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L'APPROCHE QUALITATIVE DES ÉQUATIONS DIFFERENTIELLES EN CLASSE DE TERMINALE S : Est-elle viable ? Quels sont les enjeux et les conséquences ?

Abstract : Differential equations play an eminent role in mathematics and other disciplines. Historically, the field was dominated by the algebraic approach, however two other approaches later emerged: qualitative and numerical. Nevertheless, an analysis of teaching shows that it is dominated by the algebraic approach. The content, therefore, does not reflect the richness of this field and furthermore, a number of studies have detected a weakness of motivation among students approaching differential equations in this limited way. Because of this, in the past two decades a number of works have appeared which attempt to integrate other approaches into teaching at the university level. Motivated by the curriculum of the French secondary schools, we explore in this thesis the viability of the qualitative approach at the level Terminale S (18-19 years). To do this, we prepared a didactic engineering using the concepts of semiotic register and conception, according to the model ck¢ of Balacheff. This thesis consists of four parts: In part A, after a short historical study, we present the three approaches and explain our reasons for supporting the qualitative approach. We review the constraints which resist its integration, some of which our choice of didactic tools is intended to remedy. In part B, we analyze curriculum documents and textbooks, in order to identify the prior knowledge of the students, so that we can turn it to good account in our didactic engineering. Part C is devoted to the presentation of the a priori and a posteriori analysis of the engineering. Finally, part D concludes the thesis.
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https://tel.archives-ouvertes.fr/tel-00009594
Contributor : Salahattin Arslan <>
Submitted on : Friday, June 24, 2005 - 4:06:48 PM
Last modification on : Friday, November 6, 2020 - 4:08:43 AM
Long-term archiving on: : Friday, April 2, 2010 - 10:40:55 PM

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Salahattin Arslan. L'APPROCHE QUALITATIVE DES ÉQUATIONS DIFFERENTIELLES EN CLASSE DE TERMINALE S : Est-elle viable ? Quels sont les enjeux et les conséquences ?. domain_stic.educ. Université Joseph-Fourier - Grenoble I, 2005. Français. ⟨tel-00009594⟩

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