College Math Teaching

December 28, 2016

Commentary: our changing landscape and challenges

Filed under: calculus, editorial — collegemathteaching @ 10:34 pm

Yes, I haven’t written anything of substance in a while; I hope to remedy that in upcoming weeks. I am teaching differential equations this next semester and that is usually good for a multitude of examples.

Our university is undergoing changes; this includes admitting students who are nominally STEM majors but who are not ready for even college algebra.

Our provost wants us to reduce college algebra class sizes…even though we are down faculty lines and we cannot find enough bodies to cover courses. Our wonderful administrators didn’t believe us when we explained that it is difficult to find “masters and above” part time faculty for mathematics courses.

And so: with the same size freshmen class, we have a wider variation of student abilities: those who are ready for calculus III, and those who cannot even add simple fractions (yes, one of these was admitted as a computer science major!). Upshot: we need more people to teach freshmen courses, and we are down faculty lines!

Then there is the pressure from the bean-counters in our business office. They note that many students are avoiding our calculus courses and taking them at community colleges. So, obviously, we are horrible teachers!

Here is what the administrators will NOT face up to: students frequently say that passing those courses at a junior college is much easier; they don’t have to study nearly as much. Yes, engineering tells us that students with JC calculus don’t do any worse than those who take it from the mathematics department.

What I think is going on: at universities like ours (I am NOT talking about MIT or Stanford!), the mathematics required in undergraduate engineering courses has gone down; we are teaching more mathematics “than is necessary” for the engineering curriculum, at least the one here.

So some students (not all) see the extra studying required to learn “more than they need” as wasted effort and they resent it.

The way we get these students back: lower the mathematical demands in our calculus courses, or at least lower the demands on studying the more abstract stuff (“abstract”, by calculus standards).

Anyhow, that is where we are. We don’t have the resources to offer both a “mathematical calculus” course and one that teaches “just what you need to know”.

August 11, 2016

Post Promotion Summer

Filed under: editorial, topology — Tags: — collegemathteaching @ 12:02 am

This is my first “terminal promotion” summer. And while I have something that I have “sort of” written up…I just don’t like the result; it basically fills in some gaps in a survey article. But I think that my thinking about this article has lead me to something that I can add to the paper so that I’ll actually LIKE what I submit.

Then again, my quandary can be summed up in this tweet:

goodgreatperfect

If I wait until I am absolutely in love with my work before I send it out, it will never get sent out.

Hopefully, I’ll have more material to add to this blog this semester.

What I am working on: equivalence classes of simple closed curves; these are one to one, continuous images of the unit circle in 3-space. The objects that I am studying are so pathological that these curves fail to have a tangent at ANY point. One of these beasts can be constructed by taking the intersection of these nested, solid tori.

bingsling

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

Bedside manner

Filed under: editorial — Tags: — collegemathteaching @ 7:53 pm

One of the things I’ve had to change is how I related to students.

I grew up playing football and wrestling. I went to a service academy and served in the Navy. Then, of course, I got pushed in graduate school.

I cannot treat my students the way that I got treated; they would break down rather than get motivated; in general they have trouble handling even a hint of anger.

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.

January 20, 2016

Congratulations to the Central Missouri State Mathematics Department

Filed under: advanced mathematics, editorial, number theory — Tags: — collegemathteaching @ 10:43 pm

The largest known prime has been discovered by mathematicians at Central Missouri State University.

For what it is worth, it is: 2^{74,207,281} -1 .

Now if you want to be depressed, go to the Smithsonian Facebook page and read the comment. The Dunning-Kruger effect is real. Let’s just say that in our era, our phones are smarter than our people. 🙂

October 29, 2015

A quick break from the routine…

Filed under: editorial, topology — Tags: — collegemathteaching @ 9:23 pm

This came as an advertisement. I got some good natured ribbing.

notablepaper

But this semester, I’ve been up to my eyeballs in this new (to me) course. If I never see actuarial mathematics again, it will be too soon. 🙂

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. 🙂

appliedvspuremath

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