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La fabrication d'un enseignement de l'analyse en France au XIXe siècle : acteurs, institutions, programmes et manuels

Abstract : Differential and integral calculus has been taught at the École Polytechnique since its creation in 1794. But the different conceptions of the calculus principles led to changes in curriculum and teaching. Rapidly, the elements of calculus were taught in the main preparatory classes to the entrance examination to the École Polytechnique. The notion of derivative function appeared in the curriculum of this examination in 1851, consecrating then a common practice. During the following half century, pressure of teachings in the preparatory classes, whose tracks are found in textbooks, led to changes in the curriculum. Authors, who were simultaneously professors in preparatory classes, assessors at the entrance examination to the École Polytechnique and the École Normale Supérieure and teachers in these schools, published textbooks whose contents surpassed the official curriculum and initiated debates. Thus, at the end of the 1880’s, irrational numbers construction, notions on set theory and Riemann's integral were present in textbooks dedicated to the preparatory classes. Some of those contents were integrated to the curriculum. The arithmetical foundations of Analysis considered too abstract caused in 1896 the suppression of the notion of definite integral introduced in the curriculum in 1885. The study over half a century of interactions between curricula, textbooks and teachers of the different orders of education allows to understand the introduction of the derivative function in 1891 in the last grade of modern education, considered at that time as a second-class teaching, then in 1902 in the classical education.
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Submitted on : Friday, February 2, 2018 - 9:01:33 AM
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Hervé Renaud. La fabrication d'un enseignement de l'analyse en France au XIXe siècle : acteurs, institutions, programmes et manuels. Histoire, Philosophie et Sociologie des sciences. Université de Nantes, 2017. Français. ⟨tel-01699107⟩