By investigating the probabilistic content knowledge of prospective mathematics teachers, my research, in general, contributes to the (documented) limited research on teachers’ probabilistic knowledge. More specifically, my work has led to the development of a variety of theories, models and frameworks, which account for relative likelihood comparisons made by prospective teachers. Currently, I am incorporating more recent developments from the field of cognitive psychology (e.g., attribute substitution), which (I argue) have largely been ignored by those investigating probabilistic thinking and the teaching and learning of probability in the field of mathematics education; and, in addition, I am establishing that informal logical fallacies (e.g., the fallacy of composition, the appeal to ignorance and others) are an effective means to account for normatively incorrect, inconsistent, sometimes inexplicable responses to a variety of probabilistic tasks.
Other research interests include: (classical, frequentist, and subjective) interpretations of probability, coin flips, sample space, abduction, equiprobability, perceived randomness, heuristic and biases, relativism, and coin flip sequence multivalence.
The new math, the new new math, the math wars and, especially, exposing and exploring the false dichotomy (i.e., traditional versus reform) associated with teaching and learning mathematics: by (1) modelling the reform approach to teaching and learning mathematics and (2) illustrating – as a character (cf. Colbert) – certain absurdities associated with the traditional approach to teaching and learning mathematics.
probability, combinatorics and alternative base arithmetic (especially base golden ratio).
stand up comedy (e.g., Richard Jeni, Greg Giraldo, Jeremy Hotz, Louis C. K., John Pinette, Jeffrey Ross, Danny Bhoy, Tommy Tiernan, Mitch Hedberg, Kathleen Madigan), sports (e.g., squash, tennis, golf, ball hockey, Moksha Yoga, U of S Faculty/Staff Hockey League), Apple Inc. (e.g., iPhone, iPad, iMac, MacBook Air), walking (my dog), my dog Scout's behaviour, playing the lottery (e.g., Lotto 6/49), poker, television, podcasts (e.g., The Age of Persuasion), non-fiction (e.g., earlier Chuck Klosterman), social media (for mathematics education).