Failure to construct and transfer correct representations across probability problems

Previous studies carried out on "purely random" situations (with dice or poker chips) show the difficulties encountered by people in such situations, however simple they may be. In fact, in this type of situation, prior knowledge guides spontaneous representations, and the "errors" observed could be explained by the activation of "implicit models" which form the basis of erroneous representations. 42 statistically na?ve undergraduates were given several variants of a probability problem on which errors are common. In a learning phase, subjects were given four problems involving geometric figures which were pairwise related by complementarity and equivalence relations. In a subsequent transfer phase, they were given a fifth problem involving poker chips, which was structurally isomorphic to the fourth geometric-figures problem. The findings show that people do not realize the relations between problems, and that transfer occurred only for the subset of subjects who performed correctly on the training problems of the learning phase. These results appear to have some significant implications in teaching mathematical concepts.