Acquiring Skill at Mental Calculation in Adulthood: A Task Decomposition

Abstract

Sixteen young, middle-aged, and old adults practiced an algorithm for squaring a subset of numbers between 1 and 99 mentally, as well as simple multiplication of single digits for six consecutive sessions, and after a 1-month delay. Performance was assessed on isolated components of the algorithm and on a transfer set of problems before and after practice and after the delay. The component tasks and practice/transfer tasks examined the concepts of strengthening, composition, and proceduralization outlined in Anderson (1983). Results show that about 70% of the speedup during skill acquisition involves compiling the procedure (composition and proceduralization), and the rest is due to speedup on the components (strengthening). The finding of imperfect transfer to equivalent problems and component tasks indicates that compilation occurs within 5 trials for practiced problems. Older adults learn and forget at about the same rate as younger ones, but their calculation speed is about half that of the young. The middle-aged group resembles the old group initially but is closer to the performance level of the young after practice. It takes about 3 min practice per year of age difference for the old group to equal the initial performance of the young group. The variety of reaction time (RT) measures gathered also permitted a direct test of the age-complexity hypothesis within subjects. Contrary to previous results based on group means, a moderate linear relation was found between RT and task complexity as a function of age. © 1988 American Psychological Association.