My main current research focus is on, broadly, undergraduate mathematics education. This includes the following:

  • Understanding and developing flexible procedural knowledge in undergraduate mathematics students (joint work with Jon R. Star).
  • Developing a theory of mathematicians’ future thinking – something I call mathematical foresight (joint work with Bill Barton, Reece Roberts, and Donna Rose Addis).
  • Evaluating classroom models and their influence on student academic achievement and mathematical understanding.

Publications in undergraduate mathematics education are below.

Other education publications are as follows.

I also have an interest in (community/technical) college mathematics education.

In an alternate life I research mathematical biology. My primary focus was on the influence of population structure on the evolution of social behaviours, but have also worked on spider web geometry. The following are my published mathematical biology articles.