Division by multiplication

Abstract

In two experiments, item-specific transfer was examined in simple multiplication and division with prime and probe problems separated by four to six trials. As was predicted by Rickard and Bourne's (1996) identical-elements model, response time (RT) savings were larger with identical (e.g., prime 63 divided by 7, probe 63 divided by 7) than with inverted (63 divided by 9 and 63 divided by 7) division problems, whereas identical (7 x 9 and 7 x 9) and inverted (9 x 7 and 7 x 9) multiplication problems produced equivalent transfer. Nonetheless, there was statistically significant transfer between inverted division problems. Furthermore, RT savings in the multiplication-to-division transfer conditions (e.g., prime 7 x 9, probe 63 divided by 7) indicated that multiplication mediated large-number division problems. These latter effects are not predicted by the identical-elements model but may be reconciled with the model by distinguishing associative transfer (facilitation owing to strengthening of a common problem node in memory) from mediated transfer (facilitation owing to mediation by a strengthened, related problem). Skilled adults can exploit the conceptual correspondences between multiplication and division facts in a highly efficient way to facilitate performance.