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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 16 2005
Way too much to include the quote, so I'll talk about something related
...although it impacts also heavily on my own generally successful methods of
teaching high school mathematics [I'm now retired.]  Just one point on
generalisation:  It is wrong to say "children" in any sort of generalised
statement.  They are all different, and will remain so, hopefully.  If some do
poorly under certain circumstances, so will others when those circumstances

On "drill and kill": There's no such thing; there is "practice", of one sort or
another.  I play the piano, and have played most of the classics, even some
quite "difficult" [La Campanella, Chopin's waltzes, Blumenfeld's etude for the
left hand, Rustle of Spring ....].  At a party recently, I was entertaining, and
heard a parent say to his daughter, "See.  You have to practice every day."  I
disagreed.  I practiced every day because I wanted to practice every day.  God
knows how I knew at a tender age, but somehow I had faith in that teacher who
knew something while I knew nothing.  So I practiced, and informed the parent
that pushing someone to practice what they don't want to do is quite wrong.  I
"held my hands correctly", I slogged through [not the right expression really,
since it required careful concentration on each finger] all of my scales,
chromatics, chords, variations, chromatics, major and minor ...ALL of them.  I
practiced two hours a day from age 9.  Entering two major competitions each
year, I would practice at times just two or three bars of the piece at hand,
joining them as time went on into longer stretches to finally complete the
piece.  There is a world of difference between playing and practicing.  If you
can't play a pice slowly, then you can't properly play it quickly.  People
hammer through a fast piece, and miss half of it and perhaps all of the
subtelty.  Those not paying close attention to detail miss the musicality of
more complex pieces.

My teacher was, well, STRICT!  ...and we all, each and every student, loved her.
She is long dead, and I still have the utmost respect and gratitude for what she
did for me.  It shows ...every single day.  Once you don't have to pay attention
to the technique, you can pay attention to the music.

Now?  I'm way too old for that sort of thing, but now, when I play, I still do
it with relative ease, reading music like you might read a book.  I don't have
to think about where my fingers fall.  A glance at the music and not only do
they fall into place, but automatically are ready for the next group of notes,
and I'm here to tell you I can't play any more; not like it should be played.
And that's the entire point of it....

Students meeting me for the first time have wondered what was going on, but one
summarised it, "Sir, at first, I hated your guts, but now I think you are the
best math teacher I ever had."  No, he wasn't sucking up, for he'd already
succeeded.  I had made him slog through his fundamentals, and surprise! he had
learned something useful.  However, there was always room for more.  I didn't
play just scales and arpheggios, and he met the challenges given later ...after
showing some mastery of the fundamentals, and not before.  Lately tutoring a
student in calculus who already has 90% average, I saw that student falter on
something that should have been learned in grade 10.  The problem was that it
was a variation on what she did know, but because she had not gone through the
exercises for such, she simply did not recognise it.  Had she, she would have
been able to handle it easily.  It was not the first time.

When a student is learning to swim, it is necessary to first practice in the
shallow end, and it's not nearly as exciting as being first to the raft.  Those
who don't want to practice will not swim nearly as well on the whole as those
who do. Those who do will be first to the raft.


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