Collaborative gesture as a case of extended mathematical cognition.

• Learners use collaborative gestures when proving mathematical conjectures. • Types of collaborative gestures include mirror, echo, alternate, and joint gestures. • Collaborative gestures show how mathematical cognition becomes extended. • Gestures should be considered alongside collaborative talk moves. Gestures have been shown to play a key role in mathematical reasoning and to be an indicator that mathematical understanding is embodied – inherently linked to action, perception, and the physical body. As learners collaborate and engage in mathematical discussions, they use discourse practices like explaining, refuting, and building on each other's reasoning. Here we examine how gestural embodied actions become distributed over multiple learners confronting mathematical tasks. We define collaborative gestures as gestural exchanges that take place as learners discuss and explore mathematical ideas, using their bodies in concert to accomplish a shared goal. We identify several ways in which learners' gestures can be used collaboratively and explore patterns in how collaborative gestures arise while proving geometric conjectures. Learners use collaborative gestures to extend mathematical ideas over multiple bodies as they explore, refine, and extend each other's mathematical reasoning. With this work, we seek to add to notions of important talk moves in mathematical discussions to also include a consideration of important gesture moves. [ABSTRACT FROM AUTHOR]