Mathematics education, especially in school settings, is too often a disempowering experience for learners, who come away with the educationally and economically limiting impression that mathematics is not for them. I seek to broaden participation in mathematical practices by exploring the theoretical implications and design heuristics that can be gleaned from contextualizing geometric and spatial reasoning within play in the form of a collaborative, body-scale game.

My work is informed by theories of learning as materially and socially situated and of cognition as inextricably rooted in embodied, physical experience. The analyses presented herein use both close case analysis and qualitative coding techniques to identify and characterize interaction behaviors.

This dissertation contains three papers. The first paper focuses on the interpersonal dynamics of parent-child player groups and characterizes participatory facilitation, a pattern of flexible adoption, adaptation, casting-off, and redeployment of scaffolding behaviors by adults toward alternating pedagogical and performance goals. The second paper zooms out to examine the learning opportunities available through observation of gameplay. I identify range of participation roles – from player to spectator and some in between – that constitute a rich learning ecology and document the ways participants fluidly within it. Finally, my third paper zooms out again to consider how the social relationships that players bring to the body-scale game shape their collaborative movement patterns and resultant learning opportunities.

Throughout, I propose theoretical constructs about the role of material and social forces in informal learning and re-assert the role of these forces in mathematics learning. I also inform the design of other embodied mathematics learning activities by implicating particular design decisions as enabling or constraining the documented interactions.