What’s the purpose of mathematical modeling? The easy answer is something like, to understand the real world. When I look more deeply, however, I see distinct reasons to model—and to model in the classroom. I hope that trying to define these will help me clarify my thinking and shed light on some of the worries I have about how modeling might be portrayed.
Let’s look at a few purposes and try to distinguish them. To save the casual reader time, I’ll talk about prediction, finding parameter values, and finding insight. I think the last is the most subtle and the one most likely to be missed or misused by future developers.
Maybe I’ll post more about each of these in detail later, but for now I’ll move quickly and not give extended examples.