Interactivity has been linked to better performance in problem solving, due in part to a more efficient allocation of attentional resources, a better distribution of cognitive load, but perhaps more important by enabling the reasoner to shape and reshape the physical problem presentation to promote the development of the problem solution. Interactivity in solving quotidian arithmetic problems involves gestures, pointing, and the recruitment of artefacts to facilitate computation and augment efficiency. In the experiment reported here, different types of interactivity were examined with a series of mental arithmetic problems. Using a repeated-measures design, participants solved series of five 11-digit sums in four conditions that varied in the type of interactivity: (i) no interactivity (participants solved the problems with their hands on the table top), (ii) pointing (participants could point at the numbers), (iii) pen and paper (participants could note interim totals with a pen), and (iv) tokens (the sums were presented as 11 numbered tokens the arrangement of which participants were free to modify as they proceeded to the solution). Performance in the four conditions was measured in terms of accuracy, calculation error, and efficiency (a ratio composed of the proportion correct over the proportion of time invested in working on the sums). These quantitative analyses were supplemented by a detailed qualitative examination of a participant’s actions in the different conditions. The integration of artefacts, such as tokens or a pen, offered reasoners the opportunity to reconfigure the physical presentation of the problem, enacting different arithmetic strategies: the affordance landscape shifts as the problem trajectory is enacted through interactivity, and this generally produced better “mental” arithmetic performance. Participants also felt more positive about and better engaged with the task when they could reconfigure the problem presentation through interactivity. These findings underscore the importance of engineering task environments in the laboratory that offer a window on how problem solving unfolds through a coalition of mental and physical resources.
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