Teaching

My philosophy

I believe that students learn best by doing. This philosophy can be a challenge to realize for students whose background is not primarily mathematical, in a topic that is largely mathematical. In smaller groups I encourage students to search for and quantify the models that underlie their understanding of ecological phenomena. One powerful tool I have found is the ‘gaming simulation’. Converting a situation or process into a game demonstrates the essentials of model building, while leaving the mechanisms relatively transparent to all. In addition, a careful gaming simulation encourages participation simply because it is fun. In the past I have made use of ‘Darwinopoly’ to communicate the effect of natural selection on behavior to non-biology majors. I have recently collaborated in the development of a conservation-oriented game tentatively titled “Buy-o-diversity”, in which students compete to build privately funded nature reserve systems.
My primary educational goal is to give students an appreciation of what mathematical models can and cannot do. Models cannot provide a perfect description of reality. They are necessarily a simplification of reality, designed to be understandable. Models can help us to make predictions, or management decisions, based on explicit assumptions; these assumptions are then exposed for all to see, critique, and improve. I will achieve my goal as an educator if my students emerge with an appreciation of mathematical models in ecology, the ability to think critically about the models they come across, and to apply the models of others to their own data and problems. I will excel as an educator if some of my students attain the ability to construct their own models to describe their data and problems.
My secondary goal is to teach statistics as the science of fitting models to data. Hypothesis testing is also a part of statistics, but a part that is overemphasized when teaching statistics to ecologists. Even a t-test imposes a model on the data; that variation in a sample is described by a normal distribution. That model has two parameters, a mean and a variance, which we ‘fit’ to the data using formulas derived from a maximum likelihood approach. Taking the view that we are fitting models to data immediately raises the question of what other models might be better descriptions of the variation in a sample, and how do we estimate the parameters of those models? Hypothesis testing then arises naturally as a consequence of deciding which model best describes the data.

Last updated on June 6, 2005 . Email Webmaster.