My research is driven by a desire to understand how humans have access to something as powerful and certain 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.
We are currently conducting a study on Coherence in Mathematical Development, with seed funding from the Adaptive Brain & Behavior destination area. The study involves qualitative analysis of students' videotaped 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.