Reformists, pay attention
I strongly believe that in a few years the thrust of an education reform will converge on the web. The process has begun even if not yet sunctioned by powers that be at the US Congress. The best universities put up their courses online, see, for example, a New York Times article.
The general accesibility of the web and the induced healthy competition between various online sources will necessarily make the education incomparably less coercive. The eventual result will justify the foresight of such pioneers of math education as Louis P. Benezet and Harold P. Fawcett.
Informal development of critical thinking skills will precede formal instruction as I believe it should. Mathematics will be taught as a useful toolset or for its own sake, as a beautiful, cultural subject. The idea that the study of geometry or algebra is a vehicle for brain development has never been proved and is most certainly incorrect. Thinking skills may be and are being successfully taught independent of any math instruction; at the same time more mature minds have less difficulty grasping formal concepts and a better chance of enjoying the latter.
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