It seems to me that nobody teaches anybody how to think. Instead we teach people to do things that require thinking, and trust that they will develop an ability to think as a “byproduct”. Which is a bit strange to me, since there are definitely some general principles that can be taught.
I took a class psychology class on learning that was superb.
It taught how to memorize stuff: spaced repetition and semantic encoding. Spaced repetition is reviewing the thing at increasingly spaced intervals of time. Semantic encoding is coming up with connections to the idea. The wilder the better as that tends to be memorable.
The class taught some strategies for creativity such as use of analogies and trying to combine disparate ideas.
The class also taught cognitive biased, like loss aversion.
This class was life changing. It was also easy because the teacher applied the best practices she was teaching.
I would say something like that class is the basis for teaching people how to think.
Breaking a problem down into smaller problems, solving those that are immediately obvious or known from experience, for harder or new problems: gathering evidence if available, coming up with a hypothesis, testing this against the available evidence, looking for reasons why the hypothesis must be wrong and abandoning it if reasons are found, iterating on the hypothesis until an adequate one is found (adequate being provably correct, or "sounding sensible" based on solutions to similar problems). My 2c is being ok with uncertainty and being wrong, and an awareness of cognitive biases can be helpful.
Traditionally? Humanities. Those fields have the advantage of starting with common experience and a natural-language corpus, so there isn't as high a barrier to entry as STEM disciplines. But, you know... we don't do that anymore. (And yes, I know, some of the reasons are intrinsic to choices made by people within the Humanities.) We've abandoned that, but not found a better way.
