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I've been thinking a bit of this comment and the following one:

  • "(Look at all the complaints we get about kids who can't combine fractions!)"
  • "Because it is not about you. Not about Robbie. But about the student. (This is a classic confusion I see on this board, confusing what is easy/interesting for an individual, versus what is needed for the class."

And I think I just disagree with it. Referencing the second point, rather than making it about me or the student," it's about the class."

If, for example, I'm teaching a calculus course, then it's a calculus course - not one on pre-calculus (which seems to be algebraic manipulation), and it's definitely not a pre-algebra course (which seems to be arithmetic with variables). Not every student has to be in every course or that particular course. But once they're in that course, I feel they really should learn that topic, rather than spend class time doing things they should already know because such things were supposed to be covered in the prerequisites.

With a set amount of class time, you have to pick and choose what to cover. And if I choose to review rather than focus on the current material, then it most likely means other things will be rushed or simply not covered. This results in students possibly passing the course but then messing them up for a future course where the one I taught was a prerequisite. (In effect, I pass on a problem to another teacher)

Ultimately, I'm pretty strict on prerequisites since I can foresee bigger problems if I'm lax on them. I'd much rather have a student do a course later than try to rush when they're not ready. In fact, before registering for a course, students can see the required prerequisites and the minimum grade needed. (But then, of course, there might be the issue of inflated grades)

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    What is the question here? – Adam Oct 29 '20 at 00:35
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    @Adam, see the title. – Zuriel Oct 29 '20 at 01:32
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    The "guest" who wrote the comment you link to is a regular troll here, who writes "ignore concepts, do more mindless drill" to pretty much every question here on ME.SE. He can be safely ignored. Related: https://matheducators.meta.stackexchange.com/questions/675/turn-off-unregistered-guest-answers – Daniel R. Collins Oct 29 '20 at 03:42
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    In math major classes I am pretty strict because the material is precious and must be covered in its entirety. For general ed classes, it really depends on the class. Sometimes you have a class where doing some prerequisite review in lecture makes your life overall much easier. They can deny having seen it in a previous class, it's far harder to deny having seen it after you just did it in their class... But, yeah, this can only go so far. I refuse to teach Calculus I in Calculus II etc... However, I will teach algebra in DEqns, go figure. – James S. Cook Oct 29 '20 at 04:39
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    @JamesS.Cook: When teaching the inverse Laplace transform in a DE course, I revisit completing the square and partial fractions. – J W Oct 29 '20 at 07:54
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    I teach at a community college. Our goal is to help students learn. I explain every step of my reasoning, and if students need a richer explanation, I offer it. If one particular student is way behind the rest, I offer help in my office. If they need more help than I can comfortably give, I recommend the college's tutoring services. More students learn more of the math if it is explained carefully and fully. – Sue VanHattum Oct 30 '20 at 02:10
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    @JW indeed, I do enough examples that it probably amounts to revisiting partial fractions. Personally, I actually learned completing the squares in DEqns, I just never needed it before that point ( of course, I did need it before, I just didn't know it and my grades did not suffer my ignorance...) – James S. Cook Oct 30 '20 at 15:55
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    @SueVanHattum “I thought I was bad at math because I couldn’t really understand the concepts in high school. But turns out all I needed was an instructor who was patient and open to helping others like me. No matter how small my question was, you answered it with kindness, intrigue [sic], and clarity. I appreciate the space you’ve created for inquisitiveness.” — Note from a student. – user1815 Nov 01 '20 at 03:58

1 Answers1

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For several decades, this issue has plagued me, at all levels, from calculus to grad-level courses.

First, my conclusion by this point is that very few people truly "have" the prerequisites for any course, even with an excellent performance in the prerequisites, if only because they do not assiduously review and practice in the interim. People forget lots of things over the summer, or during winter break.

And my experience is that explicit review is most often very inefficient, especially with lower-division undergrads, because they believe that they don't need the review (due to their good previous grade), and ignore what the instructor says "in review".

So, finally, I do not really-really assume that everyone has mastery of the prerequisites, but/and do many by-the-way reviews, or, really, as in @SueVanHattum's comment, I just spell out lots of details "from the prerequisites", rather than assuming without comment that everyone remembers.

I think the point is that the student populations that show up for courses mostly must be dealt with as-is, and it is unworkable to "hold to standards" that are not actually manifest in the rest of the system. The popular mythology in math classes of acting as though everyone has perfect recall of all their math classes so far is destructive.

There's also the far-more-true motto that in many endeavors we don't really come to understand topic X until we take the course for which X is a prerequisite. :)

So, no, I am not "strict in enforcing prerequisites".

paul garrett
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  • +1 for the next to last paragraph. Not surprisingly my experience is very similar. While I do some reviewing, for example of linear algebra when teaching vector calculus, I intentionally come through as a being more strict as you seem to indicate. Basically it is to drive home the point that the students are here to become professionals, and a part of that is to realize that they need to do a lot of reviewing under their own steam. – Jyrki Lahtonen Nov 16 '20 at 07:34