Identical elements model of arithmetic memory: Extension to addition and subtraction

The identical elements (IE) model of arithmetic fact representation (Rickard, 2005; Rickard & Bourne, 1996) was developed and tested with multiplication and division. In Experiment 1, we demonstrated that the model also applies to addition and subtraction by examining transfer of response time (RT) savings between prime and probe problems tested in the same block of trials. As is predicted by the IE model, there were equivalent probe RT savings for addition with identical repetition (prime 6 + 9 -> probe 6 + 9) or an order change (9 + 6 -> 6 + 9), but much greater savings for subtraction with identical repetition (15 - 6 -> 15 - 6) than with an order change (15 - 9 - 15 - 6), and no savings with an operation change (15 - 9 -> 6 + 9 or 6 + 9 -> 15 - 6). In Experiment 2, we examined transfer in simple multiplication and division and demonstrated symmetrical transfer between operations. Cross-operation RT savings were eliminated, however, when the RT analysis included only trials on which both the prime and the probe problems were reportedly solved by direct retrieval. An IE model extended to accommodate savings associated with procedural strategies provides a coherent account of facilitative transfer effects in simple arithmetic.