Many arithmetic problems can be solved in two ways--by a calculation involving several steps and by direct retrieval of the answer. With practice on particular problems, memory retrieval tends to supplant calculation--an important aspect of skill learning. We asked how the distribution of practice on particular problems affects this kind of learning. In two experiments, subjects repeatedly worked through sets of multiple-digit multiplication problems. The size of the trained problem set was varied. Using a smaller set size (with shorter average time between problem repetitions) showed faster responses and an earlier transition to retrieval during training. However, in a test session presented days later, the pattern reversed, with faster responses and more retrieval for the large set size. Evidently, maximizing the occurrence of direct retrieval within training is not the best way to promote learning to retrieve the answer. Practical implications are discussed.
Rickard, T. C., Lau, J. S. H., & Pashler, H. (2008). Spacing and the transition from calculation to retrieval. Psychonomic Bulletin and Review, 15(3), 656–661. https://doi.org/10.3758/PBR.15.3.656