A revised identical elements model of arithmetic fact representation

The identical elements model of arithmetic fact representation (T. C. Rickard, A. F. Healy, & L. E. Bourne, 1994) states that, for each triplet of numbers (e.g., 4, 7, 28) that are related by complementary multiplication and division problems, there are 3 independent fact representations in memory: (4, 7, x) --> 28; (28/7) --> 4; and (28/4) --> 7. In this article, the author reviews the evidence for this model, considers alternative accounts, and proposes a simple and empirically motivated revision to the model that (a) accommodates conflicting results, (b) provides a novel account of the ties effect, and (c) makes new and nonintuitive predictions for the factoring operation (e.g., factoring of 28 into 4 and 7). The author reports 3 experiments designed to test these predictions and discusses implications for arithmetic instruction.