Wednesday, October 03, 2007

It's hard out here for a math teacher

And hard to be humble

Says You is one of my favorite radio programs. I never miss it. This past weekend, host Richard Sher surprised the panelists with one of the program's least frequent categories: math terms. (Sports is another frequently neglected category, much to my satisfaction.) There was an immediate eruption of cries of dismay and anguish, but Sher pressed on, asking for definitions of vertex, axiom, pi, Bernoulli trials, and non-Euclidean geometry. The panelists struggled bravely with the terms, having particular difficulty pinning down the meaning of pi.

Amid vague comments about circles and “pi r squared,” Sher insisted on cutting to the chase: “But what does it mean?” That provoked one particularly anguished panelist. Her voice laden with angst and misery, she hissed, “It means nothing!”

Oh, I felt her pain! That's because I've seen it in so many others. I admit that I find it especially amusing how some people demand that we demonstrate the utility of mathematics to them—while they are majoring in philosophy or literature. You go first!

The Says You panelist who expressed her exasperation at being asked to define mathematical terms reminds me of some colleagues who attended a college symposium a few years ago. The statewide academic senate of the California community colleges was considering whether to recommend that the Board of Governors raise the math requirement for graduation with an associate's degree. For many years the minimum math requirement had been introductory algebra, but California high schools were requiring introductory algebra for a diploma. Shouldn't a degree from a two-year college require something beyond that for a high school diploma? The notion was surprisingly controversial.

My math and science colleagues were largely in agreement that the math requirement for an associate's degree was too low. We supported the establishment of intermediate algebra as the new requirement (which, by the way, was approved, but has yet to take effect). Strenuous opposition was expressed by colleagues from the arts and humanities. We were told that math was hard and that it was not necessary to know math in order to be well educated. Despite the vigorous dissent of a large minority, the resolution to support the higher math requirement was approved. As we filed out, I overheard two colleagues from the humanities division lamenting the result. One expressed shock that the math faculty had voted in a bloc to place an onerous new burden on the students seeking an associate's degree. Her colleague replied, his voice bitter, “Well, what do you expect from cold-blooded reptiles?”

Anything you can do...

Math classes are usually ranked by students among the “solids” in the curriculum (as opposed, I presume, to the “softs”). Our courses may not attract affection, but they usually command a grudging respect. We math teachers bask in the reflected glory of our subject. We may be reptiles, but our discipline is solid. Faculty members in less solid fields may feel a touch of jealousy. Math has a high position in the academic pecking order.

The less diplomatic math professors (mind you, I'm not claiming to be one of those) have on occasion been uncharitable enough to point out that we have a special edge over our colleagues. An incident from my own experience provides an illustration:

I had carved out some time in my schedule to enroll in a Spanish class. My instructor was aware that I was a faculty colleague, but that did not result in his cutting me any slack. I was a student among other students. At least until that one special day arrived.

My Spanish professor caught me right at the beginning of the period. He was dealing with a problem in the departmental office that required his immediate attention as chair of the department. Could I cover the class for him a few minutes until he could deal with the language department emergency? ¡No problemo!

I calmly took charge of the class and announced that I would conducting the customary vocabulary quiz with which our professor always started each session. Currying favor with my classmates, I gave them fairly easy examples to work on. With exquisite timing, our professor returned just as the vocabulary quiz was coming to an end. He thanked me effusively as I took my seat among my classmates.

“You're very welcome, profe. In return, you can substitute for me in one of my algebra classes.”

A mixed look of horror and amusement passed over his face.

“No way!” he said. “That would never work!”

I'm sure what he said was true. With extremely few exceptions, the professors in languages, arts, and humanities could not substitute for a math instructor for even a few minutes without being found out as impostors. With all due modesty, I could vamp my way through an entire class period in quite a few courses—though probably not foreign languages—without being exposed as an interloper. So could several of my math colleagues. We wouldn't do a great job because we don't have the depth of knowledge and training that the specialists on our faculty do, but that's not the point. It's all about the way mathematics sets itself apart.

Math is so extraordinarily unforgiving that it quickly exposes one's shortcomings in a harsh light. That's a contrast with more subjective subjects, where core content may be wrapped in layers of personal perspective or opinion. When a math teacher says the answer is 5, that's probably all she wrote. When a literature professor says that Shakespeare's sonnets are the epitome of that written form, others may disagree and insist on John Milton or Elizabeth Barrett Browning—and make a case for their alternatives. With enough sang froid, a math teacher could probably pose as an English teacher for a much longer time than an English teacher could do the same in a math class. Math doesn't have the wiggle room or the space for discourse that other subjects allow.

This sounds like arrogant strutting about, of course, but I mean only to highlight the distinguishing feature of math that makes it noisome to so many. It's also the feature that makes me delight in it. The techniques and solutions are wonderfully specific and, to me, mostly straightforward and clear. Similarly, to me, it would be a herculean task to master, for example, the body of written works with which an English professor must be familiar. I don't think that their achievement of mastery in words is any less an accomplishment than what my colleagues and I were required to do in numbers. There does seem to be a difference, though, and it seldom redounds to the benefit of mathematics or mathematics teachers. I think we can count on that being a constant.


Josh said...

Reminds me of this:

It would be a great thing to hang on an office door...

Steve said...

The difference is that math is a priori, so a bright student could catch the incorrect answers, whereas in most other subjects, a familiarity with previous research would be required to call the professor on his bullshit. For instance, economics is a highly mathematical field, but without a familiarity with the literature, a mathematician would not be able to relate information that coincided with the goals of the course if he or she tried to pinch-hit.

"With enough sang froid, a math teacher could probably pose as an English teacher for a much longer time than an English teacher could do the same in a math class."

Are you saying that you could deliver a lecture on a literature topic that you haven't read at least the source material on? I'm skeptical. You might be able to "vamp" as you say, but even if you had read the material, you wouldn't be able to relate correct information about standard academic interpretations of literature. This would make your answers just as wrong as if a non-math specialist attempted to teach a math course and pull answers out of the top of his head. (In music, vamping means you play a pattern of a bar or two obligato, and typically someone speaks over the vamp. It's not the same thing as a real performance, most people would leave after a few minutes of this).

"Math classes are usually ranked by students among the 'solids' in the curriculum (as opposed, I presume, to the 'softs'). "

I was never required to take any courses from the math department in college (my Washington pre-college scores placed me out), but I found the science, business, and economics courses to be graded much more easily than the social science and humanities courses. This caused me much chagrin, as my grades and test scores in non-math subjects had always been very high, and I was just a B student in math and science. I expected these courses to be a snap or "soft," but they were far from it. The grading curve was always much lower in the science, business, and economics courses.

I have also read of several people saying that math courses got easier once they went to college, and focused more on "concepts" as opposed to "rote computation." So I wonder what the real "softs" are nowadays.

Lifewish said...

Are you saying that you could deliver a lecture on a literature topic that you haven't read at least the source material on? I'm skeptical.

Never been a teacher myself (thank {deity}), but I do recall the time I got full marks on an English essay. It was a comparison of Oliver Twist and some other book you've probably never heard of. I got full marks. Apparently I was the first student that that teacher had awarded 100% to in years.

The punchline? At the time I hadn't read Oliver Twist; I'd only seen the musical. That had been enough to allow me to hunt down relevant chunks of prose, and thus achieve the high grade.

The moral here is that English Literature is apparently more about expression and modes of thought than about actual results. When people try to translate that attitude across to the sciences... well, that's when you get probability-of-abiogenesis calculations.

Interrobang said...

The moral here is that English Literature is apparently more about expression and modes of thought than about actual results.

Speaking as someone who has a degree-and-a-piece in English Literature, there's no "apparently" about it, and the expression and the modes of thought are the results. (Duh.) That's why literature majors take prosodics, poetics, and belletristics, and the really hard-core ones (*wave*) will supplement (or complement) with a course in logic.

The rest of my degrees are in rhetoric and modern languages. Not only do I know how to structure an argument in written form, but I know how to make it look/sound/feel nice, and I can deliver it in more than one language. Frankly, that makes me formidable in a lot of situations.

As to the utility of studying literature, it was the best training I ever had for my current pro-am work as a historian, because studying literature gives you a good grounding in working with primary sources, learning about things like untrustworthy sources (the literary term of art is "unreliable narrator"), and being able to separate the wheat from the chaff in terms of what assumptions you can make about people in various periods of time. What one of my profs in grad school called "hyperliteracy" is a nice bonus, as well, since any high-level cognitive skills are a net bonus, literature, music, art, math, science, computer programming, it doesn't much matter.

Not only that, but studying good (or great) literature and reading a lot is the only way to become a competent writer -- what good is squaring the circle if you can't tell anyone about it?

For what it's worth, after I got tired of ripping the whitest and deadest of the dead white men to shreds, I started studying things like discourse analytics. Zeno: Defensive much? :)

I don't have anything against math, except that I've been trying to learn algebra for 15 years and mostly failing -- damn dyscalculia and dysgraphia. I just did something else... Incidentally, English majors in universities where I went to school beat up on the history majors for having useless degrees...and now I'm a for-money historian. In the lit'ry biz, we call that "irony." :)

Steve said...

Ok, I'm going to show off my ignorance, but what does pi really mean?
I haven't used pi since high school (not really- I do visual effects for a living and pi doesn't factor in there much...) and that was almost twenty years ago.

I know you use it to find the radius or diameter of a circle, it's a tool. So what DOES it mean?

Just curious.

Anonymous said...

Pi is the ratio between the circumference of a circle and its diameter.

In other words, if a perfect circle has a diameter of 1 meter across, it will have a circumference of pi (roughly 3.14) meters.

Peter said...

Steve, and anon.,

Yes, pi is indeed the ratio of the circumference to diameter. That's fine as a first order definition. You could as easily say it's just a symbol, with Godel's blessing. But it's the higher order meanings that matter - that's where the action is.

What it means is that we need to think about it in the same way as sqrt(2) - that there are irrational numbers leads to many weighty ideas.

What it means is that we have to look at inifinity in two ways - as a mathematical symbol and as a philosophical construct.

It means the universe has a certain structure to it. What if pi had a different value? Could pi have a different value? If so, where does that lead?

Shall I go on?

Steve said...

Maybe your love of math leads you to that philosophical answer, but in the context of most people, it is just a tool. I have no idea what sqrt(2) means, but it too is probably a tool you can use to reach an answer.

I do not "get" math. I can't figure out how to solve a math problem if presented in a different order or construct, even if the type of problem is the same. And for me personally, it IS just a tool.

Pi DOESN'T have a different value. I accept smarter people's explanations of complicated ideas like that, and it means very little to me.

Now, if you want to talk about how people move when they're feeling depressed as opposed to feeling happy... Well, that's my thing. :)

Anonymous said...

The square root of 2 simply means the number for which when you multiply it by itself, gives the answer 2.

Non-Euclidean geometry means any system of geometric theorems which form their base with Euclid's first Four Postulates, but do not assume the Parallel Postulate.