Some tests of an identical elements model of basic arithmetic skills.

Two experiments tested an identical elements model of the organization of basic arithmetic skills (T. C. Rickard, A. F. Healy, & L. E. Bourne, 1994). This model assumes a distinct abstract representation for each unique combination of the basic elements (i.e., the operands and the required operation) of a problem. Participants practiced multiplication and division problems and were then tested on various altered versions of these problems. Experiment 1 confirmed the prediction of no positive transfer when the presented elements of a test problem do not exactly match those of a practice problem. Experiment 2 confirmed the prediction that there is complete transfer when the elements of the test problem match exactly with those of a practice problem. Experiment 2 also confirmed that there is both perceptually specific and nonspecific speed-up with practice. Implications for number processing and arithmetic are discussed.