Date: Apr 20, 1995 10:59 AM
Author: Michelle Manes
Subject: Re[2]: where's the math? so? (was Re: 5th Grade Activity)


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Subject: Re: where's the math? so? (was Re: 5th Grade Activity)
From: Janet V Smith <jansmit@cello.gina.calstate.edu> at internet
Date: 4/19/95 8:22 PM


>Cathy, I found your post very interesting, and quite stimulating. I am
>not at all sure I have the answer, but I have a couple gut level reactions.
>One, I do not think our students manipilate objects in space enough to
>develop spatial reasoning, flexagons does increase interest in this area.
>Second, I think we need to really look at what is important to teach. Is
>the algebra, geometry, algebra route really appropriate today? When will
>our students learn all the new math that has evolved since world war II?
>I think their future will require a lot more discrete math, and a lot
>less of the traditional curriculum. As fast as technology is changing, we
>need to quit teaching studetns for our future and start addressing
>theirs. I realize your question was not delving this deep, but it did
>stimulate me to think, thank you
>
>Janet Smith


Hi Janet. You make some interesting points. For another point of view,
I'd like to quote from the opening paragraphs of a paper that will soon
be published in the Journal of Mathematical Behavior. It was written
by Al Cuoco, June Mark, and Paul Goldenberg (my bosses), and it's called
"Habits of Mind: An Organizing Principle for Mathematics Curriculum."
I am currently working trying to design a geometry curriculum around these
ideas. (If you'd like a draft copy of the paper along with some other
information about the geometry project, email me with your snail mail
address and I'll get a packet in the mail to you.)


**************

Thinking about the future is risky business. Past experience
tells us that today's first graders will graduate high school
most likely facing problems that do not yet exist. Given the
uncertain neeeds of the next generation of high school graduates,
how do we decide what mathematics to teach? Should it be
graph theory or solid geometry? Analytic geometry or fractal
geometry? Modeling with algebra or modeling with spreadsheets?

These are the wrong questions, and designing the new curriculum
around answers to them is a bad idea.

For generations, high school students have studied something in
school that has been called mathematics, but which has very
little to do with the way mathematics is created or applied
outside of school. One reason for this has been a view of
curriculum in which mathematics courses are seen as
mechanisms for communicating established results and
methods---for preparing students for life after school
by giving them a bag of facts ... Given this view of
mathematics, curriculum reform simply means replacing
one set of established results by another one (perhgaps
newer or more fashionable) ...

There is another way to think about it, and it involves turning
the priorities around. Much more important than the specific
mathematical results are the habits of mind used by the people
who create those results, and we envision a curriculum that
elevates the methods by which mathematics is created, the
techniques used by researchers, to a status equal to that enjoyed
by the results of that research. The goal is not to train large
numbers of high school studnets to be university mathematicians,
but rather to allow high school students to become comfortable
with ill-posed and fuzzy problems, to see the benefit of
systematizing and abstraction, and to look for and develop new
ways of describing situations. While it is necessary to infuse
courses and curricula with modern content, what's even more
important is to give students the tools they'll need to use,
understand, and even make mathematics that doesn't yet exist.

If we really want to empower our students for life after
school, we need to prepare them to be able to use, understand,
control, and modify a class of technology that doesn't yet exist.
That means we have to help them develop genuinely mathematical
ways of thinking. Our curriculum development efforts will attempt
to provide students with the kinds of experiences that will help
develop these habits and put them into practice.