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.