In the last post, I focused on why we have general education requirements, mostly from the student perspective. For this post, I am going to ask the question of why we require prerequisites and focus on this topic from the university perspective. While I hope my perspective can be applied to prerequisites more generally, it is very clear to me that my view is the result of teaching physics—one of the most highly sequenced majors and one in which prerequisites play a central role.
When it comes to teaching physics at a university, there is a very strong sense that the curriculum must proceed in a fixed order: classical mechanics, electricity and magnetism, and then “modern physics”/quantum mechanics. One thing I find interesting is the way these concepts are ordered. Some departments teach all of these areas at the lower division level and then cycle through them again at the upper-division level. Interestingly, while the lower division courses are generally strictly sequenced, the upper-division courses often cover topics in parallel. Other departments may take a different approach and teach lower-division classical mechanics and electricity and magnetism and then have students progress to upper-division courses on these subjects. Then, students can move on to modern physics. (This second version is rare, but this happens to be what I experienced!)
In addition to certain physics courses serving as prerequisites for other physics courses, there are also often math prerequisites for physics courses. Again, there is some variation between how these requirements are organized: sometimes a calculus course is a strict prerequisite, and other times it is a corequisite and must be taken at the same time.
Why do I go through the physics curriculum here? Ultimately, it’s because I believe that a careful analysis of what we do in physics reveals that the belief that certain courses must be taken before others is never as absolute as we might think. If we consider the examples above, it’s clear that there are different yet equally valid ways to structure physics prerequisites. While we might have preconceptions about the necessity of teaching courses in a specific order, we have room for flexibility here.
Additionally, if we look at the relationship between math and physics, certain math concepts are often discussed as essential prerequisites for physics. However, most math classes are actually handled as corequisites in practice: physics courses tend to cover required math as it is needed, while math courses end up playing a supporting role. For example, UCI requires biology majors to take Math 2A (single-variable calculus, derivatives) as a co-requisite for Physics 3A (classical mechanics). Physics 3A involves the use of derivatives, which are covered in Math 2B. However, Physics 3A almost always uses derivatives before Math 2B teaches them! Interestingly, when I started, this was the same for physics, chemistry, and engineering students. Though now, these students take Math 2B (single-variable calculus, integrals) alongside Physics 7C (classical physics).
This illustrates that there are many different pathways through a series of courses and concepts. If Math 2A was officially a prerequisite for Physics 3A, students would have to delay Physics 3A (and therefore the rest of their physics courses) by an extra quarter. Establishing Math 2A as a corequisite enables students to get solid foundations in both math and physics at the same time while “filling in the gaps” as required.
When we consider prerequisites in more detail, I think we’ll discover that not all the material taught in any given prerequisite course will be relevant for later courses. Typically, there are a few key topics that are relevant. And, even when there is material that we expect students to learn in the prerequisite courses, the material is generally reviewed or revisited at some level in later courses. Rather than specific content, I would argue that the conceptual frameworks and approaches are actually the critical elements taught in prerequisite courses.
It would be an interesting exercise for each department to reflect on their prerequisite structure and the general structure of each major to really be explicit about what elements of each course map to other courses. Here at UCI, I would like to call attention to the History Department, which has gone through a very exciting process of mapping learning outcomes to courses. And of course, thanks to ABET, you can reach out to colleagues in Engineering who are regularly asked to analyze the mapping of outcomes to courses. This mapping will help us think through how much the order of courses really matters.
An interesting element of thinking about prerequisite courses and executing this mapping is the question of “learning context.” I do not think physics is unique in this area. As a specific example, a core concept in physics is the conservation of energy. Because of how our curriculum is sequenced, most students see this first in the context of mechanics, and most instructors assume this is the “natural” context in which to learn this concept. But, I can imagine that this concept may make more sense for some students in the context of electricity and magnetism—something research would help us understand better! I suspect other fields have similar examples. For example, when considering the first time a student is learning a particular form of critical literary analysis, we may think the specific text should not matter. However, there is a possibility that a number of students would find this skill easier to master if it was applied to a different type of text. This raises an interesting educational question—if we allowed students more flexible pathways, how could we leverage their ability to learn best in certain contexts?
One of the hidden assumptions in prerequisite structures that we need to be aware of is historical framing. It is certainly true in physics that some of our curricular design exists to support a historical narrative. This has a pedagogical use at times, but I can tell you that it has resulted in many conversations of “why is the ‘interesting stuff’ taught so late in the sequence?” I bring this element up to remind us that what may be appealing to us about the curricular structures we create may or may not serve the best interests of the students. At the very least, we owe it to our students to reflect on our structures periodically and ask the hard questions about how they might need to be changed.
Most of the time we think about curriculum and prerequisite structures from a purely academic perspective. The students need to learn X before Y. But we need to be aware of the practical element as well—prerequisites help with enrollment management. If all students need to take X before Y, we can get very predictable enrollment numbers for each course. Once we open up more flexibility, we may need to teach more sections, and we may have to do more sophisticated modeling. So, there is a risk of increased costs, and this is something we need to weigh against potential benefits to student outcomes. Of course, better student outcomes tend to lower costs, so the calculations are not straightforward!
At the end of the day, the central question we need to ask ourselves is whether or not our prerequisite structure in any given major is too constrained. Does it create artificial bottlenecks for students that limit success simply because of the structures we put in place? At the same time, we know structured curricular pathways can be incredibly helpful for student success. So a complete free-for-all does not seem to work either. This seems to be a classic Goldilocks situation where we need to get the number and type of prerequisites just right! This will only be accomplished if departments can find the time to work together to tackle this critical issue.