Learning subgoals and methods for solving probability problems

We hypothesize that typical example problems used in quantitative domains such as algebra and probability can be represented in terms of subgoals and methods that these problems teach learners. The "quality" of these subgoals and methods can vary, depending on the features of the examples. In addition, the likelihood of these subgoal's being recognized in novel problems and the likelihood of learners' being able to modify an old method for a new problem may be functions of the training examples learners study. In Experiment 1, subjects who studied examples predicted to teach certain subgoals were often able to recognize those subgoals in nonisomorphic transfer problems. Subjects who studied examples demonstrating two methods rather than one exhibited no advantages in transfer. Experiment 2 demonstrated that if the conditions for applying a method are highlighted in examples, learners are more likely to appropriately adapt that method in a novel problem, perhaps because they recognize that the conditions do not fully match those required for any of the old methods. Overall, the results indicate that the subgoal/method representational scheme may be useful in predicting transfer performance.