Large Courses Should Be Better

One of the more frustrating unexamined assumptions about universities is the myth of small course superiority: That small courses are inherently better than large ones.

I’ll concede that, at today’s universities, large courses are not invariably better than small courses—although it’s not clear that they are actually worse, or whether it’s possible to perform a fair comparison. But I also believe that large courses should be better than smaller courses, for several of the multiple meanings of should. They must be. They can be. But they also aren’t yet, frequently due to poor design and implementation decisions.

So let’s examine all three of these varieties of should. In Part 1 (“Large Courses Should Be Better”) we’ll explain why large courses must be better than small courses. Simply because, at most universities, most courses taken are large, even if most courses offered are small. That also means that the best way to improve university education is to improve large courses. We’ll also explore how large courses can be better than small courses, as the resources generated by more students create the opportunity to improve components of the course that scale infinitely well.

In Part 2 (“Why Large Courses Fail”) we’ll examine multiple reasons why large courses fail—including institutional neglect, bad decision making, and ineffective design. Several of the common mistakes that cripple large courses are directly enabled by the myth of small course superiority—for example, the common “divide and blunder” error of breaking a large course into smaller pieces.

The way universities discuss class sizes is downright deceptive. On tours and in information sessions it’s common to hear numbers quoted like average class size⁽¹⁾. But these numbers have little bearing on the student experience.

To see why, let’s imagine a university that offers 11 courses: one that enrolls 100 students, and 10 that enroll 10 students each. On the tour, you’d hear “We have an average class size of 18”. That’s true. Or “We have a median class size of 10.” That’s also true⁽²⁾.

But let’s examine the situation from the perspective of a student. Without loss of generality, assume that each student takes one course per semester, every course is repeatable, and no courses have prerequisites. If these assumptions bother you, just multiple the scenario by 10, and consider 10 100-student courses and 100 10-student courses. The math works out identically. Some of these assumptions are problematic, but they tend to further undermine claims about small class sizes. We’ll get back to this in a minute.

It’s fairly easy to see that half the time a student will be in a class of size 10 and the other half in a class of size 100. Meaning that the median and average class size experienced by a student is 55—which is substantially larger than the median (10) or mean (18). In addition, students will spend half of their time in the single large course, despite there being 10 times as many small courses as large courses. That’s not what they told us on the tour!

The problem is that large courses have a disproportionate impact on the student experience because… well, they’re large! Here’s the formula to calculate the average class size at a university: $\frac{\sum C}{|C|}$, where $C$ is the set of enrollments and $|C|$ is the size of $C$ and the total number of courses offered.

But here’s the formula to calculate the average class size experienced by a student: $\frac{\sum C^2}{\sum C}$⁽³⁾. The squared term in the numerator reflects the outside impact of large courses on the student experience. It also renders the statistics on class size flaunted by universities nonsense, and leaves many graduates wondering—what happened to all the small classes I heard about?

And the accessibility of small courses is even worse than the above analysis indicates. We’ve assumed that students can enroll in any course. But of course, that’s not the case—and it’s frequently lack of access to a course that makes it small! Small courses are more likely to occur at the end of prerequisite chains. Small courses are also less likely to meet degree or general education requirements. Small courses are also more likely to cover niche topics that few students are interested in.

Put another way, the number of small classes offered by a university primarily reflects the structure of their curriculum and the willingness to devote faculty resources to teaching advanced and specialized topics, usually to graduate students. Given that these faculty may not be teaching undergraduates, it’s even more unclear whether a plethora of small courses says anything positive about undergraduate education. A lot more context is needed.

If universities wanted to engage honestly with this aspect of the student experience, they would quote numbers on the median class size taken by a student during their undergraduate degree program. But they won’t do this—partly because the average class size numbers are invariably smaller and therefore “better”, and also partly because it would expose troubling differences between majors. Unpopular majors frequently also have small class sizes—which make the overall university statistics look better, but mean nothing to you if you are choosing to study a popular topic.

As an aside, if you’re a student and you really care about small classes, one of the best ways to achieve your dream of being seated around a small table with a professor is to select an unpopular major in a department that is overprovisioned with faculty. Just please have a plan for paying for college⁽⁴⁾!

So even if many courses offered are small, most courses undergraduates take are large—meaning that large courses have a larger impact on the undergraduate experience. It’s hard to call this disproportionate, because it’s entirely proportionate—assuming you do the math correctly.

We’ll discuss next why large courses can be better than small courses, if designed properly. But there’s already a silver lining here, even if you are still in the thrall of small course mythology. Because the fact that most courses that students take are large means that there’s an obvious way to improve undergraduate education: Focus on improving the small number of large courses.

Returning to our previous example, because 50% of the enrollment is in the single 100-student course, investments in improving that one course—out of 11—will have a disproportionate impact on the student experience. For example, finding a truly excellent faculty member to teach it; or making investments in better materials, course staff, or other forms of student support.

As a computer scientist, I find this even more satisfying, because it’s a direct consequence of Amdahl’s Law—probably one of the more important generalizable ideas in our field. There are many ways to state Amdahl’s Law, but informally, it expresses the idea that, to make something better, focus on improving the parts that have the biggest impact. Even though we have many courses in the department, the best starting point to improve education is to focus on the courses that most students are taking: which are large.

And there a ton of other reasons to focus on improving large courses. Large courses tend to cover introductory material, and can set students up for success or failure downstream. Unfortunately, many of these courses end up labeled as “weed-out” classes, reflecting their propensity to be poorly taught and thus have lower rates of student success than later courses. Of course part of this is also due to survivorship bias.

Being introductory, large courses are also the first ones students take when they arrive at college, and so play an outsized role in helping students transition to university life and academic expectations. The first few semesters at college are a big adjustment for most, and this is when we lose a lot of students from vulnerable groups. To be clear—many of these students need a variety of kinds of support, including help outside of the classroom. But it doesn’t help if they are struggling in large courses that are allowed to fail because the university doesn’t believe that they can be great.

Also note that, because large courses tend to be introductory, and because most first-year students take mainly introductory courses, it’s common for first-year students to have schedules packed with large courses. If we want to help students transition to college, improving large courses is critical.

Unfortunately, rather than focusing on improving large courses, universities in thrall to the myth of small course superiority frequently do exactly the opposite. They assume that large courses can’t be great, and give up on them entirely. Or they try to design them to appear small, in ways that both fool nobody and end up producing pieces that are far worse than the whole could be. We’ll come back to this in Part 2 when we discuss why large courses fail.

Most courses that students take are large. And large courses reflect student educational interests. So by improving large courses we can improve undergraduate education. But can large courses be improved? Or are they inherently doomed to to be worse than small courses? We’re reached the dark heart of the myth of small course superiority.

I realize I’m entering a dense thicket of university mythology here. I hope I can hack to the other side in the time your attention allows. But we’re bumping up against some very deeply-held beliefs about what makes college worthwhile.

As one example, some students are absolutely convinced that one of the most critical components of the university experience is getting to know your professors personally. Ignore the fact that, from a simple numbers perspective, this is impossible for all but a tiny fraction of students. So it’s hard to conceive how this can represent the raison d’être of university education—at least not without setting up 99% of undergraduates for failure. Ignore also that this goal seems suspicious coming from as it frequently does from faculty, eager to have acolytes gathering at their feet—or petitioning for the all-important recommendation letter.

Regardless, some people have a near-religious fealty to this idea. And graduates who managed to accomplish this task are much louder than those who didn’t, many of whom probably feel some sense of shame in failing to “get the most” out of college⁽⁵⁾.

It’s true that large courses provide fewer opportunities for contact with faculty. And so anyone with an axiomatic belief in the value of this aspect of the university experience will never be swayed by the idea that larger courses can be as good or better than small ones. If that’s you, you can stop reading now—if you haven’t already.

I’m also unlikely to convince people who subscribe to what I refer to as the “learning rays” theory of education—that knowledge is transmitted through physical proximity to the instructor, via learning rays emanating from the teacher’s forehead. Which I can only assume lose strength as $R^2$—so be sure to sit in the front row! You can also expand this cohort a bit and include those who believe that side-by-side tutoring is the only effective way to teach anything—although that also rules out even small university courses, which are already too large to provide this experience.

Given that I’m facing a fairly significant headwind of preexisting beliefs⁽⁶⁾, let me simply make one important scaling argument about what happens when a course gets larger—one that shows how large courses can be great, and guides the way.

Some aspects of a running a course represent scaling challenges as the course grows. For example, most learning management systems are clearly designed for small- to medium-size courses, and tasks that are trivial to perform for a small course and only mildly tedious for a medium-size one can become utterly tortuous for a large course. For example, until fairly recently our campus grade entry system required instructors to select individual grades for each student by hand⁽⁷⁾. Imagine doing that for 1000 students—better yet, imagine doing it accurately for 1000 students⁽⁸⁾. Instructors teaching large courses will need to be prepared to come up with new ways of addressing some of these challenges, since strategies that worked for smaller courses will fail.

Other aspects of a course scale roughly with the size of the class. Student support is a good example: answering questions on a course forum, providing help with assignments, and so on. These challenges can thus be met—if staff resources scale appropriately as the course grows. That shouldn’t be a big if. But it can be. And finding large numbers of competent staff can also be a challenge.

As an example, consider one of the assignments for a course. Assignments and assessment play a enormous role in student learning and success in any course—large or small. But as a course gets large, two good things happen. First, more students benefit from a great assignment—one that is appropriately challenging, clear, well-structured, and intellectually stimulating. The value of great materials is amplified by the size of the course.

But here’s the other great thing that’s happening—there are also more resources available to create that great assignment! We don’t need to write more assignments per student as the class size grows, so it’s straightforward to see that the tuition dollars we can allocate to each assignment is increasing with the size of the course. We still have to allocate those resources properly to achieve the benefits—and not doing this well is a very common mistake made by many large courses that we’ll revisit. But the resources are there.

At the same time that the impact of great materials for students is growing, the resources available to make them great is also growing. Properly combined, these two forces make it possible for large courses to provide substantially better materials than smaller courses. And materials here is a broad category that encompasses

1. instructional content that students use while learning: text, diagrams, animations, videos, worked examples, interactive walkthroughs, practice problems, etc.
2. assessment content that we use to support and motivate their learning: homework problems, quiz and exam questions, assignments, projects, labs, etc.
3. course management content used to onboard and train course staff, and
4. any technology or other systems used to support the course.

Pretty much anything that contributes to the course and isn’t breathing falls under the category of materials.

Given that improving large courses is the best way to improve undergraduate education, and that large courses have the potential to be great by creating excellent materials, the obvious question is: Why aren’t large courses great? We’ll address this question in a separate post detailing how and why large courses fail.