Proceedings of the Annual Meeting of the Cognitive Science Society

Students often have difficulty solving homework assignments in quantitative courses such asphysics, algebra, programming, and statistics. We hypothesize that typical example problemsdone in class teach students a series of mathematical operations for solving certain types ofproblems but fail to teach the underlying subgoals and methods which remain implicit in theexamples. In the studies reported here, students in probability classes studied example problemsthat dealt with the Poisson distribution. In Experiment 1, the four examples all used the samesolution method, although for one group the examples were superficially more dissimilar than forthe other group. All subjects did well on the Near Transfer target problem that used the samesubgoals and methods as the training examples. However, most did poorly on two Far Transfertarget problems that had different subgoal orders and different methods. These results suggestthat subjects typically iearn solutions as a series of non-meaningful mathematical operationsrather than conceptual methods in a subgoal hierarchy. In Experiment 2, one group studiedproblems that demonstrated two different subgoal orders using different methods while the othergroup received superficially different problems which had identical subgoal orders and methods.Both groups still had difficulty with the Far Transfer problems. Subjects who received exampleswith varied subgoal orders and methods seemed to isolate the subgoals, however, but not themethods. This result suggests that goals and methods may be useful ways of characterizingtraining problems. However, students may require explicit instruction on subgoals and methods inorder to successfully solve novel problems.