by Alex Perkins
Our department is currently considering the possibility of some changes to our graduate curriculum, which could include reductions in coursework requirements. These changes are motivated by a desire to empower our students to devote more of their time to their research, given the importance of that for enabling them to be productive in grad school and successful in their future careers.
One concern that has arisen during these discussions is how reductions in coursework requirements might impact enrollment in the graduate classes we offer. That concern could affect how much of a reduction in coursework we adopt and inform strategies that we might take to mitigate the impact of a coursework reduction on enrollment in graduate classes. Either way, this is a question that our graduate curriculum committee felt would benefit from some modeling.
Our graduate curriculum committee thinking through all scenarios to avoid a bad outcome for our department. We hope that we’ll arrive at a better outcome than this cat!
Defining the parameters of the model
The first thing we had to think about is what factors play a role in determining enrollment in our classes. This influences which parameters need to be included in our model.
Some parameters that are within our control as a matter of policy include the following.
Parameters that are, for all intents and purposes, beyond our control include the following.
Average enrollment per class
With these parameters specified, a natural thing to do is to calculate average enrollment per class.
To do that, first take the number of students per cohort (25) and multiply it by the credit hours required per student (21) to get the credit hours required per cohort (525). Those credit hours get divided over how many semesters students take classes (4) and multiplied by how many cohorts are taking classes in a given year (2), resulting in credit hours taken per semester (262.5). Not all of those credits are taken in our department (80%), resulting in the number of credit hours taken by our students in our department each semester (210). Most classes have historically been offered for 3 credits, giving us the number of classes taken by students in our department each semester (70). Undergrads and grad students from other departments also take our classes (20), resulting in the total number of all students taking graduate classes in our department each semester (90). Dividing that by the number of classes offered per semester (13.5) gives us average enrollment per class (6.67).
This illustrative calculation was based on the midpoints of the ranges of each parameter. How much variability in average enrollment per class is there based on variability in these parameters? To assess that, we can perform this calculation repeatedly using Monte Carlo sampling of parameters from their ranges.
Variability in average enrollment per class. This variability is due to variability in several factors that affect enrollment. Distributions are shown under current (red) and proposed (blue) coursework requirements.
Doing this shows that 95% of parameter combinations result in 4.7 - 9.7 students per class under our current requirements (24 credit hours over 4 semesters) and 3.0 - 6.5 students per class under the proposed requirements (12 credit hours over 3 semesters). Although the proposed requirements would lower enrollment, the average would mostly stay above 3 students per class, which is a minimum that we would like all classes to remain at or above.
Thinking beyond averages
Looking at average enrollment under different scenarios is helpful for getting a rough idea of the consequences of alternative policies, but it does not tell us what we really want to know. If average enrollment is above our minimum of 3, but 40% of classes have 2, 1, or even 0 students, that’s bad. What we really want to know is the proportion of classes that would have enrollment below our minimum of 3 students per class.
To quantify that, we can take many of the same steps as in the calculation of average enrollment per class. Specifically, I have boiled this down to the following question.
If there are X students taking Y classes each in a given semester and there are Z classes being offered, what proportion of classes will have fewer than 3 students?
For a given set of parameters, this can be simulated by allowing each of X students to randomly select Y classes from the set of Z classes being offered by sampling classes without replacement and then counting up what proportion of the Z classes end up with fewer than 3 students. X, Y, and Z all depend on parameters of the model, which leads to differences in the proportion of classes with fewer than 3 students as a function of differences in the model’s parameters.
One additional assumption that needs to be specified is whether some classes are more popular than others. Although it would be possible to estimate heterogeneity in class popularity based on past enrollment data, I have not taken the time to do that. Instead, I assigned each class a relative popularity such that the top 10% of classes attract twice as many students as the bottom 10% of classes, on average.
Variability in the proportion of classes with fewer than 3 students. This variability is due to variability in several factors that affect enrollment. Distributions are shown under current (red) and proposed (blue) coursework requirements.
Based on our current requirements, the model predicts that 5% (95% uncertainty: 0 - 17%) of classes that we currently offer end up with fewer than 3 students per class. Although we have not looked at data on how often classes that are currently offered end up with fewer than 3 students, it is possible that a small proportion do. Professors may either offer those classes anyway or not end up teaching them.
Regardless of whether this baseline prediction is correct, we can still use these calculations to get a sense of the relative impact of a change in coursework requirements on the proportion of classes with fewer than 3 students. Under the proposed change to 12 credit hours over 3 semesters, the model predicts that 20% (95% uncertainty: 5 - 43%) of classes that we offer would end up with fewer than 3 students per class. Whether this is correct in an absolute sense, this amounts to a prediction that changing our coursework requirements could lead to an approximately fourfold increase in the proportion of classes with fewer than 3 students.
Can we make the proposed changes work?
There are a few strategies that could be taken to mitigate the impact of the proposed coursework reduction on the proportion of classes with fewer than 3 students. How much of a difference would those mitigation strategies make?
Along with a reduction from 24 credits over 4 semesters to 12 credits over 3 semesters, consider the following mitigation strategies.
A. Reduce the number of classes offered per semester. This could be achieved by encouraging more co-teaching or having some faculty teach an undergraduate class in lieu of their graduate class. Consider a reduction from the current range of 10-17 to a new range of 8-10.
B. Reduce the credit hours per class. Reducing this from 3 to 2, or having more of a mixture of 2 and 3 credit classes, means that students would take more classes to meet their credit hour requirements.
C. Increase the number of undergraduates taking graduate classes. With some effort to recruit additional undergraduates, as well as grad students from other departments, consider an increase from the currently assumed range of 10-30 to a new range of 30-40.
D. All of the above.
Effects of different mitigation strategies on the proportion of classes with fewer than 3 students. Variability in each distribution reflects variability in these and other model parameters.
The mitigation strategy with the biggest effect appears to be reducing the number of classes that are offered. This alone could offset the effects of reducing coursework requirements on class enrollments. The other two strategies are also capable of helping, albeit to a somewhat lesser extent. In combination, all three of these mitigation strategies could reduce the number of classes with fewer than 3 students even beyond what it is now.
The graduate curriculum committee’s proposal to reduce coursework requirements from 24 credit hours over 4 semesters to 12 credit hours over 3 semesters would have an impact on class enrollment. From the perspective of the proportion of classes with enrollment below an acceptable minimum of 3 students per class, this change in policy would increase the number of classes in this category by approximately fourfold.
Three different mitigation strategies each have potential to offset these undesirable changes. With a concerted effort to reduce the number of classes offered, reduce the number of credit hours per class, and boost enrollment from undergraduates and grad students outside the department, average course enrollment could increase by 46% and the proportion of classes with fewer than 3 students could decrease by approximately tenfold. Both of those changes are relative to current enrollment, meaning that enrollment could actually increase relative to what it is now, despite a major reduction in coursework requirements.
In conclusion, this analysis suggests that with a multipronged approach, our department could simultaneously reduce the coursework burden on its students (thereby increasing their research productivity) and increase enrollment in our classes (thereby enhancing the viability of a greater diversity of classes).
With the right updates to our graduate curriculum, we all stand to benefit!
Thanks to the graduate curriculum committee for many helpful ideas that informed this analysis. The committee is co-chaired by Beth Archie and Cody Smith and also includes Jeni Prosperi, Matt Ravosa, Jason Rohr, Felipe Santiago-Tirado, and Siyuan Zhang.