Friedman: Invent, Invent, Invent
nytimes.com
nytimes.com
All this yak about raising the education standard in the USA, when we've got Ph.D.'s in unemployment lines is disheartening. Retraining is the greatest joke. If you're an unemployed IT worker, what is the "next tier up" on the ladder to success? Material physics, which requires 5 years study to get online?
Economics and economists have some credibility in microeconomics, but outside that limited subject they are herd-oriented and usually wrong, wrong, wrong. Ask Nicholas Taleb what he thinks about the economics profession. Hell, look out the window and remember what economists have told you about the economy over the last 20 years. Were their predictions ever better than a crapshoot?
It seems like there might be a good idea there. But of course Friedman is just talking about making sure everyone suffers through algebra II even if they learn nothing from it.
There's an article here about them:
http://www.spiegel.de/international/0,1518,416564,00.html
I found it to be just plain weird.
This would help a lot. I find I can reliably challenge most advanced math students in the United States just by serving them problems from grade-level standard curriculum textbooks from Singapore. For my best students, I have to turn to problems adapted from "key" school textbooks from China.
If it's not asking too much, can you give some examples? Are these contest-style problems, or computational problems?
http://www.singaporemath.com/Placement_Test_s/86.htm
give some idea of problem types at different grade levels. They are not exhaustive, of course, as the distributor of the books doesn't want to give away all their content for free online.
"A bell rings every 25 minutes while another bell rings every 40 minutes. Suppose they rang together at 6 a.m., when will they ring together again?"
Very cute. Do you find that students prefer such problems to the normal "plug and chug" type? (Also, when you say "advanced math students", what age are you talking about?)
Most of the questions I saw were just annoyances dealing with fractional/decimal arithmetic. There were some interesting word/figure problems, but the difficulty in those usually lay in doing the arithmetic by hand.
Same request as the friendly request above to which I responded: what resources would you suggest for examples of "actual math" appropriate for elementary-age students.
I use a great variety of problem sources, published in both English and Chinese, to teach various learners of elementary math supplementary lessons, which is my current occupation. But one can never have too many sources of problems, so what sources do you suggest? There's no "ceiling" of difficulty level, because I have early-elementary-age students who are already well along in secondary-level math, so I have to keep looking for more challenging material all the time for my most advanced students.
Basically, I tried to relate the math to solving a real problem they might be interested. Limits to money problems (e.g., could you retire on a Million dollars? Now take into account inflation, interest, etc)., differentials to sports/computer-games (plot the trajectory of the ball), random riddles, etc.
I'm not really sure how well that would translate to younger kids though ... My elementary school aged nephews/nieces tend to enjoy geometry problems (find the pattern ...), 'shortcuts' (FOIL, etc), and morphisms, but I fear my experience with kids that young is too limited to draw any general conclusions.
http://www.artofproblemsolving.com/
http://www.amazon.com/Art-Craft-Problem-Solving/dp/047113571...
I wish I had access to people who were really good at problem solving when I was in my pre-university days. The intention is not to really become an ace problem solver, but to give the brain a real good workout.
If you wanted to graduate this year, this is the problem you had to solve: http://www.maths-express.com/bacs/2009/FranceSjuin2009.pdf (in PDF, easy to read).
(even if you don't speak the language, it's math, so you can probably figure out what the questions are, the formulas themselves are universal)
I still wouldn't expect the Americans to come out on top but the distinction might be less than you think. I remember in school that word problems tended to be written very stereotypically for any given book or curriculum, and students who just barely managed to learn how to do that stereotypical set might have a lot of trouble doing problems from a different "word problem tradition" (if I may coin the phrase). You might find more Singapore students have trouble doing the American problems than you expect, even though as I said I'd still expect the Singapore students to come out on top in general.
My two older children have lived in both Taiwan and the United States, as my wife and I have at various stages of life.
- All SBA loans should come with free lifetime supplies of Provigil
- We should send our kids to Singapore to learn math and physics
- Earlier specialization
Also, judging from the admissions behavior of top PhD programs in quantitative subjects (and assuming they know what they're doing), high performance in math competitions is a good indicator of both critical thought and creativity.
(Also, I hope it was clear that my list was being a bit ironic...)
I didn't really say critical thought and creativity are the same thing but yeah, I shouldn't have lumped them together. From my experience, critical thought is much more common here than creativity but even that is not applied to anything outside quantitative subjects, such as politics or philosophy.
P.S. There are many creative, smart people here but they are creative because they are creative not because of the school system. What happens to these people later in life? Why don't they found companies? I suspect the answer here is because of the Singaporean mentality where entrepreneurship isn't valued as much as a stable job. But even more that, it's because these people are often given scholarships to study overseas. These scholarships have bonds where you have to work for the company (in most cases, the government) for 5/6 years. By the time they get out of their bond, there are already ~30 or older, have a family and can't bothered to switch/start companies.
In fact, it is sufficient for it to be perceived that it limits your top-end gain, even if it doesn't, and I think that I confidently say that such a perception exists in many people's minds, even though I could not say a word about SarbOx's true effects.
Hmm, make something people want. I heard that somewhere else too.
3) lower the corporate tax rate
Government funding of scientific research is the problem. About two thirds of scientists make their living off the government, directly or indirectly. We need less of that, not more. Scientists need to stop making ultimately useless death machines for the DOD and other government agencies and they need to start working on technologies for the free market. Eliminating DARPA and throwing all the scientists who depend on it out of work would be a good start. They'd be forced to come up with business ideas.
The problem with health care in America isn't that too many aren't "covered," it's that too many can't afford medicines and procedures because they're too expensive. Costs and prices need to be driven down. That would happen right away if you eliminated the tax deductibility of health care benefits. (Maybe give an offsetting tax credit to make it political palatable.) Millions of people would opt out of their employer provided plans and go comparison shopping for much cheaper high deductible plans so they could pocket the savings. This consumer driven pressure would force insurance prices down dramatically. The high deductibles of these cheap plans would have people comparison shopping for the cheapest medical services, which they basically don't do now. This would drive down prices dramatically.
Put the bankers in check, put the media conglomerates in check, put the politicians in jail and put everybody else to work.