Mathematics is a particularly notable domain in which to understand the role of body movement for improving reasoning, instruction, and learning. One reason is that mathematics ideas are often expressed and taught through disembodied formalisms--diagrams and symbols that are culturally designed to be abstract, amodal, and arbitrary (Glenberg et al. 2004)--so that these ideas are regarded as objective and universal. This stems from a Cartesian view of knowledge that separates mental experiences from physical experiences and ways of knowing (Lakoff & Núñez, 2000; also called the "romance of mathematics," p. xv). This Cartesian "duality" carries forth to the various fields touched by mathematics that also strive for objectivity and universality--topics as vast and diverse as the physical and social sciences, business, civics, and the arts. There is a growing appreciation, however, that for effective education, mathematics must be meaningful to novices and that this can occur by grounding the ideas and notations to learners' physical experiences and ways of knowing (Nathan, 2012). Grounding can occur when an abstract idea is given a concrete perceptual referent so that it is more readily understood (Goldstone & Son, 2005). One way that ideas can become grounded is through gesture. Gestures are spontaneous or purposeful movements of the body that often accompany speech and serve as a way to convey ideas or add emphasis to language as well as mathematics (Goldin-Meadow,2005). Gestures can act as a grounding mechanism by indexing symbols and words to objects and events, and by manifesting mental simulations of abstract ideas using sensorimotor processes (Alibali & Nathan, 2012). The grounding of novel, abstract ideas and notational systems through gesture, action, and material referents is part of the emerging framework of grounded and embodied cognition. Grounded cognition is a general framework that posits that formal notational symbol systems and the intellectual behavior are "typically grounded in multiple ways, including simulations, situated action, and, on occasion, bodily states" (Barsalou, 2008, p. 619). [This is a chapter published in: Macrine, S. L., Fugate, J. M. B. (Eds.), "Movement Matters: How Embodied Cognition Informs Teaching and Learning" (pp. 131-145), 2022, Cambridge, MA: MIT Press.]