Bridges in Mathematics

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For the Fun of It

By Dr. Eugene Maier

"Few pleasures equal the joy of the mind when it's being put to creative use."—Lewis Lapham.

Dick Feynman, a Nobel prize winner, tells of the time while on the Cornell faculty that physics became drudgery for him. He used to enjoy doing physics and now it was beginning to disgust him. He wondered why. He decided that he once did physics because it was interesting and amusing to play with, and not because someone else thought that what he was doing was important, or that it was advancing the state of nuclear physics. He resolved to recapture his playfulness; to "play with physics Ä without worrying about any importance whatsoever."

A while later he was in the cafeteria when a prankster threw a plate in the air. Feynman noticed the Cornell medallion on the plate going round faster than the plate was wobbling. He was struck by what he observed and decided to see if he could figure out what was going on. He established that the rate of rotation was twice the wobble rate; that is, the plate rotated twice for every time it wobbled up and down. He told a colleague what he had discovered. His colleague found it interesting but questioned its importance and wondered why Feynman was doing it. "There's no importance whatsoever," Feynman replied, "I'm just doing it for the fun of it."

Current programs fostering math reform are criticized by some for their emphasis on making math fun. As one critic, for whom enjoying math class is of no import, maintains: "Math is Ä hard work, requires discipline and lots of practice." Which, without enjoyment, strikes me as a recipe for the affect that afflicted Feynman: drudgery.

To me, the position that enjoying math is of no consequence to the learner is untenable. Hardly anyone would quibble with the statement that, given their druthers, a person will spend their time and energy doing something they enjoy rather than a task that brings no pleasure. Also, learning something well brings a sense of satisfaction—good feelings, if you will—especially if one values what it is one has learned. If a student isn't feeling good about mathematics, they haven't learned much or they are not valuing what it is they have learned. Neither bodes well for a future in which mathematics plays a significant role. The vast hordes of mathophobes and math avoiders abroad in our land didn't get that way because they were feeling good about math. Stanislaw Dehaene, who has studied math cognition extensively, is convinced that children of equal abilities may become excellent or hopeless at mathematics depending on their love or hatred of the subject.

One can slog one's way through a math class, get a passing grade and not enjoy it at all. But it's questionable whether one has accomplished anything beyond meeting a math requirement. It's also true that one can have a lot of fun in math class and not learn anything. But that's not the point. The point is that feeling good about math is—in mathematical parlance—a necessary, but not sufficient condition, that effective learning is taking place. It's a consequence of learning and not a guarantee for learning. Rather than fretting about programs that seek to make math fun, one ought to be concerned about mathematics classrooms in which nobody is having any fun.

For many folk, learning math requires diligence, but it doesn't have to be drudgery. Enjoying what one's doing, doesn't mean one isn't working hard. The more students find pleasure and satisfaction in their learning, the more industrious and successful they become. Thus, the classroom environment ought to be conducive to having fun. While I know of no way to create a setting which guarantees fun for everyone—what's fun is a subjective matter—one can provide a setting which doesn't preclude it.

A first step is to remember that students are human beings and not calculating machines. Human beings have an innate intuition for numbers and space; they are capable of introspection, relish creativity and have emotions which are linked to all that befalls them. Instruction that builds and informs students' intuitive knowledge, connects with and extends their existing understanding, allows them to exercise their creativity, and provides interesting problems for their consideration, has a much greater chance of leading to a pleasurable—and, in the long run, more productive—learning experience than any amount of drill on facts and procedures learned by rote. Despite his colleague's skepticism, Feynman continued working on his wobbles. One thing led to another and before long he was involved in his prize-winning work on the motion of elementary particles. "ƒthe whole business I got the Nobel Prize for," Feynman reports, "came from that piddling around with the wobbling plate." Just for the fun of it.