Specificity of learning through memory retrieval practice: the case of addition and subtraction.

The identical elements (IE) model (Rickard, Healy, & Bourne, Learning, Memory, and Cognition 32:734-748, 1994) of fact representation predicts that, in both verbal and numerical domains, performance gains with retrieval practice on multielement items will be specific to the practiced stimulus-response combinations, failing to transfer even to altered stimulus-response mappings of practiced items. In the case of arithmetic, the model predicts no transfer across either complementary operations (e.g., 4 × 7 to 28 / 4) or complementary division or subtraction problems (e.g., 28 / 4 to 28 / 7). Although that model has successfully described transfer effects in the domains of multiplication-division and episodic cued recall, it is challenged by a recent demonstration of positive cross-operation transfer for addition and subtraction (Campbell & Agnew, Psychonomic Bulletin & Review 16:938-944, 2009). We report results of a new addition-subtraction transfer experiment, the design of which closely matched that of a prior multiplication-division experiment that supported the model. The transfer results were consistent with the IE model. A two-component model of memory retrieval practice effects is proposed to account for the discrepant experimental results for addition and subtraction and to guide future work.