This is a great article on the failures of K-12 mathematics education. Descartes would be ashamed.
The thought process so essential to math has been all but eradicated in school. We are taught not to think philosophically (math is philosophical!); but to take in formula after formula, and find new way to spit them out through exercises and word problems. I especially enjoyed the section on proofs- the bane of all geometry students' existence! They create an illusion of the process that goes into thinking mathematically, but are really something else entirely. Geometry proofs once again involve the memorization of removed postulates, and finding inaccessible and uninteresting ways to "solve a problem".
What is sad is that we are all asked to wait eleven or twelve years to find out if we are ready to think mathematically. We can not be trusted with our innate ability to reason until we have taken in numerous rules and formulas that we have no understanding of.
