The most important thing, I think, is the fundamental lesson that you
CAN reason things out. All else is just learning tricks for doing
it. The point in "Surely You're Joking Mr. Feynman" where people
expressed surprise to the young Richard Feynman that he would
successfully fix appliances after "thinking about them". Most people
don't *try* to think things out when confronted with a novel problem
-- they just flail. The very idea of using a systematic approach is
crucial.
The biggest lesson is simply "try to think how what you are concerned
about works and then think about what the results of your actions will
be". Thats the cornerstone of all problem solving -- the seed from
which it springs. Unless you have the systematic/thinking approach in
mind to begin with, the very idea that there might be tools like logic
to help you in your thinking never even comes up.
I don't know if this can be taught, or if it can be taught, if it can
be taught past the age of three.
>From there, there appears to be a second big leap -- the leap to
understanding abstractions. By this, I mean the ability to do
"empirical" thinking -- to note that certain patterns are repeated in
different realms and abstract them out into general rules. Some people
"get" abstractions, and "get" the idea of modeling a system in terms
of them, and some people don't. I don't know if this can be taught,
either, or if it is just something you learn when you are very, very
young.
I've noticed, btw, that neither of these "core skills" seems to be
correlated with social station in an absolute way. I've met lawyers
who *could not reason*, and stone masons who were fine at inventing
solutions to problems on the fly.
Perry