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Simulation informatique d'expérience aléatoire et acquisition de notions de probabilité au lycée

Abstract : The mathematics curriculum claims that simulating a random experiment amounts to the simulation of the underlying probability distribution. We show here that this is not a necessity. We performed an a priori analysis of the task of simulating a random experiment without deriving it from its probability distribution. This led us to clarify the connections between a random experiment, its probabilistic modeling and its simulations. We propose a model for these links with a pre-modeling step, which is common to the simulation and probabilistic modeling tasks and during which the modeling assumptions are chosen. A simulation which imitates closely the random experiment can then be constructed from specifications that describe its list of actions and how they are linked to each other. Computer simulation appears as a core activity of algorithmic type. We conducted an experiment with high school students to observe which techniques they implement to simulate a random experiment and how they use the probabilistic model or simulations to solve a problem of decision making in situations involving randomness. Once the hypotheses of the model are chosen, the imitation of the random experiment does not make use of probability theory. Some problems solved by a statistical study of simulations may therefore help to introduce the concepts of probability theory such as risk, confidence interval, level of confidence, relevance of a probabilistic model to experimental data.
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https://tel.archives-ouvertes.fr/tel-00826073
Contributor : Françoise Gaydier <>
Submitted on : Sunday, May 26, 2013 - 5:59:37 PM
Last modification on : Friday, October 23, 2020 - 4:42:42 PM
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  • HAL Id : tel-00826073, version 1

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Gaydier Françoise. Simulation informatique d'expérience aléatoire et acquisition de notions de probabilité au lycée. Education. Université René Descartes - Paris V, 2011. Français. ⟨tel-00826073⟩

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