TC: A Revised Identical Elements Model of Arithmetic Fact Representation

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) 3 28; (28 / 7) 3 4; and (28 / 4) 3 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. There is general agreement in the cognitive literature that adult performance on single-digit multiplication and division problems (e.g., 4 7 and 28 / 7) primarily involves fact recall (for reviews, see Ashcraft, 1992, 1995), although other strategies are sometimes used (e.g., LeFevre & Morris, 1999). There is debate, however, on the relation between multiplication and division fact representa-tions. At the broadest level, there are two opposing theoretica