Representation in Skilled Mental Arithmetic
Abstract
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1998
- Accession Number
- ADA350002
Entities
People
- Timothy C. Rickard
Organizations
- University of Colorado Boulder