Moebius Stripper, whose blog is unfortunately defunct, wrote back in 2004 about course descriptions that describe. She points out that traditionally, course descriptions of mathematics classes are ridiculously uninformative and basically boil down to transforming the table of contents of a textbook into a run-on sentence. And then we wonder why students see math as a bunch of disjointed pieces of information with no overarching narrative to tie them together... don't we come into the classes with that attitude?

See, for example, my institution's mathematics course listing. Physicists do the same thing. Historians, for example, don't. People in the English department don't do it too much, although one does find the occasional list of books to be read in a course description. I am not sufficiently interested in this question to systematically study it, and even if I were there are other more interesting things to study first.

I'd heard this idea before; I'm not sure if I had it originally, if I got it from Moebius Stripper back in 2004, or elsewhere, but I know I think it every time I read course descriptions. Fortunately I will never be reading course descriptions from the point of view of a student taking courses again. (For those of you who don't know, this is my last semester taking courses. Today I was on campus and saw a pile of Fall 2008 course timetables. I almost took one. Then I realized that for the first time in many, many years, I will not be taking classes next semester.)

This may have something to do with the fact that it's expected at most universities that students shopping around for "elective" courses that they don't know much about are probably going to take more humanities-like classes; I don't have hard data on this, though. There's less of a point in trying to craft a good course description if you figure that nobody who's reading the course catalog looking for something to take will even look in your department. In fact, I don't even have anecdotal evidence for this claim, because I went to MIT for undergrad, and the normal rules don't apply there.

## 13 March 2008

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## 8 comments:

"Theorems A and B of Cartan" for example is certainly not very helpful in describing the content of a course. Unless you've already taken a course in several complex variables and are deciding whether you should take this course....

But what else would you put in a description? 'Like complex variables but moreso'. I guess you could explain why it's important or interesting. Maybe that would be more interesting and just as useful.

Martin,

that's exactly what I'm saying course descriptions

shouldsay. Don't tell me which theorems I'm going to learn. Tell me what I'll be able to do at the end of the semester that I couldn't do at the beginning.My course description (as it exists http://ece493t3.uwaterloo.ca) does describe the course, I think, in a way similar to what MS advocates. It's certainly more useful for students. (It is indeed unfortunate that MS is not blogging anymore!)

However, I will note that a "traditional" course description is useful for people who are looking at applications and trying to figure out the scope of the classes that a prospective student has taken. I remember that MIT's graduate school application was a bit weirder in that it also required applicants to list course texts that they used.

One distinction that could be worth making is that (in my experience) in the humanities courses are mre often tied to a specific professor, whereas in math (and the sciences more generally) the course is more often tied to specific material.

For example, the storylines I choose to emphasize in linear algebra are very different from those that one of my colleagues likes to teach -- even though we both cover systems of linear equations, eigenvalues, and the other things currently listed in the catalog. This would make it harder for us to agree on a description of the kind that you are proposing -- even though I completely agree with your sentiment.

Calculus I -

A study of the nature of continuous change. Introduces a set of tools for understanding how changes in one quantity affect changes in another quantity. Some emphasis is placed on the notion of "limit", which allows us to understand how a continuous change behaves at one point by considering its behavior at nearby points. Concludes with an investigation of how to calculate areas of irregular figures, and how this process is related to the earlier topics.

Calculus II -

Continues developing the tools needed to calculate areas of irregular figures. Extends the concept of limit to discuss extrapolations of observed patterns "to infinity". Applies this concept to understand aggregates of infinite collections.

Multivariable Calculus -

Further develops the tools in Calculus I and II. Applies these tools to study the geometry of irregular shapes in two and three dimensions.

At my college we're all awash in the effort to define "student learning outcomes." The SLOs are supposed to be included in each official course description so that students will know what they will learn by the end of the course. For example, we're looking at the SLOs devised by one college for Calculus III, which includes language like "compute the curvature at any point on a space curve using vector operations; optimize a multivariate function on a space curve or plane region; utilize multiple integrals using rectangular, polar, cylindrical, or spherical coordinates in problems involving volume, moments, and mass; set up and evaluate line and surface integrals."

It's not a bad start.

(And I miss Moebius Stripper, too!)

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