Although such a correlation is undoubtedly not huge, there is almost surely a noticeably positive correlation between a country's training of the most talented young mathematicians and the math education provided in the country as a whole. Such a correlation need not hold in every country, of course, but just if you could fairly measure both variables in a large number of countries with one 2D data point for each country — say those that belong to the U.N., just to have a concrete. I also doubt that the correlation that I suspect exists is teeny, either. If I had to guess, I'd put it somewhere between 30% and 60%. —Dan P.S. We could estimate the correlation from a) IMO results and from b) widespread international standardized test results.
On Feb 9, 2016, at 5:19 PM, Adam P. Goucher <apgoucher@gmx.com> wrote:
From my experience, there is little or no correlation between the quality of education [as provided to the country as a whole] and that of the training delivered to prospective competitors in mathematical olympiads (which tends to be considerably better, at least in the UK, since skilled volunteers devote their time to helping the next generation). This is actually very fortunate, since it means that the best young mathematicians are able to thrive irrespective of the ineptitude of their schoolteachers.
Sent: Wednesday, February 10, 2016 at 12:56 AM From: "Henry Baker" <hbaker1@pipeline.com>
FYI --
http://science.slashdot.org/story/16/02/09/149224/an-advanced-math-education...
The Atlantic has an extended article on the recent surge in advanced math education at the primary and secondary levels in the U.S., arguing that last year's victory for the U.S. in the Math Olympiad was not a random anomaly.
Participation in math camps, after-school or weekend math "academies," and math competitions has surged in recent years, with many programs having long wait lists.
Inessa Rifkin, co-founder of one of these math academies, argues that the problems with math education begin in the 2nd and 3rd grades: ""The youngest ones, very naturally, their minds see math differently.... It is common that they can ask simple questions and then, in the next minute, a very complicated one. But if the teacher doesn't know enough mathematics, she will answer the simple question and shut down the other, more difficult one."
These alternative math programs put a greater focus on problem-solving: "Unlike most math classes, where teachers struggle to impart knowledge to studentswho must passively absorb it and then regurgitate it on a testproblem-solving classes demand that the pupils execute the cognitive bench press: investigating, conjecturing, predicting, analyzing, and finally verifying their own mathematical strategy. The point is not to accurately execute algorithms, although there is, of course, a right answer... Truly thinking the problem throughcreatively applying what you know about math and puzzling out possible solutionsis more important."
http://www.theatlantic.com/magazine/archive/2016/03/the-math-revolution/4268...