One line of research I'm currently studying is the role of epistemic cognition in the professional development of mathematics teachers. For instance, I'm studying how preservice elementary and secondary math teachers develop epistemic beliefs about mathematics, and how these beliefs interact with their beliefs about mathematics instruction and with their knowledge of curriculum standards to shape their future practice.

Another topic I'm interested in is the identification of cultural and socio-cognitive factors that frame mathematical learning. For example, how word-problems have been used in the past and presently to demonstrate mastery, how learning empirical or naive rules may facilitate or hinder knowledge transfer, and whether viewing mathematics predominantly as a technology or as a theoretical science makes a difference in one's teaching practice.

A third research interest is the establishment of mathematics as a model for second-order knowledge in science and philosophy. This took place over centuries of contact between East and West intellectual traditions. Despite its long history, however, the initial conditions of second-order knowledge in mathematics remain obscure, given the appearance of e.g., Euclid's Elements springing, fully formed, out of nowhere. Understanding the historical circumstances that preceded this phenomenon may shed light on our own mathematical practices today.