[geeks] Education

[der Mouse]

>> But even a student knows when they have mastered a particular
>> excersize, and repeating it doesn't help.

Unfortunately, neither part of this is "true".

Students regularly *are* wrong about whether they have mastered things,
and repetition *does* help make sure they really have.

I'm perfectly willing to believe that you are an exception for the
subjects you were writing about.  I'm an exception in some cases too.
But I am *not* an exception in most cases, and neither are most
students.

I'd be the last person to defend your schools for attempting to teach
you stuff you already knew long before in ways that were stultifyingly
boring to you.  I suffered through two half-school-years of
increasingly frequent strep throats for exactly the same reason, in a
day when there *weren't* gifted-&-talented programs.

But I've also done a little teaching, and watched a lot of learning
(including my own), enough to know that students *are* mistaken and
repetition *does* help.  In general.  I wouldn't trust a random
student's estimation of having mastered something unless said student
were already learning at least one level past it, preferably two.  And
repetition - about the only time I've seen when repetition *isn't*
helpful is when there's a lightbulb moment such as the ones we've seen
mentioned here, when all of a sudden something connects and starts
making sense.  Even techniques such as, oh, say, converting a/b w c/d
into a/b W d/c and thence to ad/bc, even things like that need to be
practiced until they become automatic.  To this day I have to re-derive
(or look up) the formula for, eg, sin(a+b) when I need it because I've
never practiced it enough.

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