Public schools (and arguably private schools as well; I wouldn't know) teach students what to think, not how to think.
On LessWrong, this insight is so trivial not to bear repeating. Unfortunately, I think many people have adopted it as an immutable fact about the world that will be corrected post-Singularity, rather than a totally unacceptable state of affairs which we should be doing something about now. The consensus seems to be that a class teaching the basic principles of thinking would be a huge step towards raising the sanity waterline, but that it will never happen. Well, my school has one. It's called Theory of Knowledge, and it's offered at 2,307 schools worldwide as part of the IB Diploma Program.
The IB Diploma, for those of you who haven't heard of it, is a internationally recognized high school program. It requires students to pass tests in 6 subject areas, jump through a number of other hoops, and take an additional class called Theory of Knowledge.
For the record, I'm not convinced the IB Diploma Program is a good thing. It doesn't really solve any of the problems with public schools, it shares the frustrating focus on standardized testing and password-guessing instead of real learning, etc. But I think Theory of Knowledge is a huge opportunity to spread the ideas of rationality.
What kinds of people sign up for the IB Diploma? It is considered more rigorous than A-levels in Britain, and dramatically more rigorous than standard classes in the United States (I would consider it approximately equal to taking 5 or 6 AP classes a year). Most kids engaged in this program are intelligent, motivated and interested in the world around them. They seem, (through my informal survey method of talking to lots of them) to have a higher click factor than average.
The problem is that currently, Theory of Knowledge is a waste of time. There isn't much in the way of standards for a curriculum, and in the entire last semester we covered less content than I learn from any given top-level LessWrong post. We debated the nature of truth for 4 months; most people do not come up with interesting answers to this on their own initiative, so the conversation went in circles around "There's no such thing as truth!" "Now, that's just stupid." the whole time. When I mention LessWrong to my friends, I generally explain it as "What ToK would be like, if ToK was actually good."
At my school, we regularly have speakers come in and discuss various topics during ToK, mostly because the regular instructor doesn't have any idea what to say. The only qualifications seem to be a pulse and some knowledge of English (we've had presenters who aren't fluent). If LessWrong posters wanted to call up the IB school nearest you and offer to present on rationality, I'm almost certain people would agree. This seems like a good opportunity to practice speaking/presenting in a low-stakes situation, and a great way to expose smart, motivated kids to rationality.
I think a good presentation would focus on the meaning of evidence, what we mean by "rationality", and making beliefs pay rent, all topics we've touched on without saying anything meaningful. We've also discussed Popper's falsificationism, and about half your audience will already be familiar with Bayes' theorem through statistics classes but not as a model of inductive reasoning in general.
If you'd be interested in this but don't know where to start in terms of preparing a presentation, Liron's presentation "You Are A Brain" seems like a good place to start. Designing a presentation along these lines might also be a good activity for a meetup group.