Design of a Learning Environment in Combinatorics based on Problem Solving: Modeling Activities, Problems and Errors

  • Authors:

  • Françoise Le Calvez;Hélène Giroire;Gérard Tisseau

  • Affiliations:

  • University Pierre et Marie Curie (Paris 6), LIP6-MOCAH, 104 avenue du président Kennedy, 75016 Paris, France. E-mail: {francoise.le-calvez,helene.giroire,gerard.tisseau}@lip6.fr;University Pierre et Marie Curie (Paris 6), LIP6-MOCAH, 104 avenue du président Kennedy, 75016 Paris, France. E-mail: {francoise.le-calvez,helene.giroire,gerard.tisseau}@lip6.fr;University Pierre et Marie Curie (Paris 6), LIP6-MOCAH, 104 avenue du président Kennedy, 75016 Paris, France. E-mail: {francoise.le-calvez,helene.giroire,gerard.tisseau}@lip6.fr

  • Venue:
  • International Journal of Artificial Intelligence in Education
  • Year:
  • 2008

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Abstract

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.