Abstract
This paper presents an approach to the design of a learning environment in a mathematical domain (elementary combinatorics) where problem solving is based more on modelling than on deduction or calculation. In this approach, we want to provide the student with a presentation which is close to the natural language formulations that she tends to give spontaneously, while ensuring a rigorous mathematical reasoning. To do so, we have introduced three modelling levels: first a mathematical formalisation of the students’ intuitive process, then a conceptual and computational model allowing mathematical reasoning as well as communication with the student, and finally a presentation consisting in several interfaces, each one grouping problems of some class. These interfaces are viewed as nondeterministic “machines” that the student uses to build a configuration satisfying some constraints.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Abidin B., Hartley J.R., Developing mathematical problems solving skills, Journal of Computer Learning (1998) 14, 278–291.
Annell M., Malthet V., Giroire H., Tisseau G., Construction d’interface de saisie d’un problème de dénombrement. Rapport interne Lip6 janvier 99.
Cox R., Brna P., Supporting the use of external representations in problem solving: the need for flexible Learning Environments. JAIEd, 6,2/3, 1995, p. 239–302.
Dubois J.-G., Une systématique des configurations combinatoires simples. Educational studies in Mathematics 15 (1984), p. 37–57.
Duma J., Giroire H., Le Calvez F., Tisseau G., Urtasun M., Mise en évidence de styles de résolution, évolution de l’interface dans le projet COMBIEN ?, Actes des 4èmes journées francophones EIAO, ENS Cachan, T. 2, Guin, D. & al. (eds.), Eyrolles, 1995, p. 245–256.
Fischbein E., Gazit A., The combinatorial solving capacity in children and adolescents. Zentralblatt für Didaktik der Mathematik, 5, 1988, 193–198.
Guin N., Changing the representation of a problem in order to solve it: use of classification, in proceedings of AI-ED 97, Kobe (Japan), August 18–22, 1997, p. 583–585.
Le Calvez F., Urtasun M., Giroire H., Tisseau G., Duma J., Les machines à construire. Des modèles d’interaction pour apprendre une méthode constructive de dénombrement. EIAO’97, actes des 5èmes journées EIAO de Cachan, Baron, M., Mendelsohn, P., Nicaud, J.-F., (eds), Hermès, 1997, p. 49–60.
Nicaud J.-F., Building ITSs to be used: Lessons Learned from the APLUSIX Project, Lessons From Learning, Lewis, R & al. (eds), IFIP, North Holland, 1994, p. 181–198.
Tisseau G., Duma J., Giroire H., Le Calvez F., Urtasun M., Spécification du dialogue et génération d’interfaces à l’aide d’interacteurs à réseau de contrôle. Actes de la 11ème Conférence francophone IHM’99 p. 94–101.
White B.Y., Frederiksen J.R., Causal model progressions for intelligent learning environments. Artificial Intelligence, 42, 1990, p. 99–157.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Tisseau, G., Giroire, H., Le Calvez, F., Urtasun, M., Duma, J. (2000). Design Principles for a System to Teach Problem Solving by Modelling. In: Gauthier, G., Frasson, C., VanLehn, K. (eds) Intelligent Tutoring Systems. ITS 2000. Lecture Notes in Computer Science, vol 1839. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45108-0_43
Download citation
DOI: https://doi.org/10.1007/3-540-45108-0_43
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67655-3
Online ISBN: 978-3-540-45108-2
eBook Packages: Springer Book Archive