Learning Iteration and Recursion from Examples

Recursion is basic to computer science, whether it is conceived of abstractly as a mathematical concept or concretely as a programming technique. Three experiments were carried out on learning iteration and recursion. The first involved learning to compute mathematical functions, such as the factorial, from worked out examples. The results suggest the subjects are quite able to induce a computational procedure for both iterative and recursive functions. Furthermore, prior work with iterative examples does not seem to facilitate subsequent learning of recursive procedures, nor does prior work with recursive examples facilitate subsequent learning of iterative procedures. The second experiment studied the extent to which people trained only with recursive examples are able to transfer their knowledge to compute other similar recursive mathematical functions stated in an abstract form. It turned out that subjects who transferred to abstractly stated problems performed somewhat worse than they had performed previously when given examples. However, they did far better than a control group trained only with an abstract description of recursion. The third experiment involved comprehension of iterative and recursive Pascal programs. Comprehension of the iterative program was not affected by prior experience with the recursive version of the same program. Comprehension of the recursive version was only weakly affected by prior experience with the iterative version.