As the world demands increasingly innovative ways of thinking, it is important for us to consider learning as a complex interaction between a given learner’s existing knowledge, new knowledge and experiences, and the rules and conventions of a given discipline. In a series of interviews with expert mathematicians, I explored how experts connected their informal and formal knowledge to make sense of an unfamiliar mathematical proof.

From this data I developed the Resources and Acts for Constructing and Understanding Mathematics (RACUM). I found that experts deconstructed and reconstructed the mathematical objects presented throughout the proof, in an effort to test and establish relationships between their symbolic, empirical, and intuitive understandings. I plan to extend this work to look at learning across varying levels of expertise, and across fields.

See more about my work with expert mathematicians:

Wilkerson-Jerde, M. & Wilensky, U. (2011). How do mathematicians learn math?: Resources and acts for constructing and understanding mathematics. To appear in Educational Studies in Mathematics, 78(1), 21-43 [Link]