College Math Teaching

March 24, 2020

My teaching during the COVID-19 Pandemic

My university has moved to “online only” for the rest of the semester. I realize that most of us are in the same boat.
Fortunately, for now, I’ve got some academic freedom to make changes and I am taking a different approach than some.

Some appear to be wanting to keep things “as normal as possible.”

For me: the pandemic changes everything.

Yes, there are those on the beach in Florida. That isn’t most of my students; it could be some of them.

So, here is what will be different for me:
1) I am making exams “open book, open note” and take home: they get it and are given several days to do it and turn it back in, like a project.
Why? Fluid situations, living with a family, etc. might make it difficult to say “you HAVE to take it now…during period X.” This is NOT an online class that they signed up for.
Yes, it is possible that some cheat; that can’t be helped.

Also, studying will be difficult to do. So, getting a relatively long “designed as a programmed text” is, well, getting them to study WHILE DOING THE EXAM. No, it is not the same as “study to put it in your brain and then show you know it” at exam time. But I feel that this gets them to learn while under this stressful situation; they take time aside to look up and think about the material. The exam, in a way, is going through a test bank.

2) Previously, I thought of testing as serving two purposes: a) it encourages students to review and learn and b) distinguishing those with more knowledge from those with lesser knowledge. Now: tests are to get the students to learn..of course diligence will be rewarded. But who does well and who does not..those groups might change a little.

3) Quiz credit: I was able to sign up for webassign, and their quizzes will be “extra credit” to build on their existing grade. This is a “carrot only” approach.

4) Most of the lesson delivery will be a polished set of typeset notes with videos. My classes will be a combination of “live chat” with video where I will discuss said notes and give tips on how to do problems. I’ll have office hours ..some combination of zoom meetings which people can join and I’ll use e-mail to set up “off hours” meetings, either via chat or zoom, or even an exchange of e-mails.

We shall see how it works; I have a plan and think I can execute it, but I make no guarantee of the results.
Yes, there are polished online classes, but those are designed to be done deliberately. What we have here is something made up at the last minute for students who did NOT sign up for it and are living in an emergency situation.

March 9, 2010

The Importance of Integrals and Standards

One of the challenges of teaching lots of “service” courses is that one sometimes comes under heat from client departments if one flunks too many of their prospective students (especially in the engineering/math/science calculus sequence)

Sometimes, we are told that we are too hard on them or teach students what they don’t need to know.
So, it was “art to my eyes” to read the following post at Cosmic Variance:

Having recently slogged through grading an enormous pile of graduate-level problem sets, I am compelled to share one of the most useful tricks I learned in graduate school.

Make your integrals dimensionless.

This probably seems silly to the theoretical physicists in the audience, who have a habit of changing variables and units to the point where everything is dimensionless and equals one. However, in astrophysics, you frequently are integrating over real physical quantities (numbers of photons, masses of stars, luminosities of galaxies, etc) that still have units attached. While students typically do an admirable job of setting up the necessary integrals, they frequently go off the rails when actually evaluating the integrals, as they valiantly try to propagate all those extra factors.

Here’s an example of what I mean. Suppose you want to calculate some sort of rate constant for photoionization, that when multiplied by the density of atoms, will give you the rate of photo-ionizations per volume. These sorts of rates are always density times velocity times cross section: […]

the integral reduces to something that you can start to wrap your brain around:

Basically, they were talking about a change of variables. Of course, the integral is NOT elementary and one would have to use some sort of technique (residue?) to evaluate it.

But the point is that the people in physics EXPECT their students to be able to handle the mathematics.

But about the heat we catch for our flunk-out rates:

to be honest, not everyone is down on us for that:

We make rules we think will help our students–you fail if you don’t do the reading, you fail if your paper isn’t turned in on time, you can rewrite anything you fail, ad infinitum–thinking it will help. Then I come to RYS and see the bodies dropping all over the damned place.

That’s why, this semester, I started to bend instead of break. Kid wants to turn it in late? Okay. Kid can’t be in class. Who cares? I go in every day, try to start a discussion, give an impromptu lecture on days they won’t bite, let them out early once I’ve told them what I guess they probably have to know. If I can make out what the paper is about, I give it at least a B-minus. I mark the hell out of them–I write comments in the margin till there ain’t no margin left, and no ink to write in it with. But the grade is always a B-minus or higher, because if it isn’t, they’ll come to my office requesting a checklist of things they can do to write more effective essays, by which they mean essays that will get better grades. […]

So I inflate grades. So should you, unless you’re teaching your students math or anything related to keeping buildings or airplanes or economic systems from falling apart.

Emphasis mine. What can I say? 🙂

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