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Mastery approach, etc.

Just some observations on the whole test taking/retaking thing that's being
kicked around (and, in some cases, just kicked).

Traditional grading and testing, as far as I can tell, was really a
negative influence on my education.  I learned that I could make it through
with high grades with minimal effort.  I thought that grades _were_ the
point.

In graduate school, I still had plenty of raw understanding ability, but
didn't really know how to study, since nothing I had encountered until then
really encouraged me to dig into things and find them out for myself.

I did find in grad school that the only way I knew how to learn was to
explain things to people.  Apparently, when I explain things to other
people, my mind is willing to work really hard to find different ways of
thinking about it so that I can find a way that will work for them.
Naturally, that clarifies lots of things for me--however, I haven't been
able to convince myself that I should explain things to myself the same
way.  I think that when I am looking at it myself, I just get an almost
subconscious understanding of what is going on, and then my attention
deficit peaks.

As I noted above, this is possibly only relevant to the way I learn, but I
think that it is generally true that we don't understand things until we
explain them to people, or at least that we don't understand them as well
as we will when we do.  (Parse that one...)

In essense, I guess I'm saying that the standard "test performance = grade"
system and the accompanying "grade = course" interpretation that students
come up with fails to serve the "high acheivers" (as measured by grade) as
well as they might fail to serve those that could learn more with retaking.

It is possible that retaking (or "the masery approach"  although I agree
with whoever said that this terminology seems to have a lot of baggage
associated with it) just encourages people to slack off.  In my experience,
however, the normal system encouraged me to cruise through without really
working.  I saw no _need_ to work harder (good grade = mission
accomplished), perhaps in much the same way that a person that wasn't
acheiving in the same manner saw no _hope_ in working harder (since you
already have that one bad grade messing up your average).

I am impressed with the people that are putting effort into making the
students realize that they are responsible for getting what they can out of
a class, etc, and I am sure it takes a lot of effort.  I, for one, was very
socialized into believing that maximizing grades and minimizing my effort
was the way to go.  I wasn't doing it intentially or maliciously, really--I
just never realized that there was a reason to do it any other way.

I think this is part of the reason that Saxon (disclaimer--all I know about
Saxon is what I've overheard as people have torn at each other's flesh over
it here) appeals to some teachers.  It at least breaks kids out of the
"learn it for this test and forget it" mode.  (As I recall, one teacher
said that his students complained when he pulled out the Saxon books
because they knew that meant they had to really learn it, as opposed to
just getting it well enough to perform on a test.)  That is a worthwhile
achievement, even if all it does is show kids that there _is_ something
more than test-and-forget.  (Note that I'm not saying that Saxon is or is
not a good thing--I don't know if I could stand another round of that at
this point.)

Anyway, I guess I should get back to work, but thought I'd throw in a few
ruminations.  I understand that there is value in teaching kids that there
are times in life when they're just going to have to do it and do it right
and there's only going to be one shot at it.  But that's probably more
often the exception than the rule.  At least as far as actually doing real
mathematics is concerned, there is a lot more of "guess, wonder, discuss,
try something else, think about your general approach" than there is of "do
it now, and get it right or else."

Okay, that's really all I'm going to say.  And if you think _this_ is bad,
wait until you see my upcoming half-baked (meaning that it will be
half-baked when you see it) "How I would change mathematics education if
the school systems were foolish enough to listen to me" post.  If you're
just looking for something to flame, wait until that comes out, because it
will be an even easier target than this.

Later,

mike
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