Just perusing over an article about teaching in the Washington Post.
Most articles about teaching occurs where teaching is most desperately needed, i.e., in schools where students do poorly. It's elitist of me to say this, but people also need to care about teaching where students do well. I'll tell you why.
On the one hand, if we don't teach those who are hard to teach, we're creating a generation of Americans that are more likely to lead lives of crime, whose opinions are likely to be easily swayed, who don't look beyond the immediate gratification of what they can purchase.
To be fair, these attitudes can strike the most well educated and the most affluent. Advertising is insidious, and even as the well-educated can now buy things that show their education, utensils that show their research (Jeff Smith's enduring suggestion of the Susi Garlic Press, or high quality kitchen-aria are the purview of the rich and educated), they still buy. My parents, frugal as they are, find that if the items they own still work, they have no desire to get anything new to replace it. Thus, a redesign of a kitchen, or something to replace the gaudy 70s style wallpaper is seen as frivolous. There is many an item they have that's 20 years old or more.
Even so, education, as slow a process as there is, has value that carries on, and yet, it must be repeated generation after generation, as kids often want some easy way out, that takes less time, that offers quicker rewards.
This style of education, as laudable as it may be, is much like training those worst in basketball to play basketball. True, basketball lacks the kind of social climbing that education does, but humor me a moment, while I explain.
Imagine if we spent all our effort trying to train the worst athletes in basketball. We'd, in effect, have very few elite players. These players may still come around anyway, but I doubt, to the extent they appear today, where we can take one limitation (poverty) and use that as an excuse to teach the disadvantaged how to play basketball.
Even so, people (apparently) want to see great players, and are willing to shell the bucks to watch Senor Iverson or Senor Bryant square off against Messrs. Wade and Nash.
Similarly, when we educate, we also need to educate to the best, to make them better.
Some of this education is not education per se. It's merely giving assignments to the bright, and using a sink-or-swim philosophy to see how well they do. Our brightest minds lack the ability to educate, at least, in any conventional sense of the word. Instead, they rely on their ability to pick interesting problems and hope the best can indeed learn these lessons, however indirectly.
This method's success tends to work only on the best of the best, which is why graduate schools primarily recruit the best of the best. Those that are in the average range, not great, nor hideously awful, might do well to have inspirational teachers, but such teachers are in rare supply, especially at the college level, because teaching requires two parts: teaching and knowledge. And knowledge is a rare commodity.
The solution, which has generally been advocated, but rarely followed up on, is to get these smart folks to think about teaching. Train that keen intellect upon the problem of education. This act has benefits. The organization of knowledge in one's mind enhances that information. Thus, the adage that the one who learns most from teaching is the teacher.
The reason we should care to educate those that are already quite well educated? Because it's those at the top of the education heap that can make the biggest differences in society.
Consider a country like India, with a population soaring above a billion. The literacy rate isn't particularly high, but India is willing to educate its very best to the best of its ability. Were it to focus all its effort on educating the least able, it would be money partly wasted. That money, for a relatively peaceful country such as India, is better spent on the very top, so they can supply the brainpower.
Admittedly, such funding may lead to elitist among the educated, and eventually create a rift among the educated and not so educated, but if a country is to move into the 21st century, with its dependence on success firmly tied to technology, they must have hyper-educated citizenry, and so to educate the few so they may be the intellectual and technological leaders of today and tomorrow, as elitist as this may be, creates a situation where trickle-down may actually work.
So I applaud articles as the above that reward innovation in teaching, but I say that the innovation must come from all over, top to bottom, not just those in the greatest need of teaching, but to improve the average of the well-educated so their standards are pushed higher.
A country can only benefit if this attitude is taken.
Three opinions on theorems
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1. Think of theorem statements like an API. Some people feel intimidated by
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