# College Math Teaching

## April 12, 2016

### At long last…

Filed under: academia, editorial — Tags: — collegemathteaching @ 9:17 pm

I’ve been silent on this blog for too long. Part of what is happening: our department is slowly morphing into a “mostly service courses” department due to new regulations on “minimum class size” (set to 10 students for upper division courses). THAT, plus a dearth of “mathematics teaching majors” is hurting our “majors” enrollment.

So it has been “all calculus/all the time” for me lately. Yes, calculus can be fun to teach but after close to 30 years…..zzzzzz….

And it would be unethical for me to try something new just because I am bored.

But I finally have something I want to talk about: next post!

## February 9, 2016

### An economist talks about graphs

Filed under: academia, economics, editorial, pedagogy, student learning — Tags: , — collegemathteaching @ 7:49 pm

Paul Krugman is a Nobel Laureate caliber economist (he won whatever they call the economics prize).
Here he discusses the utility of using a graph to understand an economic situation:

Brad DeLong asks a question about which of the various funny diagrams economists love should be taught in Econ 101. I say production possibilities yes, Edgeworth box no — which, strange to say, is how we deal with this issue in Krugman/Wells. But students who go on to major in economics should be exposed to the box — and those who go on to grad school really, really need to have seen it, and in general need more simple general-equilibrium analysis than, as far as I can tell, many of them get these days.

There was, clearly, a time when economics had too many pictures. But now, I suspect, it doesn’t have enough.

OK, this is partly a personal bias. My own mathematical intuition, and a lot of my economic intuition in general, is visual: I tend to start with a picture, then work out both the math and the verbal argument to make sense of that picture. (Sometimes I have to learn the math, as I did on target zones; the picture points me to the math I need.) I know that’s not true for everyone, but it’s true for a fair number of students, who should be given the chance to learn things that way.

Beyond that, pictures are often the best way to convey global insights about the economy — global in the sense of thinking about all possibilities as opposed to small changes, not as in theworldisflat. […]

And it probably doesn’t hurt to remind ourselves that our students are, in general, NOT like us. What comes to us naturally probably does not come to them naturally.

## February 8, 2016

### Where these posts are (often) coming from

Filed under: academia, linear albegra, student learning — Tags: , — collegemathteaching @ 9:57 pm

Yes, my office is messy. Deal with it. 🙂 And yes, some of my professional friends (an accountant and a lawyer) just HAD to send me their office shots…pristine condition, of course.
(all in good fun!)

Note: this semester I teach 3 classes in a row: second semester “business/life science” calculus, second semester “engineering/physical science” calculus and linear algebra. Yes, I love the topics, but there is just enough overlap that I have to really clear my head between lessons. Example: we covered numerical integration in both of my calculus classes, as well as improper integrals. I have to be careful not to throw in $\int^{\infty}_{-\infty} \frac{dx}{1+x^2}$ as an example during my “life science calculus” class. I do the “head clearing” by going up the stairs to my office between classes.

Linear algebra is a bit tricky; we are so accustomed to taking things like “linear independence” for granted that it is easy to forget that this is the first time the students are seeing it. Also, the line between rigor and “computational usefulness” is tricky; for example, how rigorously do we explain “the determinant” of a matrix?

Oh well…back to some admin nonsense.

## January 26, 2016

### The walk of shame…but

Filed under: academia, research — Tags: , — collegemathteaching @ 9:07 pm

Well, I walked to our university library with a whole stack of books that I had checked out to do a project…one which didn’t work out.

But I did check out a new book to get some new ideas…and in the book I found a little bit of my work in it (properly attributed). That was uplifting.

Now to get to work…

## September 23, 2015

### Intelligence doesn’t show outwardly….

Filed under: academia, editorial — Tags: , — blueollie @ 12:02 pm

This semester has been the “semester from hell” in that I am teaching a class in actuarial mathematics and I have never seen the material before. So I am doing a “self-study” course on my own just ahead of the students.

I’ve done things like this before, but almost always it has been in classes where at least I understood both the notation and the point of the material fairly well.

The upside: I am learning something new.
But one consequence is that I have had little to share on this blog this semester.

I will make one comment though:

I am giving the first exam back in my “calculus II” (of 3) courses. This is the “off semester” which means that I’ll have students who placed out of calculus I and I’ll have those who have either flunked this course once (or several times) or I’ll have some who have been through our remedial calculus preparation program.

Hence, my grading curve looks like a “bathtub” curve.

But, time and time again, I am fascinated by the fact that all of the students, both the smart ones and the not-so-smart ones, “look alike” in that you can not distinguish them by appearance.

This is just the opposite from sports.

In a 5K race, if I see some tiny, slender but muscular person I know that I won’t see them after the start of the race. In the gym, if i see some guy who looks like he was carved out of marble, I know that I’ll be lifting about half of what he will.

But intelligence just doesn’t show in the same way.

## September 18, 2015

### Teaching a class that one is unqualified to teach…

Filed under: academia, editorial — Tags: , — blueollie @ 11:39 am

I haven’t posted much lately. I might post some this weekend, IF I ever get caught up. I have a couple of homework sets and one set of exams to grade.

What is going on: originally, I had a 3 preparation schedule: second semester calculus (the usual), first semester “business” calculus and numerical analysis. The latter is a time suck, but I’ve taught this course multiple times and have the details reasonably well worked out.

Note: my research specialty is topology though I’ve published an elementary analysis paper as well.

Anyway, it turns out that our part time instructor who teaches our “theory of interest” and “life contingencies” class got called away and we had no one to cover a class that had 18 students enrolled. A call for volunteers was put out and I said “if no one else….” BIG MISTAKE.

I am ok with it being an evening class.

But:

1. The amount of preparation time is incredible; basically I am teaching myself this material about 1 week (if that) ahead of walking into the class. I do ALL the homework to make sure I can do it correctly.
2. While the nuts and bolts are elementary on mathematical grounds, I have very little extra insight to offer. In the other classes, I can give a bit of perspective on “what is out there”. Not so in this class. I can teach “how to use the table”.
3. I am one who needs to know the stuff really, really well (at almost an unconscious level) to be comfortable in the class room. I don’t “fake it” well.

On the other hand, this is one of the things about having earned a Ph. D. and continuing to do research (though not this semester): I know how to learn and how to test my own knowledge on something. That is an ability that allows for me to “sub” in an area that I am not qualified to be in.

Of course, I still think that our university is obligated to hire a qualified person in this area if it wants to offer an actuarial program, though our increasingly corporate administration disagrees.

## August 21, 2015

### Just shoot me. Now. (personal…and my screw up…)

The upcoming semester line up:

1. My original schedule called for science/engineering calculus II, “business calculus” I, and numerical analysis. No, my specialty is pure math (topology) but I got roped into teaching this course a few years ago, and because no one complained…guess who is stuck with it now? 🙂 (and yes, as an undergraduate, and once as a part time graduate student, I made C’s in this class)

2. But a part time faculty who taught our actuarial mathematics classes got called away so..I said “if you can’t find anyone else…” and so I got stuck with that class (in lieu of the “business calculus” class)

3. I get an e-mail about the class; I read the Fall 2014 syllabus and so prepare based on that (since it is Fall 2015)..but the topics for that class go “spring, fall, off, fall, spring” instead of “fall/spring”…so I had prepared FOR THE WRONG CLASS and ordered THE WRONG BOOK.

I caught that a week prior to classes starting..hence frantic e-mail to the department chair and secretary….and I’ll have to really work some this weekend.

Fortunately much of the stuff in this topic (“life contingencies”) is like reliability engineering and I’ve had that class. Things like the “survival function” and “bathtub curve” are familiar to me. The mathematics won’t be hard; I’ll have to focus my self study on definitions and notation.

Still, this is more interesting than I’d hoped that it would be.

The positive: I’ll have learned some new mathematics (I always learn something new every time I teach numerical analysis) and new applications of mathematics (the life contingencies …and I’ve already learned a little bit of interest theory by preparing for the class that I thought that I was teaching..)

The university
But our university (6000 students, 5000 undergraduates) is suffering from an enrollment slump for the second year in a row. We are at about 85-88 percent of what would be a “healthy” enrollment. The place is in turmoil; we lost our athletic director, provost (left) and president, the flagship basketball team has hit rock bottom and things are in disarray.

So we have a second “small” class but this time: enrollments are UP in our remedial sections. UP. And many who couldn’t place into our regular calculus sequence have been admitted…by …engineering. Seriously. They are hurting that badly, and when they hurt, WE hurt.

I’ll be shielded from much of that in the classroom because of the classes I am teaching BUT with these changes come “changes in major”; we are going to try to make our major easier to navigate by trying to maximize flexibility by making our “required courses” less prerequisite dependent. It will water down the major somewhat but hopefully make it more likely that we keep a major.

Oh well…this is what I get for taking my Ph. D. in pure mathematics instead of applied. 🙂

## May 4, 2015

### Teaching evaluations ….

Filed under: academia, editorial — Tags: , , — collegemathteaching @ 4:48 pm

When I was in grade school, I was evaluated by people with undergraduate degrees.
When I was in high school, I was evaluated by people with undergraduate degrees, and occasionally by someone with a masters degree.
When I was an undergraduate, I was evaluated by Ph. D. holders and an occasional masters degree holder.
When I was a graduate student, Ph. D’s with impressive research credentials evaluated me.

Now..as a college professor…I am evaluated by those with high school diplomas ….things have come full circle, huh? 🙂

In all honesty, at least my department does “peer classroom visits” at least with non-tenured faculty, and on occasion, with some tenured faculty (the latter is mostly voluntary).

## April 9, 2015

### I’d be a better mathematician if I weren’t so freaking dumb!!!!

Filed under: academia, editorial — Tags: — collegemathteaching @ 7:45 pm

I have some time to think about things, and I got hung up on a detail…and the resolution of said detail was realizing, that if $f$ is a bijection (one to one and onto), then $(f^{-1})^{-1} = f$.

ARRRGGGHHHHH!!!!!!!!!!!!

Back to work.

## April 1, 2015

### My topology class April Fools me…

Filed under: academia, pedagogy — Tags: — collegemathteaching @ 9:41 pm

My topology class has 6 students and all usually sit in the first or second row of the class room. They are NEVER late.

As I walked to the classroom about 1-2 minutes before the start, the lights were out..and of the desks I could see…empty.

I walked in, looked at the back and said “Happy April 1”.

I LOVED it!

I joked that today, we were having the final exam and they had to prove the Tychonoff Theorem from scratch…full version (infinite product of compact spaces is compact in the product topology).

I gave them all 1 extra point on their homework assignments.

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