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Etude didactique de l'introduction d'éléments d'algorithmique et de programmation dans l'enseignement mathématique secondaire à l'aide de la calculatrice

Abstract : There is a fundamental solidarity between mathematics and computer science that is based on the history and the current practice of these two disciplines. A proof of this is constant resort to algorithms in the resolutions of fundamental mathematical problems, and the existence of algorithmics as constituent domain of computer science alongside others, like the theory of languages or the theory of robots.
Our research studies the question of the introduction of elements of algorithmics and programming in the secondary mathematical teaching. It relies on epistemological and institutional analyses that show, on one hand that the notions of loop and computer variable are built at the same time as the architecture of the machine is transformed. On the other hand, it testifies the difficult presence of the elements of algorithmics and programming in secondary teaching in France and in Vietnam. The results of these analyses build the conception and the realization of a didactic engineering in a computer environment. It is conceived as an experimental genesis of the machine of Von Neumann and programming through the writing of the successive messages (programs) to machines endowed with different characteristics. This conception uses the tools of the theory of Didactic Situations to organize, from a fundamental situation of algorithmics and programming, a first encounter with different types of memories of the machine, in particular erasable memories. This first encounter allows for the emergence of the notion of computer variables and the loop in our didactic engineering. For the need of our research, we constructed an emulated calculator, named Alpro. This emulator is based on the model of calculator existing in the secondary teaching of the two countries and having the additional capacity to record the history of the pressed keys at the time of a calculation.
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https://tel.archives-ouvertes.fr/tel-00011500
Contributor : Chi Thanh Nguyen <>
Submitted on : Tuesday, January 31, 2006 - 12:04:22 PM
Last modification on : Friday, November 6, 2020 - 3:49:05 AM
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Chi Thanh Nguyen. Etude didactique de l'introduction d'éléments d'algorithmique et de programmation dans l'enseignement mathématique secondaire à l'aide de la calculatrice. Mathématiques [math]. Université Joseph-Fourier - Grenoble I, 2005. Français. ⟨tel-00011500⟩

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