Research in mathematics education has established that gestures--spontaneous movements of the hand that accompany speech--are important for learning. In the present study, we examine how students use gestures to communicate with each other while proving geometric conjectures, arguing that this communication represents an example of extended cognition. We identify three kinds of "collaborative gestures"--gestures that are physically distributed over multiple learners. Learners make echoing gestures by copying another learner's hand gestures, mirroring gestures by gesturing identically and simultaneously with another learner, and joint gestures where multiple learners collectively make a single gesture of a mathematical object using more than one set of hands. The identification and description of these kinds of collaborative gestures offers insight into how learners build distributed mathematical understanding. [For complete proceedings, see ED581294.]