A General Model of Algebraic Problem Solving for the Design of Interactive Learning Environments

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.