AN EXPERIMENT IN LEARNING ALGEBRA WITH AN INTELLIGENT LEARNING-ENVIRONMENT

This paper presents a new prototype of an intelligent learning environ ment and the results of an experiment in learning by problem solving. Forty-six French secondary school students solved problems of polynomi al factorization by interacting with the learning environment during f our forty-five-minute sessions. The intelligent learning environment i s a new version of the APLUSIX system, called APLUSIX/MO-V2, that has been implemented on a Macintosh computer. This system checks the valid ity of the actions a student wants to perform, tells the student why a query is invalid, does the calculations for the student, and gives ad vice if asked for help. The objective of the learning experiment was t o enable students to acquire (i) knowledge in matching formal rules of transformation with a given expression; and (ii) heuristics of choice between possible transformations. The results confirmed the existence of several different levels of matching knowledge as well as several different student learning paths in the acquisition of matching knowle dge. Heuristics appeared to be fairly easily learned with the APLUSIX learning environment.