Learning to solve polynomial factorization problems: By solving problems and by studying examples of problem solving, with an intelligent learning environment

The relative merits of these two modes of cognitive skills acquisition is still a matter of much debate. Solving factorization problems is an important skill in algebra. it implies, in particular, the sub-skill of recognizing how to match an algebraic sub-expression with a transformation rule, and strategic knowledge for choosing the transformation rules to be applied. An intelligent learning environment (ILE) was developed which can either solve problems and progressively exhibit the search tree it generates, or let the student solve the problem while alerting him (her) of his (kr) mistakes. We conducted an experiment in which we compared four groups of students who learnt to solve difficult factorization problems. The first two groups learnt by studying examples. The third and fourth groups learnt by solving problems. The results suggested that learning by doing favored the acquisition of factorization problem solving skills.