Collaborative gestures in the mathematics classroom occur when multiple learners coordinate their bodies in concert to accomplish mathematical goals. Collaborative gestures show how cognition becomes distributed across a system of dynamic agents, allowing for members of groups of students to act and gesture as one. We explore ways high school students gesture collaboratively while proving geometric conjectures in the sociotechnological context of an embodied video game in their classrooms. We find that students use their bodies and joint action to reason together and establish intersubjectivity. Gestures can both allow learners to access mathematical ideas and exclude peers. We also find that gestures generally, and collaborative gestures specifically, are associated with powerful forms of mathematical reasoning about generalizable properties of space and shape.