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At heart I'm a mathematician. Of all intellectual pursuits, I have found mathematics to be the truest and the most faithful. It has beauty and chaos, but there's always a hard diamond at its core.

I spend my research time either as a biologist (using an inclusive fitness approach in the evolutionary modeling of behaviour) or as an educator (developing curriculum, both at the high school and university level). All this involves lots of beautiful (and elementary) math, so I'm pretty happy with my work. I am cross appointed to both the Biology Department and the Faculty of Education.

Current Projects (August 2016)
Inclusive Fitness:

My main interest is in the relationship between inclusive-fitness models and other standard measures of trait (allele) fitness, for example, invasion fitness and fixation probability. Principal collaborators are Corina Tarnita (Princeton), Alan Grafen (Oxford) and Danny Krupp (One Earth Future).

Game Theory:

My long-time interest in evolutionary game theory has morphed into a fascination in how humans behave and I feel that the time has come for a much more mainstream evolutionary point of view. To begin this quest in a simple way I am looking at interactive games such as prisoner's dilemma and the ultimatum game. At one time this was the domain of economists and psychologists, and the biologists looked after the animals. But now both sides are interested in both sides. It needs to be said that humans add a significant new flavour to the these contests, and here I am not thinking of rationality, but rather something akin to what is called "fairness." My principal collaborators are Andrew McEachern (Queen's) and Danny Krupp (One Earth Future).

High School Math:

In the midst of millions of words of confusing rhetoric on what's wrong with math education, my own view is that the problem is with the structure of the curricula -- that this has led to a network of topics and tasks that are little consequence and totally lack sophistication (my current favorite word for what is lacking). In short the material we currently work with is not math but is a pale technical shadow of real mathematical activity. And our students (all of them) deserve better. My curriculum redesign project Math9-12 seeks to build sophisticated units to replace as many of the standard high school curriculum strands as possible. A good example is found in the Transformation10 unit that we workshopped in July 2016 with a number of students entering grades 9 and 10. We plan to take this unit into the classroom in November 2016. Principal collaborators are George Gadanidis (Western), Nathalie Sinclair (Simon Fraser), Walter Whiteley (York), Miroslav Lovric (McMaster), Ami Mamolo (UOIT), Andrew McEachern (Queen's) and Kinga Petrovai (Oxford).

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