Watered-down Courses?

I’m now a little over half-way through Mankiw’s Econ 101 book. One thing that stands out is that the text presents very little quantitative math. There is qualitative math in the way of supply curves and the like, but there are very few calculations going on. The exercises at the end of each chapter are trivial, mathematically speaking.

Even granting the lack of math, the book does seem to be a bit light on content for its size. Each chapter presents one main idea, with some motivation and a few examples. I have no grounds for knowing whether that’s normal or not for an econ book, but I do remember people in college saying that Econ 101 was harder than this seems to be.

I poked around the web for reviews of the book, and they seemed to be consistent with my experience. People who liked the book were impressed by the clarity and freshness of the exposition. Critics thought it was watered-down, sometimes severely so.

It’s interesting to ponder whether this style is a good thing or not.

Again, I’m don’t know enough about the subject matter to judge what’s important or not in the long run. So I thought about the same issue in a subject that I do understand, calculus. I can summarize fairly quickly what I would want a student to get out of their Calc 101 class:

1. There is a mathematical operation called the derivative, which tells how fast a function is changing at a given point in time.
2. There is another mathematical operation called the integral, which can sum the values of a function between two points.
3. The derivative and integral operations are inverses. You get an A+ if you can explain why this makes sense.
4. A smooth function takes on its extreme values where the derivative is zero. This gives you a way to calculate the maximum/minimum values of a function.
5. In general, high-school algebra and trig give you tools for analyzing linear functions. Calculus gives you the power to analyze more arbitrary, curved functions.

Wow, that’s pretty brief. But extremely few students who passed Calc 101 could tell you this a year later, especially if they haven’t taken additional math courses to drive the points home.

Note that I didn’t include anything about the actual techniques to take a derivative or integral – which is most of what the calculus curriculum is all about. Quite frankly, I don’t know how important that is. If you ever needed to differentiate a function on the job and didn’t know how … well, calculators and computers can do that sort of thing; not to mention that you can hire a starving grad student for cheap.

Of course, you will need to know how to do calculations if you take additional math or engineering courses, just to be able to do the calculations in those classes. But I don’t really know important being able to do those calculations are in the long run, either.

But anyways, it’s the concepts that are important, and yet when I taught the course, most of the homework I gave involved just drilling students on techniques. I guess the philosophy was that you hope that somehow the drilling will give people a foundation that they can then rise above to get a better perspective with? Or, more likely, that it’s easier to teach, learn, and grade technique, so everyone’s happier, rather than trying to focus on the more intangible fundamentals. On the other hand, it sounds quite challenging to teach the concepts to people without strong quantitative skills.

Getting back to Mankiw’s book, I guess my current thinking is that it works just fine for me. I have good enough quantitative skills that I can pick up the high-level points fairly well, and I can see how to map them into tangible calculations if I ever needed to. But it’s less clear whether the “watered-down” approach is better or worse for students without good math skills.