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Article Dans Une Revue International Journal of Artificial Intelligence in Education Année : 2008

Design of a learning environment in combinatorics based on problem solving: modeling activities, problems and errors

Résumé

In this paper we present the design of a learning environment in a mathematical domain (elementary combinatorics) where problem solving is based more on modeling than on deduction or calculation. In this approach, we want to provide students with a presentation which is close to the natural language formulations that they tend to give spontaneously, while ensuring a rigorous mathematical reasoning. To do so, we have introduced three modeling levels: first, a mathematical formalization of the students' intuitive process, that we called the constructive method, then a conceptual and computational model that allows mathematical reasoning as well as communication with the student, and finally a presentation consisting of several "machines". We show that, in such a system, error detection is specific. We present an incremental mechanism of error detection. Specific knowledge necessary to detect and explain the errors is organized into a database of error schemas. The system Combien? founded on this research, has been used by university students since 2002.
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Dates et versions

hal-01174429 , version 1 (09-07-2015)

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  • HAL Id : hal-01174429 , version 1

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Françoise Le Calvez, Hélène Giroire, Gérard Tisseau. Design of a learning environment in combinatorics based on problem solving: modeling activities, problems and errors. International Journal of Artificial Intelligence in Education, 2008, 18 (1), pp.59-94. ⟨hal-01174429⟩
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