TITLE: Math Blues
AUTHOR: Eugene Wallingford
DATE: September 05, 2007  7:48 PM
DESC: 
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BODY:
I used to be a member of the IEEE Computer Society.  A few
years, a combination of factors (including rising dues, a
desire to cut back on paper journal subscriptions, a lack
of time to read all the journals I was receiving) led me
to drop my membership.  In some ways, I miss receiving the
institute's flagship publication, <EM>Spectrum</EM>.  It
was aimed more at "real" engineers than software types,
but it was a great source of general information across a
variety of engineering disciplines.  My favorite column in
<EM>Spectrum</EM> was Robert Lucky's "Reflections".  It is
written in a blog-like fashion, covering whatever neat ideas
he has been thinking about lately in a conversational tone.

For some reason, this week I received a complimentary issue
of <EM>Spectrum</EM>, and I immediately turned to "Reflections",
which graced the last page.  In this installment, Lucky writes
about how math is disappearing from the practice of engineering,
and this makes him sad.  In the old days engineers did more
of their own math, while these days they tend to focus on
creating and using software to do those computations for them.
But he misses the math, both doing it and thinking about it.
Once he came to appreciate the beauty in the mathematics that
underlies his corner of engineering, and now it is "as if my
profession had slipped away while I wasn't looking".  Thus his
title, "Math Blues".

I appreciate how he must feel, because a lot of what used to
be "fundamental" in computer science now seems almost quaint
these days.  I especially feel for folks who seem more
attached to the old fundamentals, because today's world must
seem utterly foreign to them.  Of course, we can always try
to keep our curriculum
<A HREF="http://www.cs.uni.edu/~wallingf/blog/archives/monthly/2007-03.html#e2007-03-10T12_39_33.htm">
   focused on those fundamentals</A>,
though students sometimes realize that we are
<A HREF="http://www.cs.uni.edu/~wallingf/blog/archives/monthly/2007-04.html#e2007-04-27T18_04_34.htm">
   living in the past</A>.

I felt some math blues as I read Lucky's column, too, but of
a different sort.  Here is the passage that made me saddest:

<BLOCKQUOTE><EM>
I remember well the day in high school algebra class when
I was first introduced to imaginary numbers.  The teacher
said that because the square root of a negative number
didn't actually exist, it was called imaginary.  That
bothered me a lot.  I asked, If it didn't exist, why give
it a name and study it?  Unfortunately, the teacher had
no answers for these questions.
</EM></BLOCKQUOTE>

What great questions young Bob asked, and what an opportunity
for his teacher to open the student to a world of possibilities.
But it was a missed opportunity.  Maybe the teacher just did
not know how to explain such an advanced idea in a way that
his young student could grasp.  But I think it is likely that
the teacher didn't understand, appreciate, or perhaps even
<EM>know</EM> about that world.

Maybe you don't <STRONG>have</STRONG> to be a mathematician,
engineer, or scientist to be able to teach math well.  But
one thing is for certain: not knowing mathematics at the
level those professionals need creates a potential for
shallowness that is hard to overcome.  How much more
attractive would a college major in science, math, or
engineering look to high school students if they encountered
deep and beautiful ideas in their courses -- even ideas
that matter when we try to solve real problems?

Outreach from the university into our school systems can help.
Many teachers want to do more and just need more time and
other resources to make it happen.  I think, though, that a
<A HREF="http://www.cs.uni.edu/~wallingf/blog/archives/monthly/2007-08.html#e2007-08-08T15_40_18.htm">
   systemic change</A>
in how we run our schools and in what we expect of our
teaching candidates would go even farther.
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