On the cognitive structure of basic arithmetic skills: Operation, order, and symbol transfer effects.

Abstract

In 2 experiments, college Ss practiced extensively on single-digit multiplication and division problems (e.g., = 6 × 9; 42 = × 6) and were tested on both practice problems and several altered versions of those problems, which were constructed by changing the required operation, operand order, or arithmetic symbol. There was strong positive transfer to test problems that had exactly the same elements (the numbers and the required operation) as a practice problem, regardless of whether other factors such as operand order or symbol were changed, but little if any positive transfer to test problems that did not have the same elements as a practice problem. An identical elements framework is used to interpret these results and implications for existing computational models of arithmetic fact retrieval and for the development of arithmetic skill are discussed