Abstract
Task-relevant actions can facilitate mathematical thinking, even for complex topics, such as mathematical proof. We investigated whether such cognitive benefits also occur for action predictions. The action-cognition transduction (ACT) model posits a reciprocal relationship between movements and reasoning. Movements-imagined as well as real ones operating on real or imaginary objects-activate feedforward mechanisms for the plausible predicted outcomes of motor system planning, along with feedback from the effect actions have on the world. Thus, ACT posits cognitive influences for making action predictions regardless of whether those actions are performed. Using a two-by-two factorial design, we investigated how generating task-relevant action predictions or performing task-relevant directed actions influenced undergraduates' (N = 127) geometry proof performance. As predicted, making action predictions significantly enhanced participants' proof production. No evidence suggests that combining action predictions and directed actions provided additional benefits, supporting the claim that predicting and performing actions engage overlapping processes, as theorized by ACT. Gestural replays, reenactments of previously performed actions during explanations, were associated with significantly better insight and proof performance for both (actor-generated) predicted actions and (investigator-generated) directed actions. Prompting people to predict task-relevant actions enhances mathematical cognition, possibly through simulated actions of transformations on imagined mathematical objects, as revealed by increased production of speech describing mathematical operations and increased production of gestural replays. We discuss the theoretical implications of these findings regarding the influences of embodied simulation of movements on cognition, and the educational implications of facilitating mathematical reasoning through interventions prompting students to perform and imagine performing task-relevant body movements.