College Math Teaching

June 20, 2018

Editorial: one major disconnect between us and much of the public ..

Filed under: editorial — Tags: , , , , — collegemathteaching @ 1:52 am

The University of Chicago decided to stop requiring the ACT/SAT of its applicants. Now never in a million years would I give a suggestion to the University of Chicago (or any other elite school) as to what their admissions/applicant policies should be.

But there is a broader “scrap the college entrance exams” movement out there and much of the justification you hear is just complete nonsense. Example: “we have data that says the high school gpa is a better predictor of X”. (X meaning “first year success”, or “graduation”) Now that may be true, but why stop with just one bit of information if the second bit, taken together, increases predictive power?

And there is a second claim from those who admit that not all high schools are created equal, and an A in, say, high school calculus in one school might mean less than an A from another school: admitting that the quality of high schools vary means that you are just punishing the students from the academically weaker high schools a second time when you use a college entrance exam.

That claim misses the point entirely. Many schools (like ours) uses the score, at least in part, for placement purposes (we aren’t that tough to get into). And we have have decades of data that shows that, yes, the math ACT score matters, in terms of success in first year calculus. This isn’t our school (it is the University of Michigan), but we have very similar results.

And this brings us to the disconnect in attitudes.

1. We use scores to determine if the student has a reasonable probability of success in, say, a freshman calculus course. Now of course, sometimes someone under the cut-off has success. But if you give too much benefit of the doubt to prospective students, your DFW rate (D’s, F’s, Withdraws) will climb and administrators such be made aware of the trade-off.

2. We also understand that aptitude matters. There are many (more than you think) that aptitude has no role, or a very minor role (“you can do anything you want to do if you put your mind to it”, etc.) and some who embrace “blank slate” thinking (to them, aptitude is a fiction).

I suppose that people who REALLY believe “2” believe that, say, recruiting plays no role in the success of college sports team..a good coach can just draw from the student body and win games.

3. Part of the role of, say, the calculus sequence is to identify those who have a good probability of success in certain majors. Let’s face it; if you really can’t calculate \frac{d}{dx}sin(2x) you have no business being an engineer. Yes, on rare occasion, I’ve had students flunk my class in science/engineering calculus class because they really could not do that.

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June 18, 2018

And my “clever proof” is dashed

Filed under: complex variables, editorial, knot theory, numerical methods, topology — Tags: , — collegemathteaching @ 6:03 pm

It has been a while since I posted here, though I have been regularly posting in my complex variables class blog last semester.

And for those who like complex variables and numerical analysis, this is an exciting, interesting development.

But as to the title of my post: I was working to finish up a proof that one kind of wild knot is not “equivalent” to a different kind of wild knot and I had developed a proof (so I think) that the complement of one knot contains an infinite collection of inequivalent tori (whose solid tori contain the knot non-trivially) whereas the other kind of knot can only have a finite number of such tori. I still like the proof.

But it turns out that there is already an invariant that does the trick nicely..hence I can shorten and simplify the paper.

But dang it..I liked my (now irrelevant to my intended result) result!

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