Interactivity, efficiency, and individual differences in mental arithmetic.

Thinking efficiency was examined in mental arithmetic as a function of the degree of interactivity afforded by the task. Participants carried out single-digit additions, involving either 7 or 11 numbers, as fast and as accurately as possible. They completed the sums in blocks, five from the short 7-number set first, and five from the longer 11-number set second. These sets were interpolated among a series of other tasks that measured numeracy and arithmetic skills, working memory capacity, visuo-spatial processing speed, and attention switching, in such a way as to permit the presentation of the sets twice, once with each of the sums presented on a piece of paper and participants placing their hands flat on the table and once with the sums presented as a set of manipulable tokens. Efficiency was measured as the ratio of performance over time invested. A significant interaction between condition and set size was observed: Efficiency was slightly better in the static condition for short sums but declined substantially relative to the interactive condition for long sums. Twenty-two percent of the variance in efficiency for hard sums in the static condition was explained by arithmetic skills and working memory capacity, whereas 45% of this variance was explained by arithmetic skills, working memory capacity, and attention switching skills in the interactive condition. A separate sample of 17 participants who provided concurrent verbal protocols as they solved the problems revealed that paths to solution and arithmetic strategies were substantially transformed by the opportunity to manipulate tokens.