# College Math Teaching

## March 5, 2014

### Comparing calculus exams…..and university students

Filed under: academia, calculus, pedagogy — Tags: — collegemathteaching @ 2:04 am

Some people tried to argue with me about calculus; they seemed to think that calculus at one institution is the same as at another one.

Hardly.

Not only can courses vary in terms of topic and difficulty, but so can exams…and the difference might be very subtle to those who are unfamiliar with giving and grading exams.

Here is one example: suppose you want to examine the students on the Mean Value Theorem. How might you do this?

1. State the Mean Value Theorem (yes, the bad students usually can’t even do this).

2. State and prove the Mean Value Theorem (prove using what?)

3. Let $0 < x < y < 1$. Show that there exists a $c$ between $x$ and $y$ so that $y^2 - x^2 = 2c(y-x)$.

4. Use the Mean Value Theorem to show that $|cos(x) - cos(y)| \leq |x - y |$

5. Show that for all real $x, y, |cos(x) - cos(y) | \leq | x-y|$

Not only do these questions vary in difficulty, they may or may not have been covered directly in class prior to the exam; that makes a big difference.

We are doing a job search. We have someone who is interviewing; he currently teaches at a school whose student population has a median ACT that is about 3 points higher than ours. BUT his institution is “technical majors only”; they don’t have much (any) of a humanities, communication or education program. So, if you compared their calculus student ACT to our “engineering/science calculus” ACT, the difference shrinks considerably, if it remains at all. But our department does teach the “business calculus”, “baby stats” and “math for poets” courses…and he will NOT be used to that type of student.

## March 2, 2014

### Ironic….

Filed under: editorial — Tags: , — collegemathteaching @ 6:01 pm

This is a whine so be forewarned:

Today and tomorrow, I have some “recruitment” duties. Today, I’ll make some calls to some of the better students that have been admitted to our mathematics program. Yes, I volunteered ….to call the more promising ones. I refuse to call the “20 on the ACT ones” as these never make it as math majors, at least here (we have the data).

Tomorrow: I have to work a “admitted student visit day” (meet with parents and prospective students) and to meet with a candidate for one of our two open tenure track positions.

So, I am going to spend the next couple of days trying to talk people into coming here….when, to be blunt, I’d leave if I had opportunities elsewhere!

Ok, I might not be saying this if I hadn’t have just come in from shoveling snow for the thousandth time this winter; I never wanted to live in the frigging Yukon!!! It is MARCH, for crying out loud!!!!!

Ok, to be fair, our University has done a great job keeping the parking lots, sidewalks clear this winter, and it wasn’t easy to do. I can honestly say that.

### Math grad students and new job candidates: do you REALLY want one of our jobs?

Filed under: academia, editorial — Tags: — collegemathteaching @ 1:50 pm

We are in the the process of hiring two new tenure-track assistant professors. Most of those applying are new Ph. D. graduates and those coming off of post-doctoral positions. Sadly, we also got applications from those denied tenure elsewhere (and this isn’t the kiss of death; necessarily).

Applications are invited for two Tenure-Track Assistant Professor positions in the Department of Mathematics beginning August 2014.
Candidates must possess a Ph.D. in mathematics or statistics by the start date. Preference will be given to candidates who are broadly trained, have a strong commitment to undergraduate teaching, and have college-level teaching experience. Preference will be given to those applicants whose research specialty is in statistics, applied mathematics, or other areas of current interest in the department. An active research program and scholarly publication are required for tenure and advancement. Candidates must be able to work in the U.S without sponsorship.
For full consideration, applications should be complete by December 16, 2013. Other positions may become available in the future.
Please submit all application materials electronically. Post the AMS cover letter, a letter of application, vita, a copy of each graduate transcript, description of research, statement of teaching philosophy, and three current letters of recommendation (at least one of which addresses teaching and one research) on the MathJobs.org web site.
Employment with xxx University is contingent upon the satisfactory completion of a criminal background check.
xxx University is a distinctive, medium-size, comprehensive private institution of higher learning. The University is located on an 85-acre campus in [a rust belt town in the Midwest]. With approximately 5,000 undergraduate and 800 graduate students, xxxx offers the opportunities and choices of a larger university (with over 130 programs in five colleges, plus a graduate school) and the quality, personal attention, and challenge of a small private college. xxxx is rich in tradition and full of promise to become one of the nation’s best comprehensive universities

So you put out applications and maybe get interest from us. Ok, you are on our short-list. Should WE be on YOUR short list?

Here are ways you can find out:

Teaching: I suggest you go online and look at the actual class schedule and look at the listings that have the faculty of record listed. This way you can see for yourself what typical teaching loads are. You’ll notice that the vast majority of us teach three classes (typically 11 hours): typically 2 lower division courses and one “upper division/differential equations/linear algebra” course.

The lower division courses are typically the following: “math for poets”, “brief calculus” (business calculus, calculus sans proofs, etc.), “baby stats” (non-calculus based statistics) and regular calculus.
Most of us take turns doing the lower division “math for the math phobic” and “math for engineers and scientists”; remember this is over 2/3’rds of what you’ll teach.

Also keep in mind our median ACT is about 26 (one standard deviation above the national median); in the “off semester” service courses for the math phobic, your classes will consist of students who are well to the left of the bell curve; to them, a related rate problem is REALLY HARD. Be prepared for questions such as “how did you get from $3y\frac{dy}{dx} = 2x^2$ to $\frac{dy}{dx} = \frac{2x^2}{3y}$?

The “on track semester” calculus teaching isn’t bad; here the courses are populated by many students who will remind you of yourself when you were that age. Teaching these can be a lot of fun.
I suppose that my main point is that you’ll see a lot of variation between classes; some sections will have an ACT median of 30, and others will have one 10 points lower.

You might wonder about “mentoring undergraduate research”. Yes, we have a senior project and yes, faculty direct these. At our place: this is done as non-compensated overload: no teaching load reduction and NO CREDIT for research. Yes, on rare occasion an undergraduate student will get something published in a research journal (this happened exactly once this past decade at our place) but this is the rare, rare exception.

You’ll get a nice check mark on your faculty activity report, but that will be the only reward from administration.

No, we do NOT have masters program in mathematics, though some sciences and engineering departments offer them.

This brings us to the research part.
Yes, you are expected to publish, but NOT at the rate or at the quality expected at a Research I caliber university (and please, forget the marketing claim that “undergraduates at our university do “cutting edge” research”; here our faculty can’t come close to doing that…how could they given their high teaching loads?).

For us: 3-4 decent publications in research journals (your thesis plus some follow ons) should be sufficient for tenure and promotion to associate. Where I’ve published: American Mathematical Society Proceedings, MAA Monthly, MAA College Math Journal (2 classroom capsule articles, plus 3-4 Flaws, Fallacies and Flim-Flam pieces), Houston Math Journal and a few in the Journal of Knot Theory and its Ramifications (and others) So you do have to be active.

Now while it is possible that an undergraduate project lead to a publishable paper (example) trying to meet one’s research requirement by direction undergraduate research is extremely risky; I’d say that the probability of success with this strategy is low.

The other thing: you’ll do most of your research in small amounts of spare time; staying current with new developments is almost impossible after a while. Expect your discipline to pass you by. You’ll be able to tackle small “spin off” problems though; what will be difficult (if not impossible) is to keep up with increasingly sophisticated machinery. Yes, there ARE exceptions, but these are extreme outliers.

There is one upside though: because you’ll teach across the curriculum, including courses you haven’t had in a while (e. g. I am teaching numerical methods), you’ll be exposed to more. And yes, my papers included those in point set topology (or that use point set topology), splines (applied math) and, yes, real analysis.

Another upside we do have a sabbatical program, and I’ve taken a couple of these (and gotten papers out of them).

Then there is service. There is always some committee work (which can be a major time suck) and much of the committee work is wasted. And at a small, private place like ours, you’ll be expected to help out on visit days (meet prospective students) and ….yes, call prospective students! And yes, those with heavy foreign accents are not prime candidates to make the “admitted student” calls.

Now, I am not going to get into the “quality of life” part as that varies from city to city. Here: many faculty don’t live in the city itself mostly do to the poor public school system. I live walking distance from campus as I was a non-custodial parent and, yes, our university has tuition exchange with other colleges. That is saving me quite a bit of money as I write this. My “out of pocket” college expenses (room and board) are roughly what my child support payments were. That is nice.

So, are WE for YOU? I can’t say, but hopefully I’ve given you some ideas of what to ask.