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Topic:  More on Drill and Kill, practice and learning 
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Subject:  RE: More on Drill and Kill, practice and learning 
Author:  Mathman 
Date:  Jan 17 2005 
>Practice is essential,
> but for math it isn't enough.
Not trying to be argumentative, or picky here ...I never said it was "enough" in
and of itself. Of course it's not. But it IS essential. What I mean is that if
we use the analogy of a person walking through the woods trying to understand
the woods, they will learn more by turning over ALL the rocks ...well, at least
a decent number. Also, I don't mean they should spend inordinate time just
turning over rocks. What is missing today is a comparative amount of time spent
doing any turning at all. Trigonometry here is an appendix in the graduating
year. We [a long time back] spent an entire year in the study, in much more
detail. Some spend just a few days on an essential part of the study. Many
good students have a good deal of skill, but no practice into problems requiring
the least bit of insight or variation from the simplest path. As a very simple
example, the student I might have mentioned could not start a problem because
she couldn't see that x^12 + 14x^6 + 49 was a "trinomial" that could be
factored. She had seen problems involving only x, or perhaps just a one or two
variations. She had not spent any reasonable amount of time doing entire
sections dedicated to such many and varied problems. That is what I mean when I
say "practice", or, if you wish, "drill". I do recall the day when there was
time for that, as well as time to examine more interesting problems and
situations ...not quite competition level, but certainly more intriguing. There
has to be time for all to satisfy all interests.
David.
 
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