Representation in Skilled Mental Arithmetic
Annual rept. 3 Aug 93-1 Aug 94.
COLORADO UNIV AT BOULDER
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Two experiments were performed to investigate the nature of skilled arithmetic performance. In Experiment 1, college subjects were trained extensively on a set of simple multiplication e.g. 4 x 9 and division problems e.g., 56 x 8. They were then tested on each problem seen at practice, and on three altered versions of each practice problem a change in operand order v e.g., 4 x 9 at practice, 9 X 4 at test, a change in operation e.g., 4 x 9 at practice, 36 x 9 at test, and change in both operand order and operation e.g., 4 x 9 at practice, 36 x 4 at test. In Experiment 2, both multiplication and division problems were again presented at practice and test. In addition, half of the problems had the symbol x and half had the symbol . On the immediate and delayed tests, subjects again solved four versions of each practice problem the actual practice problem, a problem with the symbol reversed, a problem with the operation reversed, and a problem with both symbol and operation reversed. Results from both experiments showed 1 improvement in reaction time with practice follows a power law for all tested problem types, 2 across practice, division is more difficult than multiplication, and problems with the symbol are more difficult than problems with the symbol x, regardless of the actual arithmetic operation required, 3 transfer of learning is substantial across changes in symbol, and across a change in operand order for multiplication, but is at best minimal across all other changes that were tested, 4 there is good to excellent retention of RT improvements gained.