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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: tpowers
Date: Aug 9 2004
Hi Craig,

I don't really have anything to say against empirical evidence of the success of
the "discovery" method, because I'm not even a teacher myself.  But I do want to
respond to your post.  

On Aug  8 2004, Craig wrote:
>If, as tpowers claims, 97% of the population uses no
> more than 5th grade math, then we (math teachers at middle school,
> high school, and college levels) should put up our "gone fishing"
> signs.  It may well be true that, of the rote skills students learn,
> the more advanced skills (algebra or trigonometry, for instance) are
> used very rarely.  

I don't see the end of the teaching profession as necessarily consequent from a
disuse of mathematics.  I just believe that advanced mathematics should be
taught only to those students who wish to learn it.  Believe me, I am the
greatest proponent of pupil choice; I'm not at all saying that students must
follow a narrow curriculum.  But those that wish to do so should have the
option.

Craig continued:
>However, I would wager that the students in
> Alice's class already know that mathematics is SO MUCH MORE THAN
> those basic skills, just as English is so much more than spelling.

I don't agree with your analogy here, because knowledge of English beyond
spelling is useful throughout life, whereas advanced algebra and trig are not.
Also, if I comprehend correctly, the discovery method of teaching would be
analogous to teaching essay-writing without even a firm grasp of spelling.

Craig continued:
> Mathematics is a way of making sense of the world, a way of
> organizing thought, even a way of recognizing beauty.  Sure, as a
> teacher I want my students to get the skills down so they can do
> well on standardized tests, but I would be derelict if I stopped
> there.  I want to help my students learn to THINK in new and
> different ways; I want them to look at different sides of the
> question; I want them to question.  

Ah, here's the crux.  First, I don't think students should be forced to question
if they're not interested in doing it.  I have no problem with student apathy
towards mathematics: students should be doing what interests them.  Secondly, I
don't believe that the point of mathematics is to make students think; it's just
the contrary.  Mathematics is a tool for the vast majority of the population,
not a science.  Teaching mathematical creativity in a math class would be like
teaching hammer-building in a woodshop class.  Thirdly, I believe the
"discovery" method of learning does not give students any advantage in
ingenuity.  Solving difficult problems (even as homework) requiring ingenuity
would give students enough confidence to succeed. They don't need to re-invent
the wheel.

Craig continued:
> NCTM's Principles and Standards
> (2000) recognize and reinforce the idea that mathematics is not just
> content: it is also PROCESS.  

Math isn't just one process, it's two: the process of applying mathematics, and
the process of inventing it.  I believe the former is the only one that should
be required for students to learn.

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