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[Phys-L] initial exposure +- long-delayed mastery



Amusing anecdote: When I was in school, people tried
real hard to teach me about Fourier transforms. They
tried several times over the years, but it didn't work.
A few years later, when I actually had a need for the
technique, the best I can say is that I knew it existed,
so I could teach it to myself, with help from books and
colleagues ... and with the help of seemingly-unrelated
skills I had picked up in the meantime.

This could be considered an extreme example of the
/spiral approach/.

There are dozens and dozens of topics in the same category,
namely topics I was "exposed to" in school but didn't
understand until much later. In each case, when the need
arose, I was able to teach the topic to myself and/or ask
some smart person to explain it to me.

So far so good.

This gets tricky if you want to write a standard. There
are a lot of "hard topics" that are only marginally age-
appropriate but nevertheless ought to get mentioned.

This is a problem if the standard fails to distinguish
between stuff that requires initial exposure and stuff
that requires mastery.

This is bad news if some hamfisted bureaucrats put themselves
in charge of interpreting the standard.

It is particularly bad if they think everything on the
standard ought to be "measurable". How could they possibly
measure something by means of a multiple-guess test, on
the order of one minute per question, closed book, when
the thing that should be measured is the ability to wait
five years and then spend 10 hours figuring something out,
open book?

See also next message.