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Etude du travail de l'enseignant autour de la simulation en classe de troisième et seconde : métamorphoses d'un problème au fil d'une formation en probabilité

Abstract : The thesis focuses on teacher's work around probability simulation in grades 9 and 10 in France. We explored how mathematics teachers take on a task crossed during a training session. Our research builds on this task (the hare and turtle problem) to answer our questions about the links between random experiments and models, the place of artefacts and the proofs' nature using simulation. To make our study, we adopted the theory of Mathematical Work Spaces (MWS, Kuzniak, 2011), as well as complementary elements such as the modeling cycle of Blum & Leiss (2009). We introduced the notion of avatar to account for transformations of the task in order to follow the trajectory of successive avatars. Our specific research methodology is based on three loops, and the second one includes short continuing training course. The first loop contains the elaboration of the training with a first implementation of the problem by trainers in their class. The second loop, consisting of three stages, is the training proper. A first scenario is developed by a group of trainees following a analysis a priori of the problem. It is followed by the implementation of the task by one of the trainees in a class lent by the trainers and observed by the other participants of the course. Finally, the collective develops, a posteriori, a new avatar redesigned with regard to the analysis of the previous avatar and its implementation. The third loop includes the avatars tested by the trainees in their own class after the training.Referring to a well-defined MWS expected for the research, it lets us identify the transformations made during and after the training and relates to the cognitive routes around the problem of the hare and the turtle. The study of these three successive loops reveals the existence of breaks between random experience and mathematical models during the resolution of this problem. These breaks are due to both the numerical artefact chosen for the simulation (the spreadsheet or the Scratch software) and to the teacher's work. Through a comparison of teacher and student-led MWS plans in the model of MWS, we were able to identify a tendency for teachers to standardize the choice of model for this problem. In addition, some phases of the MWS expected defined for the research (such as the explicitness around the random experiments in play, the justification of the introduction of the simulation or the proof by the calculations of probabilities) are little represented or absent in the cognitive routes planned and borrowed in these three loops. This reflects a difficulty of articulation between probabilities and statistics around simulation in the teacher. In one case, the second loop showed a thickening of the instrumental dimension relative to the teacher's work and to the chosen digital artefacts. She also highlighted different ways of managing groups of students, transforming the initial avatar and the flow of work in the appropriate MWS. The various cognitive routes that we observed at the end of the training allowed us to identify the effects of the training and in particular the simplifying denaturations (Kuzniak, 1995) made by the teacher on the avatar or the suitable MWS.
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Submitted on : Monday, April 12, 2021 - 11:51:10 AM
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  • HAL Id : tel-02318669, version 1


Blandine Masselin. Etude du travail de l'enseignant autour de la simulation en classe de troisième et seconde : métamorphoses d'un problème au fil d'une formation en probabilité. Education. Université Sorbonne Paris Cité, 2019. Français. ⟨NNT : 2019USPCC002⟩. ⟨tel-02318669⟩



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