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Theses

Modélisation didactique de parcours d'apprentissage dans un EIAH pour l'entrée dans le raisonnement géométrique au cycle 4, en appui sur les problèmes de construction de figures planes

Abstract : This thesis is part of the MindMath project which aims at designing a Technology Enhanced Learning (TEL) for algebra and geometry in secondary schools. Our work focusses on geometry. In junior high school, students have difficulty negotiating the transition from geometry based on observation, or the use of measuring instruments, to geometry based on deductive reasoning. We hypothesise that these difficulties are not only cognitive, but are also linked to institutional discontinuities in the transition between cycles 3 (9-12 years old) and 4 (12-15 years old). Based on a synthesis of works in geometry education, we hypothesise that solving construction problems verifying the conditions necessary for taking geometric reasoning into account helps negotiating the passage from one geometry to another and apprehending deductive geometric reasoning. We therefore ask ourselves : how can we develop learning paths in a TEL involving construction problems to make students aware of the need to use deductive geometric reasoning and thighlight its usefulness at the transition from cycle 3 to cycle 4 ? For this purpose, we identify the epistemological aspects at stake in the visualization of figures, geometric reasoning and two-dimensional shapes construction problems, in particular triangles and quadrilaterals. Our work builds on mathematics education, but also on other research studies with a more cognitive perspective. These aspects form the basis of a Praxeological Reference Model (PRM) relating to the two-dimensional shapes of Euclidean geometry in the field of the cycle 3 / cycle 4 transition. We transpose to the context of geometry a method developed to regulate the learning of students in algebra in cycle 4. We define learning paths at the beginning of cycle 4 that lead students to understand the need to develop reasoning involving the properties of triangles and quadrilaterals in deductive units to construct shapes and justify the construction program. In addition, we design didactic models of knowledge, tasks, learners and learning paths to be used with the computer science elements, and in particular artificial intelligence, of the MindMath TEL.
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https://tel.archives-ouvertes.fr/tel-03404996
Contributor : Elann Lesnes-Cuisiniez Connect in order to contact the contributor
Submitted on : Wednesday, October 27, 2021 - 12:20:28 AM
Last modification on : Thursday, April 7, 2022 - 1:58:26 PM
Long-term archiving on: : Friday, January 28, 2022 - 6:15:01 PM

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  • HAL Id : tel-03404996, version 1

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Elann Lesnes-Cuisiniez. Modélisation didactique de parcours d'apprentissage dans un EIAH pour l'entrée dans le raisonnement géométrique au cycle 4, en appui sur les problèmes de construction de figures planes. Education. Université de Paris, 2021. Français. ⟨tel-03404996⟩

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