[Phys-L] Re: student mathematical capabilities

[Hugh Haskell <hhaskell@MINDSPRING.COM>]

At 07:21  -0400 9/15/05, Jeff Weitz wrote:
> My colleagues in the math department tell me that they teach math, not
> physics, not chemistry, and not cooking.  Their averaged out response to
> physics is much the same as the averaged out response of members of the
> English Department (excuse me, the Department of English). The math
> teachers do a very good job of teaching such things as solving algebraic
> equations and making graphs, but include almost no discussion of
> applications until AP Calculus where they are required to talk a little
> about kinematics and related rate problems.  For this reason, students
> get a shock when they take chem or physics because a problem described
> verbally has to be solved using mathematics.  The translation has to be
> practiced for some time before they get it.
In their effort to teach "mathematics," apparently many math teachers
have forgotten that much of mathematics has real applications to the
real world (I'm afraid that some physics teachers have forgotten that
as well, but it's apparently not so widely done as in math).

This is, I think, a relatively recent phenomenon. I vividly recall my
college calculus course, now more than fifty years past, in which the
textbook (written by the department chair), which I still have and
frequently refer to, had many practical applications, both in
examples and problems, as well as putting many of the original
derivations in an everyday context, while still retaining much of the
traditional mathematical rigor. As part of the course, I learned how
to translate "story" questions into mathematical language (actually
improved that skill since much of my math education prior to college
had emphasized that vital skill).

Later in more advanced courses, such as partial differential
equations, Fourier series, and complex variables, the material was
introduced in a solidly practical context, while still holding us to
the mathematical criteria (existence and uniqueness theorems, for
example). The opening days of the course in Fourier series involved
the derivations of the equations for the time evolution of a plucked
string, and for heat flow in a solid rod, for example, from which the
utility of learning about Fourier analysis was immediately obvious.

What this meant was that when I encountered these same ideas in my
physics classes, I was immediately receptive to the mathematical
ideas used to solve the problems (my ability to actually do so is
another issue entirely). I have also been impressed, over the years
with the number of mathematical concepts that, while being invented,
it seems, for the pure pleasure of the mathematics involved, have
later been proved to be of immense practical value. I suspect that
mamny mathematicians are not too happy about this, although I am, and
use it all the time to encourage students to broaden their
mathematical skills, even if the math teachers don't want to try to
encourage the students to understand how mathematics can be used as
more that must an intellectual plaything (I've heard mathematics
referred to as "mental masturbation" more than once).

I think that it is wonderful that there are many people who want to
do mathematics or science for the pure pleasure of doing that kind of
work, and I encourage that. But it is also important that they
understand that their pleasure isn't the only thing that drives
others. Just as many people become engineers because they want to use
the ideas of physics and other science to make things work, many
people become scientists because they see a value in using the ideas
of mathematics to help us all understand better how the world works,
and, in turn to provide fodder for the engineers to use.

And don't get me started on the reluctance of math teachers to
consider the utility of putting units on their numbers when it is
appropriate, which practice (that is, their reluctance) insures that
students will have an even greater difficulty in carrying the skills
they learn in math class into their physics and chemistry classes.

Hugh
--

Hugh Haskell
<mailto:haskell@ncssm.edu>
<mailto:hhaskell@mindspring.com>

(919) 467-7610

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