Inverted classroom and history of Mathematics: Fourier's legacy and calculus in perspective

Abstract

ABSTRACT

Objective: This work aims to strengthen the dialog between mathematics in higher education and the history of mathematics, as a way of promoting the construction of interfaces between these fields of knowledge, focusing on the work of Jean-Baptiste Joseph Fourier (1768-1830), who became famous in 1822 with the publication of the work Théorie analytique de la chaleur. Methodology: A qualitative, biographical approach with exploratory objectives involving students of the subject Differential and Integral Calculus in an Engineering course at a University Center in São Paulo. We adopted the Inverted Classroom teaching methodology and a "story" approach, according to Grattan-Guinness. Results: We considered the legacy of the character Fourier, seen as fundamental in the discussion about redefining the concept of function, by extrapolating mathematical concepts that were rooted in academic society in the eight hundreds.  The role played by the students and the time gained in the classroom for discussions about the content of Fourier's Series was a result of the methodology adopted in permanent dialog with the historical approach. The theoretical framework provided by the students - represented by most of the bibliographical references used in this article - shows signs of maturing, favoring possibilities for future didactic experiments. Conclusion: Currently, the numerous applications of Fourier's studies are present, explicitly or implicitly, in various areas of engineering, reaching our lives inexorably, often transcending the mere application of technology.