legado de Fourier e cálculo em perspectiva.
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| Title: | Sala de aula invertida e história da Matemática: legado de Fourier e cálculo em perspectiva. |
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| Alternate Title: | Flipped classroom and the history of Mathematics: Fourier's legacy and calculus in perspective. El aula invertida y la historia de las Matemáticas: el legado de Fourier y el cálculo en perspectiva. |
| Authors: | Alves de Moura, Roseli1 roselimatematica.moura@gmail.com, de Araujo Brandão, Kelven Cleyton1 kelven.cleiton14@gmail.com |
| Source: | International Journal of Higher Education / Revista Internacional de Educação Superior. 2025, Vol. 11, p1-20. 39p. |
| Subject Terms: | *Mathematics education (Higher), *Teaching methods, *Flipped classrooms, Integral calculus, Fourier series |
| Abstract (English): | Objective: The present work aims to strengthen the dialogue between mathematics in higher education and the history of mathematics, as a way of promoting the construction of interfaces between these fields of knowledge, listing as its theme the work of Jean-Baptiste Joseph Fourier (1768-1830 ), which was established in 1822 with the publication of the work Théorie analytique de la chaleur. Method: A qualitative approach, of a biographical nature and with exploratory objectives involving students of the Differential and Integral Calculus discipline in an Engineering course at a University Center in São Paulo. Through activities and literature review, we adopted the Flipped Classroom teaching methodology and an approach from a “history” perspective, anchored by GrattanGuinness.Results: We consider the legacy of the character Fourier, considered fundamental in the discussion about the redefinition of the concept of function, by extrapolating mathematical concepts that were rooted in academic society in the 1800s. The protagonism of students and the time gained in the classroom for discussions about the Fourier Series content proved to be a result of the methodology adopted in permanent dialogue with the historical approach. The theoretical framework brought by the students – represented by the majority of bibliographic references used in this report, brings signs of maturity, favoring possibilities for developments in future didactic experiments. Conclusion: Currently, the countless applications of Fourier's studies are present, explicitly or implicitly, in several areas within the scope of engineering, reaching our lives in an inexorable way, often transcending the mere application of technology. [ABSTRACT FROM AUTHOR] |
| Abstract (Spanish): | Objetivo: El presente trabajo tiene como objetivo fortalecer el diálogo entre las matemáticas en la educación superior y la historia de las matemáticas, como una forma de promover la construcción de interfaces entre estos campos del conocimiento, teniendo como tema la obra de Jean-Baptiste Joseph Fourier (1768 -1830), que se estableció en 1822 con la publicación de la obra Théorie analytique de la chaleur. Método: Un enfoque cualitativo, de carácter biográfico y con objetivos exploratorios que involucra a estudiantes de la disciplina de Cálculo Diferencial e Integral de un curso de Ingeniería en un Centro Universitario de São Paulo. A través de actividades y revisión de literatura, adoptamos la metodología de enseñanza Flipped Classroom y un enfoque desde una perspectiva de “historia”, anclada en Grattan-Guinness.Resultados: Consideramos el legado del personaje Fourier, considerado fundamental en la discusión sobre la redefinición del concepto de función, al extrapolar conceptos matemáticos que estaban arraigados en la sociedad académica del siglo XIX. El protagonismo de los estudiantes y el tiempo ganado en el aula para discusiones sobre los contenidos de la Serie Fourier resultaron ser resultado de la metodología adoptada en diálogo permanente con el enfoque histórico. El marco teórico aportado por los estudiantes – representado por la mayoría de las referencias bibliográficas utilizadas en este informe, trae signos de madurez, favoreciendo posibilidades de desarrollo en futuras experiencias didácticas. Conclusión: Actualmente, las innumerables aplicaciones de los estudios de Fourier están presentes, explícita o implícitamente, en varias áreas dentro del ámbito de la ingeniería, llegando a nuestras vidas de manera inexorable, trascendiendo muchas veces a la mera aplicación de la tecnología. [ABSTRACT FROM AUTHOR] |
| Abstract (Portuguese): | Objetivo: O presente trabalho objetiva estreitar o diálogo entre a matemática no ensino superior e a história da matemática, como forma de promover a construção de interfaces entre estes campos de saberes, elencando como temática o trabalho de Jean-Baptiste Joseph Fourier (1768-1830), que consagrau-se em 1822 com a publicação da obra Théorie analytique de la chaleur. Método: Uma abordagem qualitativa, de cunho biográfico e com objetivos exploratórios envolvendo discentes da disciplina Cálculo Diferencial e Integral em um curso de Engenharia em um Centro Universitário em São Paulo. Por meio de atividades e revisão de literaturas, adotamos a metodologia de ensino de Sala de Aula Invertida e uma abordagem sob o viés da “história”, ancoradas por Grattan-Guinness. Resultados: Consideramos o legado do personagem Fourier, tido como fundamental na discussão sobre a redefinição do conceito de função, ao extrapolar conceitos matemáticos que estavam enraizados na sociedade acadêmica nos oitocentos. O protagonismo dos estudantes e o tempo ganho em sala de aula para discussões acerca do conteúdo Séries de Fourier, revelou-se decorrente da metodologia adotada em permanente diálogo com a abordagem histórica. O arcabouço teórico trazido pelos estudantes – representados pela maioria das referências bibliográficas utilizadas neste relato, traz indícios de amadurecimento, favorecendo possibilidades de desdobramentos em experimentos didáticos futuros. Conclusão: Atualmente, as inúmeras aplicações dos estudos de Fourier encontram-se presentes, explicita ou implicitamente, em diversas áreas no âmbito das engenharias, alcançando as nossas vidas de forma inexorável, transcendendo muitas vezes, a mera aplicação de tecnologia. [ABSTRACT FROM AUTHOR] |
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| Database: | Education Research Complete |
| Abstract: | Objective: The present work aims to strengthen the dialogue between mathematics in higher education and the history of mathematics, as a way of promoting the construction of interfaces between these fields of knowledge, listing as its theme the work of Jean-Baptiste Joseph Fourier (1768-1830 ), which was established in 1822 with the publication of the work Théorie analytique de la chaleur. Method: A qualitative approach, of a biographical nature and with exploratory objectives involving students of the Differential and Integral Calculus discipline in an Engineering course at a University Center in São Paulo. Through activities and literature review, we adopted the Flipped Classroom teaching methodology and an approach from a “history” perspective, anchored by GrattanGuinness.Results: We consider the legacy of the character Fourier, considered fundamental in the discussion about the redefinition of the concept of function, by extrapolating mathematical concepts that were rooted in academic society in the 1800s. The protagonism of students and the time gained in the classroom for discussions about the Fourier Series content proved to be a result of the methodology adopted in permanent dialogue with the historical approach. The theoretical framework brought by the students – represented by the majority of bibliographic references used in this report, brings signs of maturity, favoring possibilities for developments in future didactic experiments. Conclusion: Currently, the countless applications of Fourier's studies are present, explicitly or implicitly, in several areas within the scope of engineering, reaching our lives in an inexorable way, often transcending the mere application of technology. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 24469424 |
| DOI: | 10.20396/riesup.v11i00.8674795 |
