I was listening to the BBC's Global News Podast this morning and found an interesting segment on the utility of mathematical modeling. Professor John Adam's book (which can be found here) looks at how one can model various aspects of urban life—pollution, traffic congestion, number of dentists offices, etc. I've not read the book, but Adam's message in his interview was something that I can sympathize with. In particular, Adam talks about the degree to which the educational process divorces math from any kind of applied usage. Learning math in this way, he goes on, is partially responsible for why more children/people are not as interested in mathematics as they might otherwise be.
Sure, there are the ubiquitous "if a train leaves city A at rate X, and a train leaves city B at rate Z, when will their paths cross," kind of examples. But seriously, is that the best we can do? Now, I recognize that I'm far from being the strongest, or the quickest, when it comes to picking up a lot of the methods that I've been taught over the past few years. I, like many people I suppose, was not the biggest fan of math class in high school. Some of this was laziness on my part, but some of it was also the framework in which the subject matter was taught. Even in college it was far from clear that any kind of math beyond balancing a checkbook would play as big a part in my life as it currently does. I did well enough in these classes, but it was not until graduate school that I really had to seriously engage math and statistics.
As it turns out, I've really enjoyed the quantitative side of my training here at Binghamton, and I'm far more willing to work at developing my understanding and skills now than I was when I was 16. Had I known in high school that I this stuff could be used to study things like war, human rights, etc., I might have cared a bit more. These are things that I've always been interested in. And this is perfectly rational behavior, right? If the expected utility of learning this material is zero, or even negative, then why expend the effort? Where is the payoff? If this is the case, then a major part of the reason that the expected utility of learning this material is so low is because the people that should be able to provide you with the relevant information to update your expectations simply do not do a very good job of that. In fact, I'd say that I didn't really get that at all until grad school. And being able to make that initial connection between math and statistics, and the substantive topics that I care about, has subsequently led me to develop a greater appreciation for the math itself that underlies the models I often use.
I don't have any answers for how the educational system could be modified to address this issue. I also realize that you would have to find a way to incorporate applied mathematics into most subject fields, as not everyone has the particular set of interests that would make more math in history or government class a sufficient solution to the problem. Still, there must be a better way. With folks like Neil deGrasse Tyson going around trying to promote greater scientific literacy, and the recent attacks on NSF funding for political science, it seems like there is a space for us to modify how we educate our younglings and how science, math, history, etc., can be better integrated in this process. Maybe if people developed a better understanding of science as a process, or math as something with real world and substantive applications, rather than something that existed strictly from 1pm to 1:45pm during 8th period, people would be better able to develop a more robust appreciation for how mathematics and science fit into, and matter for, our daily lives. This is fairly obvious when phrased like that, but the fact is that it's not really what we do currently, is it?
Am I missing something?
Also—and this is a total aside—Brian Rathbun at the Duck of Minerva has a discussion of how Iron Maiden material can be used to teach political science. This is perhaps a good example of what I was talking about above, so perhaps this is not a total aside, but what we have here is essentially "applied awesomeness."