It's Not Just Writing: Math Needs a Revolution, Too

It is extremely true that mathematics curricula for schoolchildren in general require reform, and most mathematicians will agree on this point. The problem with previous attempts is that they have been designed by people who do not fully understand mathematics and executed by the same. The by now infamous example of the "New Math" was satirized by popular culture because everyone seemed to miss the point. http://en.wikipedia.org/wiki/New_Math

While pieces like the well-circulated "A Mathematician's Lament" (PDF: http://www.maa.org/devlin/lockhartslament.pdf) by Paul Lockhart argue that the mathematics taught to schoolchildren ought to resemble "real math", the sort of math that mathematicians think of as math (with theorems and proofs and much less of an emphasis on computation), they neglect the unfortunate reality that compulsory childhood education still exists largely towards a pragmatic end. Children must be able to compare prices at the grocery store and be able to reason about quantities.

Hung-Hsi Wu has done a great deal of work into how to fix the mathematics curricula of today. This is in contrast to the revolutionary approach that we have tried and failed at. His work focuses largely on fixing specific weaknesses in the core standards and fixing the way mathematics is taught, rather than what is actually being taught, in many cases. http://math.berkeley.edu/~wu/

In addition, Pólya's How To Solve It is the sort of text that teachers should read and become familiar with, in order to better understand how to teach problem solving, which is much of what mathematics at the grade school level is - instruction in problem solving. In fact, I would recommend it to every HN member - it's a wonderful little book about the art of solving problems, mathematical or otherwise. http://press.princeton.edu/titles/669.html