Modeling as a Teachable Skill
I just attended a nice “panel discussion” on Teaching the Art of Modeling, put together by Jim Orlin (MIT), Stephen Powell and Rob Shumsky (both from Dartmouth). This was not your normal INFORMS session! The panelists decided to do this as an “active learning” session, so audience members had to work throughout the session. The first exercise was to think about how to model a hypothetical, but real-sounding problem: “Suppose the Red Cross was considering paying people for their blood donations. How would you provide them with a model that could help them understand the tradeoffs.” That (paraphrased) was all the information we got. We were then given 10 minutes or so to work individually on addressing this. The idea would be that this would be the first 10 minutes of whatever multiple-hour process we would go through to get a “real” model. Where would you start?
For many, the starting point was brainstorming: putting down a whole set of issues to be considered and items that might go into the model. For others, it was graphing some of the anticipated relationships between key issues. Others still used techniques such as influence diagrams to help organize their thoughts. Being a hard-core mathematical programming, I thought in terms of objectives, variables and constraints, and was pretty far along with my nonlinear, nonconvex mixed integer program when time was called.
Stephen Powell then asked some audience members what they did, eliciting the strategies given above. He has experimented with this problem with students and learned a number of things about what they do (presumably either inexperienced or novice at modeling). First, even for students who have taken modeling courses, it is surprising how little of what we teach gets used in this context. Students, when faced with a fuzzy modeling problem, often do some combination of the following:
- They grab on to data like a lifeboat, prompty multiplying or dividing every number in sight in the hope of getting the “right answer” the professor is looking for. The Red Cross example has no numbers, so they might make some up just to get going.
- They dispense with modeling and go straight to the answer: “This is a bad idea because …”
- They adopt inefficient methods and are unable to step back and recognize how inefficient they have become.
- They overuse brainstorming relative to any aspect of structured problem solving that they might have been taught.
If there is a column of numbers, you can bet that many students will immediately run a regression!
After discussing these results (there are a couple papers in the Journal of the Operational Research Society on “How Novices Formulate Models” that covers this), Jim and Rob were given a problem new to them (on a model for deciding on the best morgtage to get) and they showed how an influence diagram approach would be used to begin understanding and modeling.
Powell and his co-author Robert Batt have a book entitled Modeling for Insight (Wiley: one of the exhibitors here) .
It was great to see a session that required the audience to do some work! While I was not completely convinced by the modeling approach presented (give me my objective, variables, and constraints!), I was convinced about active learning as a way to make 90 minutes go by much faster and in a much more effective way.