Why Johnny Can’t Add Without a Calculator

The section regarding textbooks and the conflicting agencas of the teachers (use what is good and what works) and the principals (use the new shiny ones) reminded me of Richard Feynman's stint on a textbook selection committee: http://www.textbookleague.org/103feyn.htm

Compare this from the article:

  "[T]he standard geometry book for Fairfax County, which is 
  used in schools around the country, tries to explain what 
  a mathematical point is by analogy to pixels on TV 
  screens, which are not in fact point-like."

With This:

  "[T]he books were so lousy. They were false. They were 
  hurried. They would try to be rigorous, but they would use 
  examples (like automobiles in the street for "sets") which 
  were almost OK, but in which there were always some 
  subtleties."

Feyman continues:

  "The definitions weren't accurate. Everything was a little 
  bit ambiguous -- they weren't smart enough to understand 
  what was meant by "rigor." They were faking it. They were 
  teaching something they didn't understand, and which was, 
  in fact, useless, at that time, for the child."

The thing I learned about learning math is that you have to do a lot of problems. That's it. That's the trick.

Also, It's helpful to read a lot of different explanations/developments of a concept until I find one that makes sense.