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Le graphe comme outil pour enseigner la preuve et la modélisation

Abstract : In 2002, elements of graph theory entered the curriculum of Terminale ES (12th grade) in France. We first sketch a brief history of the genesis of the notion of graph (Chapter 1). We then study the way graphs entered the French high school curriculum, its transposition and realization, in particular through the study of the exercises that are proposed in the textbooks (Chapter 2). A specificity of this part of the curriculum lies on the fact that its implementation is to be based on problem-solving activities only. We demonstrate that textbooks actually never propose real problems, but only exercises. Furthermore, we discuss the dangers and drawbacks of restricting oneself to the resolution of exercises or “mathematical puzzles” only, in the sense that local resolutions do not necessary yield to the underlying mathematical concepts. In Chapter 3 we propose experimental studies on the eulerian trail problem, with learners ranging from primary school pupils to undergraduate students, and several kinds of implementations (classroom problem-solving activities, document study). We relate in details two classes with math teachers about graph theory in Terminale ES. Finally, we present in Chapter 4 a set of problems (with solutions) covering the curriculum of Terminale ES, intending to demonstrate that solid mathematics could be addressed on that occasion.    
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Contributor : Léa Cartier <>
Submitted on : Tuesday, December 8, 2009 - 4:32:49 PM
Last modification on : Wednesday, November 4, 2020 - 2:01:52 PM
Long-term archiving on: : Thursday, September 23, 2010 - 11:20:41 AM


  • HAL Id : tel-00416598, version 2



Léa Cartier. Le graphe comme outil pour enseigner la preuve et la modélisation. Mathématiques [math]. Université Joseph-Fourier - Grenoble I, 2008. Français. ⟨tel-00416598v2⟩



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