Teachers’ and learners’ gestures while giving explanations in mathematics can be categorized into three types, revealing their cognitive nature and communicative purpose: pointing reflects a grounding in the physical environment, representational gestures reveal mental simulations of action and perception, and metaphoric gestures reveal conceptual metaphors grounded in the physical human experience. Informal educators should reflect on their own gestures and those of learners, considering what they may contribute to greater learner understanding.