Earlier quoted context omitted.
> You come across patterns like that by doing the tedious work the hard way and looking for short-cuts. The thing is that you come across short-cuts like those on the larger and broader concepts as well. Tinkering around with numbers is great, but perhaps tinkering around with concepts is even better. There would be downsides to the reform. Students may not know that notice 9x = 10x - x as a calculation shortcut, but…
Maybe we're talking past each other. Could you explain your goals with this curriculum? Are you trying to reduce the teaching of mathematics to a bare minimum so people can get on with what you see as more essential subjects? My stance is that mathematics is first of all useful in the small for normal people. Everyday arithmetic, basic accounting, that sort of thing. But beyond that we need to teach mathematics for t…
Perhaps like art and music, we should only be teaching beyond the very basics to those who actively seek it out. We don't require all highshool students to learn how to play the piano, read music, or draw nudes, so why should they all learn how to invert a matrix or find its determinant by hand?