The emerging field of mathematics educational neuroscience provides researchers with new approaches to understanding mathematical development, as well mathematics itself. This paper focuses on the role of the hand in constructing mathematics through activity. In reviewing results from neuroscience studies, we distinguish three kinds of relevant activity: sensorimotor activity, internalized actions, and interiorized operations. These distinctions and related neuroscience findings contribute to a new sense of mathematical embodiment. They also provide implications for mathematics instruction.