Math is hard, Barbie, and that goes for you too, Ken. It’s hard like tennis or basketball or baseball, requiring hours of hard work on basic skills when you really have little clue how those skills will really be used. When you have the basic skills of arithmetic or of fielding and throwing the ball, then you learn how to handle symbols in a manner analogous to numbers or you learn how to turn the corner at second-base or how to position yourself for the rebound.
There are many in these United States of American who put in many an hour of practice duffing away before approaching a round of golf at par. There are many who teach their children of the need to work at those skills of skating and slapping away at pucks. There are even some, slightly old-fashioned, who see that Junior practices his latest chord before heading to his next guitar lesson and see that Missie hammers away at the animal-friendly plastic keys on her electronic musical device each every day.
We leave mathematics to the professionals and the best of parents will rarely do more than make sure Junior is getting good grades on his exams and Missie is doing her homework. We leave it to those professionals to set the standards, to decide what Junior should be learning as a freshman and Missie as a junior. My own experience, even during a slightly better period in American education, taught me — eventually — that we’re leaving some important issues to the care of some who themselves never aspired beyond the duffer stage, beyond the stage of banging out Chopsticks. This article tells us my experience might be typical for American students. There are countries which do better: Countries That Best Prepare Math Teachers Share Similarities: Several Key Conditions Generally Lacking in US.
The article tells us:
Countries that best prepare math teachers meet several key conditions generally lacking in the United States, according to the first international study of what teacher preparation programs are able to accomplish.
The IEA study, led by Michigan State University, suggests that in countries such as Taiwan and Singapore, future math teachers are better prepared because the students get rigorous math instruction in high school; university teacher-preparation programs are highly selective and demanding; and the teaching profession is attractive, with excellent pay, benefits and job security.
The key word is `rigorous’. Math is hard, but — as I’ve noted before — so are any subjects when approached properly. Rigorous is painful for a people trained to be the passive victims of canned entertainment or to consider work to be something which can be done according to a short checklist developed by some bureaucracy.
Our English departments in the American school systems aren’t in much better shape than our mathematics departments, perhaps a little better just because we’re generally born with more language skills than mathematics skills and a highly motivated man or woman will find it easier to acquire higher level skills in the nature of composition and textual analysis just by frequenting their local library or the college library even if their formal education was weak. However, just as a talented teenaged furniture maker needs to learn higher levels of skills and discipline from a master, a lover of language also needs to learn from a master to be a truly skilled and self-aware practitioner, at least at a level adequate to serious teaching — we will, of course, always need a lot of teachers who concentrate on rudimentary skills but that sort of teaching can work only if teachers of all levels of skill have a good respect for rigor and are in a system and a culture which also has that good respect.
It’s easier to motivate ourselves in fields where we generally start out with some decent level of talent. We can almost all throw a rock at a target or a ball in the direction of our father as he teaches us some athletic skills. Some of us, certainly not me, have enough coordination of limbs and of eye-hand movements to be able to advance so quickly that learning to play ball can be fun for years of development rather than a chore. Any serious athlete will tell you that even the great ones reach the point where they have to participate in special strength and skill exercises to continue to advance or to maintain very high levels of skill.
In a similar vein, many of us can more or less naturally acquire enough visual skills and enough oral language skills to become at least somewhat literate. Some have great facility with various aspects of language so that learning to recite poetry or write simple poetry or learning how to read serious narrative works is fun for many years of development. Then comes the day when you have to struggle to wrap your mind around the book of Genesis or a poem by Shakespeare or the writings of Thomas Jefferson. Back to the practice field.
One of the problems with mathematics is that there aren’t that many who naturally develop any serious skills and I learned, by experience and years of contemplation upon experience, that most educational systems — certainly the one in my hometown — have not the slightest clue how to nurture even a raw talent such as I had, high-level but not at the level of a truly creative research mathematician. I would have probably become a physicist or engineer but for learning how to hate college after going there poorly prepared in habits and attitude — I’d been able to stay even more securely in my comfort zone than most and went to college as a couch potato of sorts. When I, as a boy, had needed to learn how to work, how to learn and think rigorously, I had been encouraged by the educational system, as well as American culture in general, to stay within my comfort zone, to sit and get good grades by sleeping through class and then browsing the material in study-hall.