Curricular Complexity

Happy Friday! I’ve been catching up on my blog reading. One of the blogs I regularly read is Bryan Alexander’s (author of Academia Next), and a couple of weeks ago he posted a video and summary on the topic of curricular analytics with guest presenter Gregory Heileman, who is both an administrator and an engineering professor. The video and Q&A bring up many interesting points that could fill multiple blog posts. Today I’ll just focus on one of those: Curricular Complexity.

 

What is curricular complexity? (Watch the video!) In a nutshell, it’s an ad hoc way of quantifying who complicated it is for a student to go through the pathway of a major given prerequisites, corequisites, and timing of the classes offered. Science and engineering majors, which tend to be more hierarchical than humanities majors score high in curricular complexity – and this has potential downsides. For one, there is a negative correlation between the four-year graduation rate and curricular complexity. And once you dig into the data you find all sorts of other interesting correlations, for example, curricular complexity is inversely correlated with university reputation (at least in electrical engineering). Hmmm… I’m sure you’re starting to wonder why this might be.

 

Well, it’s complicated. Or I should say multi-factorial. We could discuss elitism, student preparedness, selection methods, accrediting bodies, history, narrow-minded professors, differences in disciplines, education costs, laboratories, bottlenecks, weed-out courses, and so much more. Many of these do not have easy answers and the relationships are a tangled web. I’m not going to do that here. Instead I turn my eye to how the curriculum in my department has changed over the years and consider some of the factors underpinning its logic.

 

First, some background: I’ve been at my institution for about twenty years and we’ve made a number of curricular changes over that time period. I’m ensconced in a liberal arts college (with no graduate programs in chemistry and biochemistry) focused on undergraduates. When I started we averaged slightly less than twenty majors per year. These days we typically have forty or so majors per year. When I started we just had a chemistry major that included a biochemistry pathway. There were only minor differences between the “straight” chem major and the biochem path. Three major factors have driven our curricular changes: rising numbers of students in our classes, the design of a new separate biochemistry major, and the addition of a research requirement for our majors. Our chemistry majors are ACS-accredited, and our biochemistry majors are ASBMB-accredited, i.e., our curriculum meets the requirements of the professional bodies in chemistry and biochemistry respectively.

 

In Heileman’s presentation (watch the video!), curricula are analyzed as graph-networks. Turns out I’ve recently taught myself the basics of network and graph theory for a grant proposal I just submitted, so I’m reasonably versed. But you don’t need those details to get the presentation (you won’t even notice the few non-crucial bits of jargon). I decided to draw out our present curricula using the framework. I haven’t included the numerical “complexity factor” because it’s not important unless you’re trying to compare across a bunch of different curricula at a bunch of different schools.

 

Here’s our current chemistry major. I’ve slotted things into semesters over a four-year plan (the large majority of our majors graduate in four years) based both on the recommended pathway and what students tend to do. Not being a large university, we do not have the bandwidth or resources to offer every class every semester. While G-Chem 1, Biochem 1 lecture, Analytical chem, Research Methods, are offered every semester; the other courses in our major are not. Both semesters of calculus and physics (taught by other departments) are offered every semester; but Physics 1 is offered mostly in the Spring and Physics 2 is offered mostly in the Fall, and I’ve placed them when many of our students take them.

 

The two key things to think about in the graph are: (1) What are the longest sequential paths through the network? (2) Where are the bottlenecks? The longest pathway is five arrows tracing from G-Chem through O-Chem to Inorganic to Advanced Synthesis. This means that technically a student can finish the major in three years, although most do it in four. There are two “hubs”: The key hub is G-Chem 2 which must be completed before getting to any of the other classes. The secondary hub is O-Chem 2 which is a prerequisite for Biochem 1 lecture, Inorganic and Advanced Synthesis. The majority of our electives require O-Chem as a prerequisite, but not all.

 

We previously had prerequisites linking up P-Chem 1 with P-Chem 2 and Inorganic, but we removed these when we redesigned our new biochemistry major. Along with this we streamlined our “senior” labs from four rotating offerings (with different prerequisites) to just two that all our chemistry majors must take. The overall effect of breaking these links is a reduction in Heileman’s definition of complexity. One could say this change makes the pathways easier for students to get through, in a sense. Has it actually been easier? I don’t know because most of our students graduate in four years both before and after the change.

 

Here’s our biochemistry major. Technically the required biology classes are independent of our chem/biochem offerings although we’ve been advising the students to take Mol Bio Techniques before they take Biochem Lab (usually in either semester senior year). Many of our biochem majors delay P-Chem until their very last semester, and find it a miserable experience. There are a variety of reasons for this including being behind in the math/physics pre-requisites, trying to shelter one’s GPA when applying for medical school, thinking that P-Chem 2 (stat them) is easier than P-Chem 1 (quantum), and others that I shall not mention as someone who teaches in the P-Chem sequence.

 

The longest path is once again five arrows starting from G-Chem 1 and ending at Biochem 2 lecture. G-Chem 2 is still a hub, but not O-Chem 2. Overall, our biochemistry major would have a lower complexity score (per Heileman) compared to our chemistry major, but not by much. On average 80% of our majors are in biochemistry with 20% in chemistry. Once again, there are a variety of reasons for this: Many students are interested in health careers and the biochemistry major fulfils the biology pre-requisites. Also, only one semester of P-Chem is required rather than two. (Most of our students don’t enjoy physics, and P-Chem is almost always rated as the hardest class, whichever semester our biochem majors take.)

 

Before the redesign of both our majors, they were more hierarchical. That is to say, they previously resembled similar majors at large public universities (that also offer graduate programs). Interestingly, small selective liberal arts colleges (SLACs) tend to have less hierarchical majors – and therefore lower “complexity” – and they offer the option of taking some additional electives if a student wants to be ACS-certified. Several SLACs now only require one semester of P-Chem (so a student who wants an ACS-certified degree opts to take a second semester). This allows a wider range of electives and for students to create different pathways through the major based on their interests. We offer a small range of electives because of other constraints at our institution. However, if we’re willing to forego the professional body certification, we could reduce the complexity of our majors. Several SLACs also have an “O-Chem first” track and/or a single semester of “accelerated” G-Chem. You can do this if you know the vast majority of your students have a solid high school chemistry background (at an “honors” or AP-level, or even just excelled at a single year of chemistry).

 

Math skills are also important for success in G-Chem, and at many SLACs, students come in “calculus-ready”, i.e., they can either comfortably slot into first-semester college calculus (and it’s a breeze) or they go directly into a more advanced math course. That’s not the case at my institution on average (although it is true for the better-prepared students). It was interesting to see this as a key factor in Heileman’s presentation of engineering pathways which have multiple math and physics prerequisites. Pondering all this has made me wonder if we should consider scrapping our Calc II and Physics II requirements and instead teach a “physics for chemistry” class that then serves as a pre-requisite for P-Chem. Students would be less shocked when they encounter P-Chem and they’d be happy to replace two courses for one (including one less lab). I need to think about this a bit more carefully before I consider proposing it to my department (and I might not).

 

One thing I have proposed is to re-envision the O-Chem sequence so that O-Chem 1 leads to Biochem 1 lecture, so that only our majors take both semesters of O-Chem. The majority of our students in O-Chem 2 (+ lab) and Biochem 1 are majoring in other departments but trying to complete requirements for pre-health majors (e.g. medical school, dental school, vet school). No, we haven’t made the change for a variety of reasons I won’t discuss here, but we typically have 150 students in O-Chem 2, most of whom hate being there. (And I know what it’s like to teach a class that students greatly dislike being “forced” to take.) Over the years, we’ve seen the elite medical schools no longer require O-Chem 2, but would like to see Biochem in a student’s transcript. Not surprisingly, other medical schools are following suit. (Roughly a third still required O-Chem 2 + lab, at least a couple of years ago when I last checked.)

 

Our department has been entertaining the idea of more flexibility and different pathways in our majors, and perhaps not being wedded to our degrees all being certified by ACS or ASBMB. This might allow more combinations and for students to choose things they are interested in. We might be able to offer a greater spread of electives more often. And we might attract more students to our majors, who are otherwise opting for other perceived “easier” options that have recently been offered in other departments that “complete the pre-health requirements”. This last point used to be something I was not concerned about (because we were seeing year-on-year increases in our major which brought its own challenges especially with our research requirement); but as I see administrative moves towards thinking of budgets more atomistically. I now see potential danger ahead that if we lose majors, we lose budgetary dollars, and one gets into a downward vicious cycle – you can see this play out across the U.S. in the humanities.

 

So how important is curricular complexity? I see moves towards decreasing complexity, for a variety of reasons – complex, multifactorial ones – and this blog post is already getting too long. One can make many arguments for and against. There might be an optimal or sweet spot, but it is likely to change over time as other factors vary. Perhaps the subject of another blog post!