From: hougen@vision.csl.uiuc.edu (Darrell Roy Hougen)
Newsgroups: sci.math
Subject: Re: Mattel says "Math is tough."
Date: 6 Oct 1992 21:39:45 GMT
Organization: Center for Reliable and High-Performance Computing, University of Illinois at Urbana-Champaign
NNTP-Posting-Host: vision.csl.uiuc.edu

holmes@opal.idbsu.edu (Randall Holmes) writes:

>1.  Math is hard (not just for girls).

This is aimed at all the people that have said that math is hard, not
just Randall.  I am surprised at the number of people on this
particular news group that think that math is hard.  I would have
thought that most of them had continued in math because they found it
to be relatively easy.  Of course, math is both easy and hard
depending upon how you look at it.

Let me clarify what I mean.  The math that students are taught in
school, up through about the first half of college, is easy.  After
that, it starts getting harder, especially if one is in math, physics,
chemistry, engineering, or some closely related major.  Some students,
such as those in psychology, don't get socked with tough math until
they are in grad school when they have to learn (real) statistics
(which is arguably a part of math).

Most of the math that is learned in primary and secondary school
requires very little thought to learn.  It is simply a set of rules,
like the rules of a game, that one must memorize and apply to obvious
problems.  If one studies the rules, which are usally handed out at a
very modest pace, they can be learned.

It is not until students are forced to apply math to difficult (real
world or artificial) problems that it gets hard.  And, it is not so
much the math that gets hard as the problems that get hard.  The
difficulty is in the logic that must be applied to the problems, not
in the mathematical formalism.  Put simply, solving difficult problems
requires a lot of thought.  The thinking involved requires a lot of
effort and dedication to carry through to a satisfactory conclusion.
I wonder how people would respond if Barbie said, "Thinking is tough!"

Yes, thinking requires mental effort, but would it be right to
discourage children from thinking for themselves by saying that it is
"tough"?  The truth is that the mathematical rules are easy to learn
if they are thoroughly learned at each phase of development and so
long as the student is not bombarded by too many new rules too fast.
I see no reason why the average person should not be able to learn the
basic techniques of mathematics up through elementary calculus.  There
simply are not that many rules and they are not that hard to learn.

Part of the problem may be that math classes are often the only
classes (besides physics which also has a bad reputation) that force
students to think by sometimes giving them difficult problems.  Even
math and physics classes rarely give problems that are terribly
difficult.  I'm not arguing that they should.  I don't think children
of that age are prepared to tackle problems at a high level of
difficulty.  In fact, I think it better for them to learn as many of
rules as they can while they are still in the rote learning mode of
early childhood and save the difficult thinking for later when they
enter the argumentative phase of adolescence and beyond, but that is
another thread entirely.

In summary, I don't believe that math is hard.  Thinking is hard, but
who would want to discourage that?

Darrell