Introduction: Hand gestures and actions-with-objects (hereafter ‘actions’) are both forms of movement that can promote learning. However, the two have unique affordances, which means that they have the potential to promote learning in different ways. Here we compare how children learn, and importantly retain, information after performing gestures, actions, or a combination of the two during instruction about mathematical equivalence. We also ask whether individual differences in children’s understanding of mathematical equivalence (as assessed by spontaneous gesture before instruction) impacts the effects of gesture- and action-based instruction.

Method: Across two studies, racially and ethnically diverse third and fourth-grade students (N=142) were given instruction about how to solve mathematical equivalence problems (eg., 2+9+4=__+4) as part of a pretest-training-posttest design. In Study 1, instruction involved teaching students to produce either actions or gestures. In Study 2, instruction involved teaching students to produce either actions followed by gestures or gestures followed by actions. Across both studies, speech and gesture produced during pretest explanations were coded and analyzed to measure individual differences in pretest understanding. Children completed written posttests immediately after instruction, as well as the following day, and four weeks later, to assess learning, generalization and retention.

Results: In Study 1 we find that, regardless of individual differences in pre-test understanding of mathematical equivalence, children learn from both action and gesture, but gesture-based instruction promotes retention better than action-based instruction. In Study 2 we find an influence of individual differences: children who produced relatively few types of problem-solving strategies (as assessed by their pre-test gestures and speech) perform better when they receive action training before gesture training than when they receive gesture training first. In contrast, children who expressed many types of strategies, and thus had a more complex understanding of mathematical equivalence prior to instruction, performed equally with both orders.

Discussion: These results demonstrate that action training, followed by gesture, can be a useful stepping-stone in the initial stages of learning mathematical equivalence, and that gesture training can help learners retain what they learn.