This post from Friday, in which I asked for reasons why business majors should be required to take calculus, has gotten a lot of comments, most of which seem to be wondering the same thing and adding disciplines like biology into the question. That post did actually come from some specific thoughts I’ve been having about making calculus a required course.
I can think of just two legitimate reasons for making any course a requirement within a major or minor field of study:
1. The course is fundamental to getting a coherent, well-rounded view of the discipline it comes from; or
2. The course has demonstrable, significant applications to that field to such an extent that teaching the material outside a traditional course is impractical.
You could also add that in some cases, a major contains a course of its own that requires prerequisite material from some other course — so much material that it can’t just be built in. That’s pretty much an alternate take on #2.
Note that I don’t include “liberal arts” or general education courses in this, because some schools care about well-roundedness while others would prefer to give a deep and not-so-broad approach to students’ education. These are two different approaches to higher ed, and the merits and demerits of each are not the issue here. We’re talking about courses within a major, thought of as integral and inextricable parts of what it means to be trained in a discipline.
If you grant me those two criteria, and only those two, then the big question becomes: Which majors can justify requiring calculus? And what of the other majors which do require calculus but can’t justify it according to our criteria?
Well, it’s pretty clear that math, physics, engineering, chemistry, (probably) computer science and (I would add) economics are definitely “yes” for requiring calculus. These are all disciplines that are either deeply rooted in the mathematical methods that arise out of calculus — so leaving calculus out would create a foundational misunderstanding of the major subject — or involve heavy amounts of calculus-based applications. Note that I am drawing a distinction between Computer Science and “information systems”; the former is more theoretical and the latter mostly applied.
It’s also clear that most of the majors that traditionally don’t require calculus — English, art history, etc. — are probably justified in not doing so.
But then we have these majors that do require calculus, but I’m not so sure — based on my knowledge of the disciplines and the people who practice them — that you can justify it. The major programs on our campus, for instance, that require calculus apart from those listed above are Accounting, Biology, Business (all tracks), and Computer Information Systems (business-oriented CS type major). What’s the rationale for requiring calculus of these folks?
Let’s take accounting and business. As I mentioned in the comments to the first post, there are actually no courses required of the Accounting or Business majors that have calculus as a prerequisite. So criterion #2 appears not really to be in effect. If calculus were that important, you would see it in courses that are required of these majors to an unavoidable extent. As for criterion #1, is it really true to say that a person simply can’t be an accountant or a businessperson without a semester of calculus — in the same sense that a person can’t really be a mathematician if they haven’t seen abstract algebra? Is calculus really that central to an understanding of accounting or business? If it is, where is it in the prerequisite list for the rest of the curriculum?
It’s certainly the case that there are concepts in calculus that are of great use to people studying accounting or business — for example, the notion of concavity and inflection points. But are there so many concepts that a semester of limits, derivatives, and integration are necessary to get them? This is like saying that everybody needs to get a little protein in his diet each day, and on the basis of that fact, requiring people to eat a five-course steak dinner every night. It seems to me that the concepts can easily be taught in the context of accounting, business, or economics courses without requiring an entire course — most of which consists of something other than the concepts students need to get. I don’t think you require an entire course of somebody, only because there are half a dozen or so important concepts embedded in the course somewhere.
Bottom line here? I think we require calculus way too much, and usually for the wrong reason or for no reason at all. The result is not more students with a calculus background. The result is more students who enter calculus with an inadequate background, struggle through the course with insufficient motivation (and an inadequate background), and very often drop out of their majors — or out of college altogether — because they can’t get past the calculus course. These are not loser students. They are bright and perfectly capable of doing well in accounting, business, biology, or what have you — and in other kinds of math, like stats or “discrete math” — but calculus drives them away, and not for anything like the right reasons.
Please don’t misunderstand me — I love calculus, and it has a special place in my life. It was the course in high school that won me over to math, the first course I ever taught, and the one course more than all the others that I teach and blog about. But I want students to have a better experience both in calculus (for the ones who truly need it) and in math outside of calculus (for the ones who don’t).