Costo de las universidades: qué y cómo calcular
Septiembre 25, 2019

September 18th, 2019 – Alex Usher

One of the things that many people misunderstand about higher education is the way the economics of classrooms actually work; in particular about the relationship between enrolments, teaching complements, teaching loads, and class sizes. Today and tomorrow, I want to tease these out a bit.
For this post, let’s take a faculty with 100 professors, which admits 500 students per year and has 10% attrition per year, which translates to 1720 students total. That means it has a student-professor ratio of 17.2 to 1. Let us further assume each student takes ten courses per year (yes, yes, I know—it’s just a model). That means 17,200 student credit-hours in total, which means each professor on average must teach 172 student credit hours every year.
Even in this kind of simple situation, faculties (or departments, or institutions) have enormous flexibility with respect to what kind of class sizes can be offered.
The first and most important variable in this equation is how to define teaching loads. Without changing the numbers of professors or students, you can vary class sizes significantly by altering teaching loads. If course loads were 3/2 (meaning three in the first semester and two in the second) and each prof taught five classes a year, average class size would be a little over 34. If, on the other hand, you have a more research-intensive institution and 2/1 or three classes per year is the standard, then average class size will be over 57.
(If you’ve ever wondered about the basic antagonism between research-intensity and the undergraduate experience, that last paragraph is it in a nutshell. More teaching-intensive institutions can produce classes which are 40% smaller for exactly the same cost—or even less, if you assume research faculty command higher salaries).
For the moment though, let’s assume a faculty half-way between those two: a four-class per year teaching average and therefore an average class size of 43. But averages are not destiny: faculties (again, departments/institutions/whatever) still have substantial control over class sizes even with a largely exogenous class average. To see what I mean, let’s look at two different class size management strategies.
The first is what I call the “Polytechnic” model because it’s closest to how polytechnics think about pedagogy and class size in their degree programs. Precisely because these programs cover somewhat niche subjects, a high proportion of classes are mandatory and so classes often move forward on what you might call a “cohort” model—that is, all the students in lockstep. So, if they have an average class size of 43, it’s a reasonable bet that 43 (or something close to it) will also be the median and the mode. Every class is a manageable 43.
The second is what I call the U15 Arts/Science model. Here, the focus is on a) allowing professors to teach a really wide variety of courses and b) making sure upper-year students at least get some very small classrooms. This is, in fact, more successful in delivering small classrooms than the cohort model: it is not actually all that hard to arrange class schedules and course loads so that half of all classes have fewer than 20 students. The only thing you have to do is accept a few classes of 500 or more.
Here’s the math: in a system where a faculty has to offer 400 classes (100 profs, 4 classes per term) and cover 17,200 student credit hours, it’s quite possible for a faculty to offer, for instance:
·        190 classes of 19 students
·        148 classes of 27 students
·        52 classes of 80 students, and
·        10 classes of 500 students
All for more or less the same cost as offering 400 classes of 43 students each (give or take the cost of a few extra TAs for those ten big classes). And depending on how these courses are designed and scheduled, that might in theory be better for students. Basically, it’s a balancing act between whether the engagement benefits of the many small classes outweigh the negative implications of the few very large classes.
In practice, of course, the U15 approach has some very big negatives: namely, because those big classes tend to be concentrated during students’ first year, before they are really comfortable with their new educational environment, they are almost certain to contribute to disengagement and drop-out when those issues are at their peak salience. But that’s not inherent to this kind of approach: there’s nothing saying these large, mondo-courses couldn’t be spread across all four years. It’s just a matter of designing a curriculum in a way that allows this to occur (in turn, this means that curricula have to be coherent, planned, unified things, not just a bunch of baskets of credits, but that’s another issue).
There are, of course, some limits to this kind of strategy: the main one being the actual sizes of available classrooms. I know some community colleges would dearly love to increase the sizes of some classes in order to preserve small classes in other areas. The problem? Architecture. You can’t have 500-person classes if you don’t have any 500-person classrooms.
Anyways, the point of all this is that small classes are always possible, even on relatively tight budgets. It’s largely a question of workloads, architecture, and a willingness to structure curricula appropriately. The more interesting question, perhaps, is: what are small classes worth? And when does the price of keeping them become too high? More on that tomorrow.




September 19th, 2019 – Alex Usher

Yesterday we covered some aspects of how to create small classes on a budget (mainly: pay for them by having a few big ones). Today I want to delve into three other questions: are small classes actually better than large ones, can small classes be conjured up more cheaply, and what is the price we are all willing to pay for small classes?
Let’s start with the question of the benefits of small classes. There is a massive amount of literature on this, most of which is pretty iffy methodologically. There are a couple of reasons for this:
  • Pretty much all literature around teaching interventions is iffy, because it’s really hard to standardize the treatments. Do all teachers have similar styles, abilities, desires to meet students after class, etc.? No? Then how do you know, when you vary the class size, that it’s the class size which is causing the variation?
  • The literature is not consistent as to the variable used to determine the output “student success,” which class size is supposed to affect. Even where you have fairly stringent controls (e.g. outcome is assessed on a standardized exam in a single course, where a randomized group of students are assigned to different course sections of different sizes), it’s not clear whether a strong result tells you anything about the effects of class sizes as a whole, or the effects of class sizes in disciplines where you can have standardized final exams with precise yes/no (mainly mathematical) answers.
Now, while the results of the literature are all over the place, I think in general they can best be summed up as 1) nobody really finds meaningful differences in outcomes, however defined, when the class size differences are small, but 2) some studies do find quite meaningful differences when we are talking about classes of 30 versus classes of 100. Why aren’t all class size differences meaningful? If I had to hazard a guess, it’s because course sizes affect the kind of material being taught in the classroom. Broadly speaking, big classes are for transmitting large amounts of material that you need to master to enter a field, and small classes are better for putting skills into practice or for improving written/oral communication skills (I know, that’s a vast generalization, YMMV, etc., but it’s more often correct than not). Because only large classes tend to have testing and assessment which is amenable to standardized outcomes measurement, what we’re really learning from these studies is that “in courses where size is largely irrelevant, size is largely irrelevant”.
The real question we should be asking is: within any given curriculum, how many courses should focus on mastering basic content, and how many should be about communications and skill development? I know, tricky question, because it implies curricula are coherent units of analysis rather than a collection of buckets into which credits are dumped, but it is the key question every department and faculty that wants to manage its resources properly needs to ask itself. Big courses where they are appropriate, small where they are not. Horses for courses (so to speak).
But here’s the problem. To some extent, every institution (or faculty) can manage its courses to keep classes small. But holding course loads constant, courses can only stay at a given average size if you keep salaries flat or if you add resources. If faculty salaries rise, or resources fall, something else has to give. And if that something else isn’t course loads, then there are only two options: reduce the number of faculty (which implicitly increases average class size) or reduce the average cost of faculty by hiring new, cheaper (i.e. sessional) faculty.
Let me spell that last piece out a little more clearly: without some kind of magic money tree, there is always a trade-off between keeping small classes and avoiding the use of sessionals. Basically, if you prioritize small class size, eventually, you are going to have to introduce more sessionals in order to reduce the average cost of teaching. That’s just math.
Now, we in Canada have been lucky enough over the past few years to actually possess a magic money tree in the form of soaring international student revenues. But as I have argued before, this isn’t going to last forever. At that point, the trade-offs are going to come fast and furious. Will faculty increase teaching loads or accept lower pay? Will politicians and students accept higher domestic student fees? No? Then you’re down to a straight choice between sessionals and larger class sizes.
An unpalatable choice, to be sure. But smart universities and colleges (and student unions!) might want to think through their preferences on that subject before any crisis actually comes. Asking what trade-offs everyone is actually prepared to make in order to keep class sizes under control is a useful way of thinking through collective academic priorities.


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