What age group are you teaching to? This will change what you have to learn.
Since I assume you'll have only classroom-level control at best, a literature search will have to be a bit selective.
A textbook might be useful... but resources for further teacher training might also work. Here and here look useful and well-sourced.
I don't have my hand in an actual classroom, unless you count the college courses I've written supporting software for. And I don't expect to: from the reports I've gotten from those teachers I admire, the sheer bureaucracy would drive me mad. Political change is slow and frustrating, and I wouldn't even know where to try to drive it.
Instead, I aim to make compelling games that effectively teach these high-level skills, whether those games are straight-up video games, or carefully-constructed ARGs, or board games, or whatever odd mashup of these is require...
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?