Discussion:  Traffic Jam Applet tool 
Topic:  Teaching Mathematics as a Science 
Related Item:  http://mathforum.org/mathtools/tool/10/ 
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Subject:  RE: Teaching Mathematics as a Science 
Author:  gchatterjee 
Date:  Aug 25 2004 
Would it be too obvious to suggest that you "get a Grip" on yourself?
After many years of experience, it has become evident to me that one of the
greatest difficulties with the teaching of mathematics in the U.S.A. is the
presence of too many "true believers" in the superiority of one teaching method
over another.
Let's be honest with ourselves: The elementary and middle school students who
BENEFIT most from the "discovery" approach (and other similarly "enlightened"
methods) are generally the most gifted students, and therefore the ones who have
the least NEED to take extensive detours from the "rote" approach. These bright
students will discover the beauty and intricacies of mathematics on their own as
they work through challenging problems with rigor, and they are generally very
irritated by a teacher's refusal to give credit for a correct solution that is
unaccompanied by the expected magical words from the approved curricular
catechism.
The lessgifted students, on the other hand, are the ones who receive the
least BENEFIT from the circuitous "discovery" approach, and have the greatest
NEED of learning a minimal amount of basic material by "rote". Frankly, I don't
know what evidence you have to suggest that the "rote" methodsaid to have
been used for centurieshas not worked for these lessgifted students. On
the contrary, it has been my experience that younger Americans whose
mathematical education was founded on the "discovery" approach often have a very
poor understanding of basic principles.
As a telling anecdote, let me mention one experience I had working with some
very bright young attorneys on a consultation a few years ago. At one point, as
I was explaining some simple arithmetical calculations, one of the attorneys
said to me: "I see that you state a x (b/c) = (a x b)/c. How do you know that
this is true?" The other attorney immediately echoed the same sentiment,
manifesting the greatest concern that I might have taken liberties with my
mathematical manipulations. Now, while I truly appreciate the profundity of the
attorneys' question (as it tests the very foundations of arithmetical
operations), I believe that these attorneys, and society at large, would be much
better off if we all could agree that a certain minimal level of "rote" factual
knowledge is a prerequisite for human discourse (and that one shouldn't be
complacent about "discovering" simple mathematical relationships at the age of
30+).
To return to my point about "true believers," let me say that it is not my
intent to argue that no students benefit from the "discovery" approach. Rather,
I believe that perhaps 10 to 20 percent of public school students may benefit
more from this approach rather than from the "rote" approach. Therefore, just
as I would never argue for applying the "rote" approach as a
"onesizefitsall solution," I would likewise prevail upon my teaching
colleagues not to impose the "discovery" approach on a "onesizefitsall"
basis.
Please take the time to test each child individually to determine which method
is most appropriate in his/her case!
 
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