There are individual rationality techniques (game theory, Bayes...), and then there is the "spirit of putting this all together and using it to win at everything".

The techniques are individually taught at many universities, and described in many books. For example, as a student of computer science, I had an introduction to probability. There is probably a great lesson for every piece of that; often many great lessons.

Putting it all together is the tricky part. Less Wrong is not literally unique -- the General Semantics movement attempted a similar goal -- but it is very rare. These attempts have no institutional support other than the one they build for themselves.

What resources are there out there to educate people about ideas in rationality?

I think it would be possible to create a curriculum containing all ideas from the Sequences, without using anything produced by the Less Wrong community -- only the existing books and university courses.

(Arguably, this might be a useful thing for people who have some aversion against Less Wrong, e.g. because it seems cultish to them. But then the problem would return on a meta level: why should they spend their time studying this curriculum, as opposed to anything else?)

But the call to put it all together and actually use it in real life to win? Other than General Semantics, I have no idea.

What attempts/barriers are there to introducing more ideas about rationality to school curricula?

Many of the techniques (probability, Bayes...) are mathematical in nature. Teaching math well is... already a known problem, and people are looking for a solution. Once it seemed like the problem was getting the knowledge to the kids, then we had Khan Academy, and now the problem is making the kids actually want to look at the knowledge.

School time is limited, and people have competing opinions on how it should be used, so it is a political problem. We might want more rationality, someone else may want more... something else.

Or, are my premises flawed and is there not a strong case to invest in the provision of rationality education more widely?

A potentially wrong premise might be that people get education from the educational system. I mean, if you put it this way, then of course, school teaches you stuff. But if we look at people who are very good at something, I would not be surprised to find out that the thing that made them "very good" as opposed to "mediocre" was something unrelated to the official education -- parents, friends, tutoring, reading books and experimenting in their free time.

In the same way, I guess the school system already teaches "mediocre rationality". We do not respect it, because it is everywhere around us so we take it for granted -- perhaps we would need to spend some time in a country where people still believe in witches, to appreciate it. And a few people learn "very good rationality" outside the system.