Today, three mathematicians wonder how to teach
math. The University of Houston's College of
Engineering presents this series about the machines
that make our civilization run, and the people
whose ingenuity created them.

I've had a running
conversation with three mathematician colleagues.
They all feel acutely that we need to improve the
public understanding of math. But none of them
knows how!

One says, "How do you get around the fact that the
media treat mathematicians as though we were
mentally deformed?" Another says, "It's like trying
to explain Mozart to someone who's never heard
Mozart -- without using sound." Another says, "It's
really easy enough to understand mathematics. You
simply learn mathematics."

These people differ greatly in temperament. Each
readily admits his temperament colors the way he
does math. Yet they share one conviction.
Mathematics is a great beauty in their lives. It
gives them pleasure. They want others to share that
pleasure.

But they also want to share the empowerment math
gives them -- the increase of options in their
lives. Whole worlds of human endeavor close off
when you don't know math. As math literacy drops,
and our young limit their lives, America suffers.
That's why I turned to these friends. And if they
don't know the answer, they certainly see the
problem. It's the Catch-22 of having to describe
mathematical pleasure to children who don't yet
know math.

And it's not just children. We in engineering still
meet students who're beyond calculus, and who
haven't yet caught that glint of beauty. These are,
by and large, students who've seen only sets of
formal steps in the math they've studied.

Of course that's the terrible trap we teachers face
at all levels. It's far easier to teach methodical
steps than to open our insides to students -- to
say, "Here's where Heaven has touched me!" Methods
are so clean and reliable. It's easy to write and
grade test questions about method.

But mathematicians are in their business to be
surprised. While method can produce surprise,
instruction based on method takes students out of
the mental frame that expects surprise. They miss
both the pleasure, and the opportunity, surprise
offers.

Mathematics is like humor. Math lets you turn
suddenly, and veer onto a side road. Method
doesn't. Well-constructed humor has a mathematical
structure to it. My favorite example is the
assertion that "There are three kinds of people in
this world: those who can count and those who
can't!" Or, if you want one with even greater
mathematical elegance, try, "All generalities are
false!"

So my colleagues and I will keep trying to reach
students after they've reached the university, even
though that's too late. The fact is, we teachers
need the help of parents and of the media. Children
need to know that math offers joyful and unexpected
forks in their road. Math offers surprises that
educational method hardly hints at. And that
includes surprise in the road of their own lives.
It means more choice, and greater freedom.

I'm John Lienhard, at the University of Houston,
where we're interested in the way inventive minds
work.

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