Who are Prerequisites For?

I’ve been thinking about course prerequisites for a while, since a class that I TA and will eventually teach at Virginia Tech is continually being revised to determine exactly how much “review” from the prerequisite statistics class is enough without spending half of a food science class teaching students statistics. For a number of frustrating reasons, many students don’t seem to learn or retain much from the prerequisite. In the background, my department has had a number of ongoing discussions about the curriculum, but for a while I was thinking about prerequisite courses in a little bubble–how do we deal with it when students pass the prerequisite, and arrive in my domain, but don’t actually have the skills we were hoping they would pick up?

I’m not the only one who’s been thinking about course prerequisites lately, it turns out, and my view of the issue was greatly expanded when Dr. Nathan Klingbeil gave the Keynote address at the Conference on Higher Education Pedagogy this year (linked video from an older, shorter talk of his on the same initiative). The argument he made was that student attrition in applied STEM fields (especially engineering) largely happened in the first few years, largely caused by the demoralizing number of out-of-major prerequisites (namely, math) that students have to slog through to make it to the in-major classes they actually signed up for and are excited about. This is even worse for under-prepared students who were placed in remedial math in high school or whose underfunded high schools didn’t offer higher-level math like precalculus. These students may have to take an extra semester or even extra year of math compared to their peers, and are likely to already be demoralized and think they’re not cut out for the whole math thing. But who’s to say that means these students wouldn’t make good scientists and engineers?

Often, we don’t think about or question this when putting college curricula together. Of course you need to know how to hand-integrate simple equations to be in a STEM field, we say, and to do that you’d better first have a solid grasp of both algebra and arithmetic. So as to not risk sounding like a petulant high school student suffering through a math class, I won’t ask the STEM majors in the audience to stop and think about when the last time you used anything from your college calculus class was (although I think it’s a good exercise), and won’t suggest that such classes need to be removed from plans of study entirely. The question I’ll ask instead is this:

What–and who–exactly are prerequisites for?

If they are for the students, to scaffold their knowledge so that they have the tools they truly, desperately need to succeed in your class… well, that’s definitely possible. If so, great! But if you haven’t actually sat down and compared the course learning objectives of the course and prerequisite in question, it’s entirely possible that this unexamined assumption won’t really hold up to scrutiny. There are many different ways to structure knowledge–and to structure a course–which very rarely have some magical, inherent sequential order that must be proceeded through to make sense. My college physics course didn’t have calculus as a prerequisite, and even though I had taken calculus before, when the professor waved his hand at the board and said “and then some calculus happens here”, I didn’t start frantically trying to derive the equation with my dusty knowledge of theoretical calculus. I didn’t need to, and neither did anyone else in that classroom. We talked about rates of change in the abstract, which I think was more than sufficient.

If they’re for you, to weed out students that aren’t going to be able to succeed in your class due to some inherent lack of skill or ability or intelligence or work ethic, or to make sure that only the best students graduate from your program, I would personally ask you to reconsider this. There’s evidence to suggest that students who get lost in weed-out classes are not doing so because of an inherent lack of ability to succeed in their chosen field.

If they’re in place to make sure that someone else deals with your major’s students in their academic infancy, does all of the pesky things like teaching them how college works and how to read and write and think critically and study and look at mathematical equations… well, would you say it’s really working?

The thing that the talk eventually built up to was the establishment of a first-year quantitative reasoning course, where all of the examples were applied to engineering, and students with varying starting mathematics competencies would all be immersed in highly-applied mathematics in the field they cared about right up front, in the hopes that it would catch them before the pre-calculus math sequence had the time to wear anyone down. It’s had some amazing impacts on traditionally under-served student groups, as have similar programs, but the thing that has really stuck with me from the talk (left me a bit obsessed, almost) was a throw-away comment that Dr. Klingbeil made about how it would be a very difficult but very educational exercise to unpick your department’s own curriculum and the chains of prerequisites to see how long it would take for students coming in with lower test scores or math class grades to get to actual in-major courses.

It has, in fact, been a pain to do. But I wanted to know where we stood, so hopefully sometime in the next week, I’ll finish writing up my discoveries for everyone here to see.

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