A Mathematician's Apology

First, the apology: I started a summer job last week and it's taking up a huge amount of time. So posts will be infrequent until my job ends in August.

But since it's on my mind, I'd like to share a bit about this job. I'm assisting in the PROMYS for Teachers program. The goal of the program is to give math teachers an experience similar to the way mathematicians do math.

We mathematicians approach math differently from the way anyone else does. Most people learn math by watching a teacher explain a concept and demonstrate some examples. Students then apply these concepts to some practice problems, and that's pretty much it.

Mathematicians are in the business of discovering new mathematics, not reproducing what is known. To do this, we do what all scientists do: we experiment. Except that for us, experimentation involves only a pencil and paper (computers are sometimes used, but not as much as you might think.) We take numbers or shapes or other mathematical objects and play around with them. This can be a frustrating and fruitless process, but eventually we hope to discover something interesting about the way these objects work.

The next step after discovery is to describe our discovery. This is harder than it sounds, because mathematical language is very precise. One's first few attempts to describe a discovery are often wrong in some way; perhaps an important qualifier has been left out. Sometimes we have to invent new language to describe a discovery.

Finally, we try to justify our discovery by proving it from first principles or from other established theorems. This process can range from easy (a few minutes of thinking) to moderately hard (a few weeks) to epic (a few centuries.) The most famous mathematical theorems come from discoveries that are simple to describe but surprisingly difficult to prove.

In the PROMYS for Teachers program, we try to give teachers a taste of this experience. We give them numerical problems that hint at deep mathematical patterns. We then ask them to describe these patterns precisely and prove them if possible. This is often frustrating for them, since they haven't been shown how to do the problems or proofs beforehand. But by making their own discoveries, they take ownership of the mathematics, and when the process works it is tremendously exciting.

This program is modelled on the Ross program at Ohio State University, which I attended as a high school student. That program basically made me into a mathematician, so it is very rewarding to me to be able to share this experience with teachers.

WSJ: Teach for America "proves" that teachers don't need pay

I know it’s my own fault for evening opening the Wall Street Journal to the editorial page. But somehting I found there last weekend irked me more than their usual “liberals are naive idiots” fare.

An editorial entitled "Amazing Teacher Facts" argued, using the example of Teach for America, that teachers don’t need to be paid any more than they currently are. If these bright young college grads are lining up to teach in inner-city schools at standard salaries, and doing a good job of it, then clearly money isn’t the issue in hiring quality teachers. The culprit must instead be the bureaucracy that requires teachers to take “education” courses (their quotes) to enter the profession the normal way.

This pinched my nerve because I did Teach for America, teaching for two years at Austin High School in Chicago. I was lost my first year and barely competent my second, but in a school with a large number of burnout teachers, this made me a valued member of the faculty.

So yes, TFA teachers do make a positive contribution to their schools. Some of them even become outstanding teachers. This despite being paid a salary that, while livable for 20somethings with no families to support, is far less than these Ivy League grads could be making on Wall Street.

But the WSJ editorial completely fails to ask the question of why, precisely, these Harvard and Yale types are flocking to teach in inner-city LA and rural Louisiana. In my opinion this is due to a phenomenal feat of marketing on the part of TFA. They managed to convince college seniors that teaching is A) a noble cause (which it always has been) and B) an attractive career move (which it never has been in the past.) Paradoxically, by admitting such a small percentage of applicants, TFA has made teaching an elite profession, at least when it is done through TFA. I can’t tell you how many conversations I’ve had that went:

“I’m a high school teacher”
“Oh.”
“...through Teach for America.”
“Oooooooooooooooooohhh!”

What the example of Teach for America proves is precisely what the Wall Street Journal was unwilling to admit: that to recruit quality teachers, you need to raise the status of the teaching profession. Our society usually equates status with money, so the most direct way to get qualified teachers is to pay them what they’re worth (six figures, at least!) TFA is bringing new respect to the teaching profession, but it will never be able to fill our massive teacher shortage while simultaneously maintaining its elite identity. Fixing public education will require a societal consensus that teaching is one of our most important professions, and they need to be paid accordingly.