Division by multiplication

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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÷7, probe 63÷7) than with inverted (63÷9 and 63÷7) division problems, whereas identical (7×9 and 7×9) and inverted (9×7 and 7×9) 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 7×9, probe 63÷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.

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