But schools are not about education. Seriously, if you're looking for examples of people actually teaching other people things that they need to know for an important reason, I don't think compulsory schooling is the place to look.
Having said that, I feel like I should be willing to offer some recommendations about what I think is the right place to look, but as I'm only just about to leave the education system, I don't really think I'm in any place to do so convincingly. Perhaps people who run some form of apprenticeship?
I want to learn what's well-understood about education. I expect to launch myself into some endeavors in teaching the first few levels of epistemic and instrumental rationality - ie., critical thinking and problem solving. I'm a little suspicious, though, of the scattered educational texts that I've so far read. In particular, education seems like a field where it's easy to have motivated thoughts, and hard to gather good data.
With my background (Math and CS) I'm a little at sea in educational literature. Does anyone know of good, reductionist-grade or evidential-grade, introductory texts in education?