Gestures have been shown to play a key role in mathematical reasoning and be an indicator that mathematical reasoning is "embodied" -- inexorably linked to action, perception, and the physical body. Theories of extended cognition accentuate looking beyond the body and mind of an individual, thus here we examine how gestural embodied actions become distributed over multiple learners confronting mathematical tasks. We identify several ways in which gesture can be used collaboratively and explore patterns in how collaborative gestures seem to arise in a learning environment involving a motion capture game for geometry. Learners use collaborative gestures to extend mathematical ideas over multiple bodies as they explore, refine, and extend each other's reasoning. [This paper was published in: "ICLS 2018 Proceedings," p552-559. ISLS.]