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[MATHEDU] More from my engineer student
Posted:
Feb 22, 2001 6:56 PM
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Here is more from the same student:
My [8th grade] teacher clearly stated that if
we didn't understand the proof, we had no business using the formula. I've
seen that attitude repeated many times by many math teachers. The attitude
is clearly endemic among mathematicians . And it comes across as
arrogance to outsiders.
Ironically, the intent is to free the student. It's a gift. "See, you
don't have to trust me, you can know for yourself." But when the gift is
refused with "I already trust you and have no need to know for myself,"
there is resentment and even hurt feelings.
I place the blame on teachers because they are to build the bridge of
understanding with the student. The student is facing the subject for the
first time. The teacher, however, has taught the subject many times to many
students. It is not for the student to understand the teacher's motives,
but rather the converse.
Besides inductive reasoning, I'd like to briefly cover three more paths to
truth.
"Test of Time". I knew that the quadratic formula was used for a long time.
(I've since learned that versions of the formula were used as early as 2000
B.C. in ancient Babylon.) As a learning 8th grader, am I really going to
find something wrong with it? If it ain't broke, don't fix it.
"Test of Authority". She has a degree; the school employs her; the book
looks important; she acts like she knows this subject. I certainly don't.
"Test of Consistency". My teacher never steered me wrong before. The
formula doesn't disagree with anything else.
Besides, math has its axioms that aren't proven.
We all have to start with some assumptions.
Now let me reverse myself and explain how useful those proofs have been.
1) Going through the "proving process" has changed my life. Deductive
reasoning is the basis of my profession. I'm certainly ahead of many of my
peers because, for instance, I still remember and apply DeMorgan's laws in
reducing predicates. I honestly don't care about "your" proofs, but they
sure helped me do mine.
2) I felt confidence knowing that a proof existed. Indeed, THE major reason
for proofs is confidence (although the point of gaining further insights
is not lost.) IMHO, this is the crux of the matter. We're back to that
emotional element. If I do the proof, then I get confidence. If I know a
proof exists, then I get confidence. Since I get the same desired result
either way, I choose the instant way. I'm not being lazy; I'm saving time.
Instead, my teacher forces me through the proof only to arrive at the same
destination. It's like arriving home only to find a cop in your driveway
telling you to drive around the block before parking so you'll really know
you're home. The end result is the same, but you feel resentful at the
extra work.
There. The teacher is resentful. The student is resentful. And it doesn't
have to be that way.
--
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Jerry Uhl juhl@cm.math.uiuc.edu
Professor of Mathematics, University of Illinois at Urbana-Champaign
Member, Mathematical Sciences Education Board of National Research Council
Calculus&Mathematica, Vector Calculus&Mathematica,
DiffEq&Mathematica, Matrices,Geometry&Mathematica, NetMath
http://www-cm.math.uiuc.edu , http://netmath.math.uiuc.edu, and
http://matheverywhere.com
"Is it life, I ask, is it even prudence,
To bore thyself and bore the students?"
. . . Johann Wolfgang von Goethe
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