Monday, March 20, 2017


The Meanings of Prerequisites

Why should courses have prerequisites?

I’m not saying that some shouldn’t.  I’m just asking what the criteria should be.

In much of the burgeoning research on student success, remediation, and community colleges, “prerequisite” is a dirty word.  Prerequisites amount to speed bumps on the road to graduation, and many students have sufficiently complicated lives that a speed bump or two is enough to send them careening off the road.  

Yet among many faculty, prerequisites are considered positive goods.  Getting a prerequisite for your class is considered a win, and any attack on a prerequisite is an attack on academic rigor, academic freedom, truth, justice, virtue, beauty, and all that is good.  

I think much of the distance between the two views comes from using the same tool to solve very different problems.

If you define the major problem as too many capable students being stopped short by arbitrary obstacles, then you put a heavy burden of proof on prerequisites.  From this perspective, prereqs are likelier to be problems than solutions, so you’d need some pretty serious evidence of their necessity before embracing them.  Yes, some students who bypass the newly-lowered gate may be pretty spectacularly unprepared, but in the aggregate, more will get through without the prereq than would have with it.  As long as that’s true, the gates should be down.  This is the theory behind co-requisite remediation, which allows students who don’t immediately place into college-level classes to take them anyway, but with extra support.  

If you define the major problem as too many underqualified students in your class, though, the gatekeeper aspect of a prerequisite may seem like a blessed relief.  Requiring, say, college-level English before students can take a biology class should make the lab reports somewhat better.  If it slows some students down, well, education takes time.

Over time, I’ve migrated from mostly in the second camp to mostly in the first.  The weight of evidence just got to be too much.

Part of what convinced me was a program review I read several years ago.  It was by, and about, a science department that had successfully pushed a couple of years prior for a new English prereq for a lab class.  It looked at data from before and after the change, which showed literally zero difference in success rates. It concluded that the prereq should stand anyway, because the prereq made a statement about the intended rigor of the class.

To whom the statement was made was left as an exercise for the reader.

But the CCRC and similar studies showing that students who skip prereqs wind up doing just as well as, if not better than, students who follow the rules suggested a deeper issue.  There’s more than one path to figuring out how to succeed.  Chains of prereqs exist on the theory that knowledge or skill is acquired linearly, and always in a set order.  But that’s simply not true.  When I took French in high school, we started with isolated words and some verb tenses, using flashcard drills and frequent quizzes.  My French is still terrible.  When I learned English as a small child, I picked it up in the course of immersive daily life.  I didn’t know what “infinitives” were until I took French, but I used them all the time.  My English is pretty good.  

We’ve had students fail the arithmetic placement test but pass the algebra test.  If knowledge were as linear as we usually assume, that wouldn’t happen; after all, if they can’t pass arithmetic, how could they possibly pass algebra? But they do, and frequently enough that it can’t be written off as a fluke.  Students take different paths to get there.

To be fair, many prereqs were put in place “for their own good.”  The idea was, at least in part, to save students from themselves.  But it’s turning out that students are often better judges of their own academic needs than curriculum committees are.  

On campus, getting from the second camp to the first is a piecemeal process, and it’s always subject to special pleading.  (“Well, yes, but my class is different because…”)  I get that; at one point in my career, early on, I would have said the same things.  It’s lucky for me I didn’t have to say them in French, though; that methodical step-by-step approach with which I learned it left me with almost rien.

It is possible to teach a physics class in such a way that it can be passed by students who failed math.

This just kicks the can down the road to the Mechanical Engineering Department, who must engage in some savage triage on students who were allowed to make it through a year (or more) of prerequisite classes before hitting some brutal doses of truth in the Statics class (generally a crucible class that requires knowledge of physics and calculus and serves as a gateway to more advanced engineering classes).

I'm in a physics department, and I have an uncomfortably large number of students who made it to my upper-division class with demonstrably poor knowledge of freshman physics concepts. I embraced the ethos of "meeting them where they're at" in the _FIRST_ course of my two-course upper-division sequence, and spent a lot of time reviewing freshman material. I gave a final that was 1/3 freshman material. At that point I had to fail 27% of the class, because in the second course in this sequence I would really like to get to some intellectually stimulating topics that some of the students (the ones who actually retain something from intro classes) are capable of tackling, and that they might benefit from in their subsequent careers.

But I couldn't do that if I didn't, at some point, engage in a brutal cut. It's really a shame that it took this long for the cut to happen, that they got this far without getting a signal that they would be better off trying something else, but people were very, um, "progressive" in grading the lower-division classes.
Three problems with the philosophy of "some students ... may be spectacularly unprepared but, in the aggregate, more will get through without the prereq than would have with it."

So, you've increased a 25 person class which 20 people pass to a 50 person class which 25 people pass. Let's even imagine you've opened up a second section, so the professor isn't overwhelmed.

Problem 1: You've changed the pass rate from 80% to 50%. Is the administration going to support the faculty in that 50% failure rate? Most professors I know would anticipate heavy pressure to bring the pass rate back where it was.

Problem 2: If there is any sort of classroom interaction, the level of discussion will be dragged down -- only a completely clueless teacher will keep a conversation at a level where half the room is lost.

Problem 3: It is just plain miserable to fail half your students.

I am willing to believe that Dean Dad is a good enough dean to deal with 1, but I don't see how 2 and 3 get solved.

(Math prof. at research university here.)
One of the things I observed back when I was still doing this stuff full-time, and was frequently on a campus curriculum committee was that a lot of the prerequisites did not seem to me to make sense. And, when asked, the department proposing the prerequisites had trouble explaining exactly what the purpose of the prerequisite was.

Some things seem pretty easy--calc 1 before calc 2, for example. Also, in a first physics-for-physics-majors course, a math requisite makes loads of sense.

But some things can be tricky...consider a small school that has only one intro econ (my discipline) track, which is primarily intended for majors. Makes life difficult for someone with an interest in econ but no intention in majoring in it. If you can distinguish between intro-econ-for-majors and intro-econ-for-non-majors, then it night be reasonable to require calc for majors, but not for non-majors. But if you can afford to run only one type of intro econ sequence, you have a problem, and I see no easy answer. And if you can run separate intro courses, what do you do with someone who takes the non-major sequence, gets really excited by the material, and wants to change majors? If your econ major is built from the ground up with the expectation that entering students have had calculus, you have a problem.

On the other hand, when I was an undergrad in the late 1960s, I talked my way into 3 courses for which I did not have the prerequisites (but I was taking 2 of them pass-fail, and the faculty knew me...)...
I have sympathies on both sides here.

I used to teach a very demanding bioinformatics course that required statistics and programming courses as prerequisites. Grad students were allowed to take it without the prereqs, and a few of them (with enormous effort) managed to pass it. Undergrads sometimes failed it even after having passed the prereqs (which turned out to have been watered down from the original courses by instructors who believed in scaffolding everything to the point where students learned almost nothing).

I see no point in letting students into a course just to fail them out of it—better to have meaningful prereqs that will tell them whether they are ready. But I'll almost always allow top students to try things without the prereqs (in fact, being allowed to skip prereqs is a common privilege granted in honors programs).

I recently reduced the prereqs required for my applied electronics course: dropping the Physics E&M course and just requiring calculus. It turned out that none of the students retained anything from the Physics E&M course anyway—I had to teach them what a capacitor was—so there was no point in having physics as a prereq. I did retain calculus as a prereq, as we did an optimization in the first lab that required taking a second derivate and setting it to zero, and all the complex impedance work requires taking derivatives of sinusoids. There is not enough time in the course to reteach calculus (though the number who could not set up the optimization problem with derivatives was distressing).

I generally favor prerequisites in which faculty can list the specific topics that they expect the previous courses to have covered. One of the few good things about the hundreds of pages of documentation needed for ABET accreditation is the explicit listing of these prerequisite topics.

I agree with Unknown that teaching a mixed group of students in which some are properly prepared and some are not is extremely difficult and generally ends up short-changing the prepared students. A continued diet of such courses (as is common in many California high schools) results in the whole class being years behind where they should be.

I think that C.P. Snow's "Two Cultures" is worth keeping in mind here. Snow argued that the arts and humanities are the area of human knowledge where we can build on what came before but we also get to completely turn things around by articulating a novel idea, and we still study the original works for their own sake. On the other hand, the sciences are the area of human knowledge that is ruthlessly cumulative, and we often study the best modern distillations rather than the original sources from long ago. In science we keep only that which has stood the test of time, but at the same time whatever we keep is often essential to what comes next.

So, it may be that some subjects naturally need fewer prereqs, because more things can be studied on their own. I say that not to disrespect them, but to admire the nature of human ingenuity in those subjects. Different subjects have different needs.
I understand everything what you really wanted to say through this post. but I want to say this literally touched my heart and all the issues i was focusing. you already wrote it.
we do have some cultural problem in here but that doesn't change the fact that no matter what we have to live in the society we are responsible in for.
With all due respect to "Dean Dad", whose writing I generally find quite interesting and I often agree with, I take considerable issue with this. Perhaps this is my privilege speaking (being a faculty member at an elite institution that fancies itself as a peer of Dean Dad's alma mater) but in my world student success means actually learning something, as opposed to graduation.

Like Unknown said, the likely outcome to removing the prereq from a course is that the standards would be redefined so that the "success" rate did not drop sharply. Which is fine if you are working under the assumption that the students don't actually need anything from that course moving forward in other courses or later in life. And perhaps that is the underlying assumption - that the useful thing about CC is acquiring the credential, not what you learned. And if that is the assumption, or even the reality, then I suppose it doesn't actually matter whether/if anyone learns anything, as long as they keep moving along that "road towards graduation".

Maybe Matt's CC is a magical place where all the students have hidden greatness that is just being squelched by evils such as the credit hour and prereqs- but that seems unlikely. At my ("elite") institution, students have certainly not been getting more prepared over time - in fact just the opposite (I put most of the blame on NCLB and other changes in our K12 system but that is a topic for another time). But at my institution, where we assume that admission indicates preparedness for any intro course at the college, the introductory science course that I teach routinely has 10% of the students drop the course in order to avoid a failing grade. I could teach a course that (almost) everyone could pass but then I would not be preparing students for the next course in the sequence (for which mine is a prereq).
I have similar objections to Matt's drumbeating for competency based education - which conceptually is a perfectly reasonable idea. But which he imagines, in some sort of a Lake Wobegone fashion, would somehow accelerate students down that road to "success". I think that the implementation of such a system would result in two things - initially students would take much longer to complete, and then standards and expectations would be redefined in order to get to the desired outcomes of completion time/rate.
I'm an academic advisor and an adjunct history instructor, both at the community college level. I'd like stricter prereqs -- because I'm a mediocre teacher. Not a terrible one, mind you. I'm worth hiring and my students leave class knowing more than when they started. But I'm sorely lacking skill when it comes to differentiation. So are a lot of my peers, both at cc's and at four-year institutions.

The best student I've ever taught sat across the aisle from a student with developmental disabilities. Trying to reach them both was an enormous stretch every single week, especially since I had to teach myself effective pedagogical techniques as I went. Prereqs may have a dubious value for students. But for me, as an instructor, the ability to say "You must be this tall before riding the ride" would be a godsend. I'm not asking for the moon and stars -- just get a C- or better in a first-semester composition class. I'll try to meet my students where they are, but if they're too far from my core discipline, I know they aren't getting my best work. Just the best I can cobble together.

And considering what adjuncts are paid, colleges are lucky to get even that level of dedication.
Two words: guided pathways. If we take the time to thoughtfully develop degree program maps that meaningfully and explicitly sequence the courses to be taken from the first semester to the last, then prerequisites are rendered obsolete.
There's another kind of prerequisite I've seen used: "you must take the can-be-taught-in-lecture-format class" before the "needs expensive equipment and small class size class". At my SLAC, it was that you had to take COMM 100 (lecture format survey of the overall field of communication) before you could take the class that taught you video editing, how to run the cameras in the campus tv studio, and other basic video production skills (this was long enough ago that we still had both analog and digital editing studios, and video cameras were something you checked out from the school rather than kept in your pocket almost by accident).

This isn't because we spent a lot of time re-visiting COMM 100 foundational content while learning how to run a 3-camera show vs a 1-camera show, but rather because the school couldn't afford to run the number of tiny sections of the video class we would need (nor the additional tv studios and editing suites they would need to build and equip) if it were taken as an elective by people with no overall interest in the field who just wanted to learn how to use fancy video equipment. Our majors and minors needed that field experience (depending on area of concentration), so we had the equipment and the course, but it's a class that almost certainly cost the college a lot more to run that they could charge in tuition.

I would imagine that there are similar classes in things like Nursing.

(Yes, this could be dealt with by restricting the video class to only declared majors and minors, but by using a prerequisite course instead they could also let probable future COMM majors who hadn't declared a major yet take the class.)

I don't personally know anyone who failed COMM 100, and it certainly wasn't a weeder class in the way that a calculus sequence often is, but requiring it was a lightweight way to gatekeep a high-interest but expensive to run hands-on class to those who were likely to need it to graduate.
I'm going to agree with Unknown. And I honestly wouldn't trust that a promise to (say) ignore the students without a prereq when calculating failure rates would survive a new administrator.

Talk to a high school teacher about getting kids who aren't ready for your course, with the expectation that you will maintain a certain pass rate no matter how many of the students are reading at a grade 4 level (or have grade 3 math when in grade 10 algebra).

I've written 16 blog posts (between 2007 and 2010) that were tagged with "prerequisites", several in response to something Dean Reed (nee' Dean Dad) wrote over that time period. You can read them by following this link

The top two, from June 27 and June 22, 2010, are particularly relevant to this blog entry as well as some of the comments here. For example, I'd wager that the faculty in the mechanical engineering department are as frustrated with the product of an intro physics class as Alex Small is in his lead comment in this thread. They should all get together and talk about their concerns.

If there is a theme to that collection, it is that the courses I worry about often fail to do their job because students fail to comprehend the very concept of "prerequisite". They have picked up the idea that it is a speed bump set up to collect tuition, perhaps from someone like our Dean, rather than something they need to know to avoid failing the next class. I think, however, that it starts in high school.
I think you err in not distinguishing between prerequisites with a curriculum (e.g. composition 1 before composition 2, or chem 1 before chem 2) and prerequisites for composition 1 or intermediate algebra. The latter are what the CCRC are talking about. The former are what college data will support. They did not arise from hidebound tradition.

You should reject that composition requirement for biology based on the data, not philosophy. However, the supporting philosophy would be that students simply do not transfer knowledge from English essays to lab reports. Essays are in one silo, and few of those skills of logical argumentation find their way from that silo into the biology silo whee they write their lab reports.

The argument against remediation is that many of those students never needed it. What they needed was to get back into a classroom, because that is where they left what they had learned about writing or math in high school. They forgot it as soon as they left the room, and will recover it (if their high school had reasonable standards) once they are back in the room. They just can't recover it on a placement test taken months after graduation and weeks before they get in a class. Putting them in a 5th or 7th grade classroom is counterproductive. They need to be in a class at the level they were in in high school. They can be pushed back one or two levels if they have an epic fail.
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