Here is a great article by V. I. Arnold on teaching mathematics.
The synopsis is that Mr. Arnold claims that mathematics should be taught as a part of the natural sciences - a tool that allows us to 'experiment' and check our hypothesis cheaply. He also argues that the abstratization that has been taking place in mathematics (mostly since second world war) only makes students more baffled and therefore more intimidated by math and therefore should be usually avoided. Here are a couple of favorite quotes from this article:
- The Arnold Principle: If a notion bears a personal name, then this name is not the name of the discoverer.
- The Berry Principle: The Arnold Principle is applicable to itself.
- "There exists yet another phenomenon which is comparable in its inconceivability with the inconceivable effectiveness of mathematics in physics noted by Wigner - this is the equally inconceivable ineffectiveness of mathematics in biology.", I.M. Gel'fand
- and “It is impossible to understand an unmotivated definition but this does not stop the criminal algebraists-axiomatisators”, V. I. Arnold