1 My Motivation
All these ideas have been churning around in my head for years. I've finally written down this draft containing some of them. Although it is very rough, and I'm sure I've left out many obvious things, I would appreciate comments.
The curriculum I'm proposing is aimed at high school and below, although obviously some of the ideas make sense in a university setting.
Just to show that I'm not completely ignorant of the situation, here is my background: I have a B.S. in mathematics from Caltech, and a Ph. D. in mathematics from Stanford. I have taught courses in mathematics and computer science at various universities ranging from Stanford to junior colleges. I have done a great deal of volunteer tutoring of mathematics, for kids and adults who have a great deal of difficulty, and for kids who are far smarter than I am, and have competed on various United States Olympiad math teams.
I also did a post-doc at Stanford in electrical engineering and have worked in industry as a software engineer for 20 years.
2 The Problem Today
I think the problem with mathematics education at the university level in this country is that it's generally taught by and aimed at mathematicians. This trickles down to the primary and secondary schools, since the committees that determine the curricula are usually packed with university-level mathematicians.
I was trained as a professional mathematician, and in my non-mathematician, non-engineering life, I have never really needed to solve a quadratic equation either.
You would think that in careers that use mathematics heavily - for chemists, physicists, engineers, and computer scientists - at least they are learning the right stuff, but I don't think that's the case. When I took third-year physics as a junior I had to work with...