I study the mathematical activity and learning of people across settings, and the role of bodies, technological tools, space/place, and participation structures. I begin with the assumption that all children have the potential to engage in rich and complex mathematics, and that students' experiences in typical classroom mathematics make contact with just a small fraction of the possibilities for learning. I'm interested in developing new accounts of what might count as "prior knowledge," "learning mathematics," and "mathematics activity" that might support the success of a broader set of mathematics learners.
The studies I conduct tend to fall into one of two categories. In the first, case studies of naturally occurring activity, I use ethnographic methods to investigate how participants make sense of mathematical activity in which they engage, and how they work together to accomplish the tasks pertinent to the setting or across settings. For example, I have been involved in studies of a group of archaeologists who study the lived experiences of Inkans under Spanish colonial rule, a competitive high school marching band, and skateboarders in local skateparks. I am just wrapping up a study of a company that designs custom crates for clients' art objects. These studies help me to develop theories of how people learn and do mathematics.
In the second category of work, I conduct design experiments to investigate how findings from case studies might inform instruction. These design experiments tend to revolve around tasks that leverage the ways of (and structures for) learning and doing mathematics found in the case study settings. These studies are meant to pilot and explore the features of novel, designed tasks, but also to expand our understanding of findings from the case studies. I am currently working on designs of what I call Walking Scale Geometry and Walking Scale Number Lines for secondary students, which involve groups of students in large spaces using their whole bodies and everyday materials to solve geometry and quantitative reasoning problems.