Abstract
A general model for a class of algebraic problems is presented as a framework for the design of Interactive Learning Environments. This model enables us to consider several levels for the reference knowledge of a learning environment. It allows us to represent knowledge for the control of the student's problem solving activity without the model tracing constraint which requires the student to follow the behavior of the reference knowledge. The APLUSIX system is an Interactive Learning Environment in the domain of factorization of polynomials which has been developed in that framework. Experiments have been conducted in France and protocols have been collected in order to study human learning process in that domain.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Anderson, J. R.: The architecture of cognition. Cambridge: Harvard University Press 1983
Anderson, J. R., Boyle C. F., Corbett A. T., & Lewis M.W.: Cognitive modeling and intelligent tutoring. Artificial Intelligence, 42(1) (1990)
Balacheff, N.: Nature et objet du raisonnement explicatif. In: Actes du colloque “L'explication dans l'enseignement et l'EIAO” (M.G. Séré et A. Weil-Barais, eds.), Ecole Normale Supérieure de Cachan, Avril 1990
Brousseau, G.: Fondements et méthodes de la didactique des mathématiques. Recherche en Didactique des Mathématiques, 7(2), 33–115 (1986)
Brown, J. S.: Process versus product: a perspective on tools for communal and informal electronic learning. Journal of Educational Computing Research, 1 (1985)
Brown, J. S. & Burton, R. R.: Diagnostic models for procedural bugs in basic mathematical skills. Cognitive Science, 2, 155–191 (1978)
Bundy, A.: The computer modeling of mathematical reasoning. New York: Academic Press 1983
Chandrasekaran B., Tanner, M. C, & Josephson, J. R.: Explaining control strategies in problem solving. IEEE Expert, 9–20 (1989)
Dillenbourg, P., & Self, J.: A framework for student modelling. Technical Report TR-AI-49, Computing Department, University of Lancaster 1990
Gilbert, G: Forms of explanation. In: Proceedings of AAAI'88 Workshop on Explanation, Saint Paul, 72–75 (1988)
Goldstein, I. P.: The genetic graph: A representation for the evolution of procedural knowledge. In: Intelligent tutoring systems (Sleeman & Brown, eds.). London: Academic Press 1982
Lewis, M. W., Milson, R., & Anderson, J. R.: The teacher's apprentice: designing an intelligent authoring system for high school mathematics. In: Artificial intelligence and instruction, application and methods (G. Kearsley, ed.). New York: Addison Wesley 1987
Nicaud, J.F.: APLUSIX: un système expert en résolution pédagogique d'exercices d'algèbre. Thèse de l'Université de Paris XI 1987
Nicaud, J.F. & Saïdi, M.: Explanation of algebraic reasoning: the APLUSIX System. Lecture Notes in Artificial Intelligence, 444. Berlin: Springer-Verlag 1989
Saïdi, M.: Evaluation optimisée et planification en résolution d'exercices d'algèbre. 2ème Journées EIAO de Cachan. Ecole Normale Supérieure de Cachan, Janvier 1991
Sleeman, D. H. & Smith, M. J.: Modelling student's problem solving. Artificial Intelligence, 171–187 (1981)
Sleeman, D. H.: An attempt to understand student's understanding of basic algebra. Cognitive Science, 8, 387–412 (1984)
Stevens, A., Collins, A. M & Golding, S. E.: Misconceptions in students' understanding. In: Intelligent tutoring systems (Sleeman & Brown, eds.). New York: Academic Press 1982
Vivet, M.: Expertise mathématique et informatique: CAMELIA, un logiciel pour raisonner et calculer. Thèse d'état, Paris VI 1984
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Nicaud, JF. (1992). A General Model of Algebraic Problem Solving for the Design of Interactive Learning Environments. In: Ponte, J.P., Matos, J.F., Matos, J.M., Fernandes, D. (eds) Mathematical Problem Solving and New Information Technologies. NATO ASI Series, vol 89. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58142-7_19
Download citation
DOI: https://doi.org/10.1007/978-3-642-58142-7_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-63483-3
Online ISBN: 978-3-642-58142-7
eBook Packages: Springer Book Archive