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 7 2004 
Bethany, you said that mathematics education was becoming more and more of a
"discovery" process. That's true, but I don't think that this is uniformly
exciting. Fundamentally, we must accept that there are people who do not enjoy
mathematics especially, and for whom mathematical "discovery" is worthless,
considering that they will never need to use anything above a 5thgrade math
education in life. We must also accept that these people are the overwhelming
majority of students, probably over 97%. By stressing communication and
discovery processes, math educators are trying to make students more like
themselves: career mathematicians who are responsible for making discoveries and
communicating them to students. But, really, it's hard to make the case that
every student wants to become a math professor.
I would say that at least 85% of students will never need to use mathematics
beyond simple calculation when a calculator isn't handy. And by cutting off the
muchderided "learning by rote," we're making mathematics that much less
useful.
Of couse, it could be argued that learning by rote "stifles creativity," but
that's not really even the case. The discovery method just substitutes
activities for proofs (in my very limited experience), but it could hardly be
said that proofs are "not creative." The only thing that stifles creativity is
teaching a process without any justification and forcing students to do it over
and over. Creativity needs motivation, and a contextual void is simply
unreasonable in this situation. Also, proofs demonstrate the fundamental truth
of mathematics, whereas activities merely portray it as some sort of fuzzy
science.
Let me quote you: "The prevading philosophy of teaching and learning mathematics
is pushing us as educators in this direction, to make math more of a discovery
process than just giving students the concepts and trying to process them."
What I have been saying is that, for a majority of students, giving and
practicing the concepts is perfectly acceptable, and "discovery" is just another
temporal roadblock to success in mathematics.
You also said that this new direction of education is bringing mathematics
closer to what it really is. But what is math, really? You define it as a
"science of quantity," and I don't think there would be anyone to disagree with
you. However, were even the ancient practices of rote memorization not related
to the "science of quantity"?
I suppose as a humble peonstudent that perhaps I am founding this argument
overmuch on semantics. I assume that you meant mathematics had a lot to do with
modeling experimental results, and, in fact, I would wholeheartedly agree.
However, that does not mean the classroom should be used as a place of
scientific experimentation. Mathematics is NOT "natural philosophy," i.e.,
things like physics or biology. Much as a hammer is not part of a finished
woodwork, applied mathematics is neither a subset nor a superset of any of these
other disciplines. If mathematics be a science, it is not practiced by
practicing physics or chemistry, but by practicing the application of math to
those sciences, or to any other problems.
What I am basically saying is that we should not have students build and launch
rockets just to introduce the idea of a parabola. A better thing to do would be
to tell the students that rockets do these things, and have them come up with
the theoretical justification based on the Law of Gravitation. Applied math is
math, and we should be practicing math in math classes, not physics, chemistry,
biology, or English.
 
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