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 a former life I researched mathematical biology. My primary focus was on the influence of population structure on the evolution of social behaviours. The following are my published mathematical biology articles.