What changes would you make to K-12 education?

I would make changes to the mathematics curriculum. In math education there are basically two sides – those pushing back to basics and those who want a more project and discovery approach. The discovery approach seems to be preferred mainly by educators, meaning that the general public wants the basics.

The general public is wrong. There are some interesting studies showing that a more open ended approach results in better scores on standardized tests and greater appreciation of mathematics by the students. Some students actually switch from hating math to loving it. If someone wanted to deliberately discourage people from appreciating math, they could not do much better than to copy the way it is currently taught.

Another change I would make is to give a brief introducation to non-Euclidean geometry when teaching Euclidean geometry.

Non-Euclidean geometry represented a major philosophical change in the way the Universe is perceived. It came as a major shock that there might be other geometries that describe our Universe and although Euclidean geometry works on a small scale, it is quite possible that on a large scale it does not apply. Our Universe may, for example, be something like a finite 3 dimensional surface of a 4 dimensional object.