Course Goals

When I started teaching my own courses, one of the less obvious things I had to figure out was how to structure my syllabi. One section that all the syllabi I looked at contained—and all the advice I read mentioned—was the section on “course goals.”

Honestly, I couldn’t see the point. The goal of a calculus course is to, um, learn calculus? But I was supposed to write a course goals section, so write one I did. It was basically boilerplate.

In this course we will master the details of differential calculus, and pursue some advanced topics and applications. We will also develop technical writing skills that allow clear communication of sophisticated ideas, and learn about some technological tools such as Mathematica useful to mathematical and scientific projects.

We will cover limits, continuity, derivatives, modelling, and applications.

That isn’t completely contentless; you can see the emphasis I put on communication and writing skills in my math classes. But honestly, that’s a secondary goal at best. If my students finish calculus 1 with an understanding of what derivatives mean, how to compute them, and how to use them, I’m happy. The goal of calculus 1 is to prepare students for calculus 2. (And the goal of calculus 2 is to prepare students for multivariable calculus, et cetera).

When I first taught an upper-division course, the “course goals” section became possibly more confusing. There is a lot more room for flexibility in designing a number theory course than there is in designing a calculus course: there’s no “next course” that it’s supposed to prepare students for, at least in our department, so I could cover basically whatever I wanted.

So fleshing out the topics list was substantially more important. I needed to decide what topics to include in my course. By the goal was, more or less, “learn some number theory”. Or maybe even just “learn some math, and this happens to be a course in number theory, but the goal is just to have you learn some more advanced math topics.” And that’s not something it really makes sense to write in the syllabus.

But I finally got it last summer. Our department reorganized our senior comprehensive project to involve interdisciplinary half-courses called Math 400, and I got to teach one of the first two we ever offered, which became my course on cryptology.

I was a little nervous about preparing this course. It was very different from any course I’ve taught, and even very different from any course our department had taught, so there weren’t a lot of resources to draw on. And it wasn’t even similar to any courses I’ve taken, so I knew I was very much making it up as I went along. At the same time, I really wanted it to be a good and positive experience for our majors. I wanted to give them something they could feel excited by and proud of for their senior capstone project.

Luckily for me, Occidental’s Center for Teaching Excellence (which is, itself, excellent) held a workshop over the summer to assist us professors with developing new courses. We formed a working group of four professors to brainstorm ideas for our courses and get feedback on our ideas and our syllabi.

Working with this group, the focus on course goals made sense.

I had fallen victim to a common problem in planning and designing processes: I had forgotten that you can’t make good plans unless you know what you’re trying to achieve. If you have goals, you can look at what you’re doing, see whether that achieves your goals, and think about ways to meet your goals better.

Without goals, you’re just doing things. You can’t tell whether they’re good things or bad things or bad things, because you don’t know what good and bad mean.

For core service courses like calculus, this isn’t much of a problem. The goals are standardized: prepare for the next course in the sequence. And the course itself is standardized. I assign homework and give tests, just like every other calculus course. The goals matter, but I don’t have to think about them too much.

With more interesting courses like my cryptology seminar, I had a lot more decisions to make. I had to put some thought into what I actually wanted my students to get out of it, and then I had to think about what course design decisions would actually accomplish those goals. Because there were more choices I could make, there were a lot more things to think about.

The other thing I realized is that most courses are more like the seminar than they are like calculus. A course on English literature, or the history of Islam, or the psychology of gender, doesn’t exist to check a box and prepare students for the next course in the sequence. It isn’t a standardized offering. And thus it demands individualized thinking about what role it does play in the curriculum—what its purpose is, what students should learn from it and assignments will actually further those goals.

(And even a basic calculus class has more of this going on than I’d realized; there’s a lot that all the calculus courses have in common, but also a lot of choices to make. Within my department, there’s wide variance in things like how much weight is put on homework assignments versus tests, or which applications are the most interesting and important to study. We still need to think about the goals of our courses if we want to teach the best courses we can.)

If we want to make good decisions about how to structure our courses, we really do need to think about what we’re trying to accomplish. What do we want our students to take away? What do we want them to learn, and experience? These are important questions, and they help us decide what’s worth spending time on, and what we can skip past.

But why is it so important to put this in the syllabus? One reason, I suppose, is that we can. If we’ve put in the work to decide what our goals are, we might as well share those. And forcing ourselves to write the goals in the syllabus imposes some discipline, and insures that we do put this thought in.

Publishing our course goals helps us interact with our colleagues and share information and expertise more easily. It’s hard to give advice to someone unless you know what they’re trying to do; certainly, in the course development workshop I went to, a lot of the discussion was about what types of assignments would actually achieve the goals I’d set out.

But most importantly, telling our students what the goals of our courses are helps them be better students. None of our students can ever remember every fact and memorize every skill we mention in our courses. They have to prioritize. And one of the most frustrating ways to underperform in a course is to work very hard on things that just aren’t important, while neglecting the most vital parts of the material.

Our students want to focus their study and their practice on the parts that are really important. But precisely because they are students, and not experts, it’s hard for them to tell which parts those are; part of our role, as instructors, is to help them figure out where to focus their efforts.

If we share our course goals, we can do a better job of designing our courses, and our students can do a better job of developing genuine mastery and understanding. The idea felt silly when I first heard of it. But more and more, I realized that the “course goals” section of the syllabus really is critical.