My research is driven by a desire to understand how humans have access to something as powerful and reliable as mathematics. I have found that many philosphical questions about the nature of mathematics have psychological answers. I ground my research in psychological models of students' mathematics, and collaborate with psychologists and neuroscientists, to find these answers.
Martha Ann Bell (Psychology) and I recently conducted a study on Coherence in Mathematical Development, with seed funding from the Adaptive Brain & Behavior destination area at Virginia Tech. The study involves qualitative analysis of students' videorecorded behavioral responses, as well as quantitative analyses of EEG data, enabling us to test three related hypotheses: (1) the cognitive demand of mathematical tasks can be predicted by models that account for the units and unit transformations required for their solution; (2) frontal-parietal coherence provides a neurological indicator of appropriate cognitive demand; and (3) mathematical development is characterized by a frontal-to-parietal shift in neurological activity.
Currently, I am completing a book entitled, Mind Your Own Mathematics (Routledge publishing), about the psychology of mathematics. The book demonstrates how you construct mathematical objects through the coordination of your own mental actions. Thus, equity and access to mathematics translates into opportunities to coordinate and reflect on your own activity, and each of us should experience mathematics as personally empowering. The web link, "Math in Action," on the right hand side of this page, includes related illustrations.