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Several years ago I discovered that my physics students in the calculus
level intro course could evaluate integrals if they were handed to them, but
they could get nowhere trying to write down an integral expression motivated
by a particular problem.
We spent weeks learning to write down integrals for electric fields due to
various charge distributions we dreamed up and I think some of the students
caught on pretty well. We used MAPLE and the numerical integration
abilities of their calculators to to evaluate them.
I had to invent all this material on my own. None of it was done in their
calculus classes and it wasn't in our physics text either. It just did the
few symmetric examples where the answer could be had in neat closed form and
avoided all others. All the exercises could be done by figuring out which
example they matched up with. So just as Lockhart says, the text led my
students to become robots instead of thinkers.
Who else is out there today trying to move things in a new direction? I'd
like to hook up with them ...
Steve Highland
Duluth MN
Quoting Paul Lockhart:
A musician wakes from a terrible nightmare. In his
dream he finds
himself in a society where music education has been made
mandatory.
³We are helping our students become more competitive in an
increasingly sound-filled world.² Educators, school systems, and the
state
are put in charge of this vital project. Studies are
commissioned,
committees are formed, and decisions are made‹ all
without the advice or
participation of a single working musician or
composer.
Since musicians
are known to set down their ideas in the form of
sheet music, these curious
black dots and lines must constitute the
³language of music.² It is
imperative that students become fluent in
this language if they are to
attain any degree of musical competence;
indeed, it would be ludicrous to
expect a child to sing a song or
play an instrument without having a
thorough grounding in music
notation and theory. Playing and listening to
music, let alone
composing an original piece, are considered very advanced
topics and
are generally put off until college, and more often graduate
school.
...
Sadly, our present system of mathematics education is
precisely this
kind of nightmare. In fact, if I had to design a mechanism
for the
express purpose of destroying a child¹s natural curiosity and love
of
pattern-making, I couldn¹t possibly do as good a job as is currently
being done‹ I simply wouldn¹t have the imagination to come up with
the kind
of senseless, soulcrushing ideas that constitute
contemporary mathematics
education.
It goes on like this for 25 pages:
http://www.maa.org/devlin/LockhartsLament.pdf
It's well worth reading. You
won't soon forget it.
Other reviewers have called the article "humorous" but
noteveryone will find it so; slapstick stops being funny if/when
you start
to identify with the guy whose kiester is gettingslapped with a stick. And
an insult hurts in direct proportionto its accuracy.
Background on the
article and the author:http://www.maa.org/devlin/devlin_03_08.html
I'm
surprised Lockhart hasn't yet been arrested and charged withcorrupting the
youth of Athens.
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PhysicsPhys-l@carnot.physics.buffalo.edu
Educators
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_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l