Mental Arithmetic Efficiency: Interactivity and Individual Differences

Thinking efficiency as a function of interactivity was examined in a mental arithmetic 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 ‘easy’ set first, and five from the ‘hard’ set second. These sets were interpolated among a series of other tasks that measured numeracy, working memory capacity, visuospatial 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 difficulty was observed: Efficiency was slightly better in the static condition for easy sums but declined substantially relative to the interactive condition for hard sums. Regression analyses revealed that in the static condition 22% of the variance in efficiency for the harder sums was explained by numeracy and working memory capacity, but 45% by numeracy, working memory capacity and attention switching skills in the interactive condition. Verbal protocols revealed that paths to solution and arithmetic strategies were substantially transformed by the opportunity to manipulate tokens.