At the moment, I believe that non-modelers (students or faculty) benefit from attempting to model simple systems. I believe that it helps them become better scientists.

I am near the end of a semester in which we tried to incorporate a little bit of modeling into an otherwise basic graduate level ecosystems course. I think I would like to reflect a bit.

For years I have helped teach a population/community grad course, where we included basic population and food web models, and a smidgen of other stuff. In that course, we started everyone out making the same assumption of ignorance for all, and we taught just enough for students to implement simple models in R. I am not sure how satisfactory it is. I think I want to teach more basic R so that students learn about R in a modeling context, not just their stats classes. I think by learning R they will learn about models even more effectively.

This semester (Winter/Spring 2011), in the ecosystems course, we started students thinking along two tracks, one of conceptual models of ecosystems and the other learning the R language. Our thought was that by the time they had learned enough about ecosystems, to create conceptual models, they would have learned enough R to begin formalizing their conceptual models. However, that has not been the case, for at least two reasons.

The first cause of sub-optimal pedagogy may have been that students new to a language (e.g., R) need to work with it at least three days/week (preferably 4-6), but I did not structure the assignments that way. They need both carrots and sticks, and assignments that require daily turn-around (e.g., automated release and deadlines, or email with 24 hours to upload answers). I would not even have to grade every one of them - just mark them turned in or not, perform spot checks, and provide detailed answers. Why didn't I do this? Several not-very-good reasons:

- I felt sorry for them,

- I wasn't 100% convinced that I should push programming and math that hard,

- it would have been more work for me,

- not everyone needed that kind of practice,

- those that needed that kind of practice COULD have done self-study.

The second reason for suboptimal pedagogy was that I tried to be more flexible with the modeling assignments than I was easily capable of -- I could create stuff, but some of it took longer than was convenient. In brief, we asked students to come up with a scientific question, explain what is known and unknown regarding that question and their study system, and design a conceptual model that captures the essence of their question and/or system. Students were then asked to formalize their conceptual model using mathematics or computer code or both. The students conceptual models were not all ecosystem models with merely pools and fluxes of all the same units and element(s). Rather, most were a hodge-podge of different sorts of variables that related typically in a mechanistic fashion, but were not comprised of, for instance, pools and fluxes of carbon. Therefore, the relatively low programming ability of the students (see first reason, above) and my desire to be flexible with regard to acceptable topics meant that I had to invent lots of unique code for each different student. And that, Virignia, is the second reason why my pedagogy was sub-optimal.

However, I think that forcing students to formalize their conceptual models has helped them see and understand their own conceptual models to a greater degree. Formalization helps them become ever more specific with regard to their conceptual model and this helps them generate more testable predictions. Formalization helps them understand what a mathematical model is and and how mathematical models provide structure to theory. The process helps show them how models are used in Science, and last, it helps them see indirect connections more clearly and accurately. Well, ... I

hope it does all that.