Re: Meaningless problems in algebra texts

[John Denker <jsd@AV8N.COM>]

Herbert H Gottlieb wrote:
> I am resending this message because it may not have been transmitted
> the first time.

1) When in doubt as to whether something was processed by
the listserv, check the archives:
  http://lists.nau.edu/archives/phys-l.html

2) Be very skeptical of messages saying your submission was
bounced because of duplication.  That is a very poorly worded
error message;  the usual scenario is that some subscriber has
misconfigured his mailer so that phys-l messages are being
forwarded back to phys-l.  You can confirm this by looking
at the headers of the bounce message if you really care.

> There is one solution that can halp to make more
> sense out of the typical algebra texts that are full of mostly
> "meaningless problems". Why not teach algebra together with physics
> in the junior or senior year of high school? It certainly makes sense
> from a logical view.  I suppose that the major problem in doing so is
> that the mathematics teachers are generally
> unable to teach physics and there are too few physics teachers
> available'

Descriptively speaking, there's quite a bit of that already
going on, as others have pointed out.  Prescriptively speaking,
it is not an entirely good thing.  If high-school physics
reviews and reinforces high-school algebra, that's entirely
good.  If college algebra reviews and reinforces calculus,
that's entirely good.  But when it is remediation rather than
review, that's problematic, for a host of reasons.

Others have argued, properly, that having to do remedial math
is bad for physics education.  I emphasize that I agree with
that ... but I won't repeat the arguments.  Today I wish to
make the additional point that relying on physics class for
remedial math is bad for _math_ education.

From a mathematician's point of view, the physics approach is
at once too broad and too narrow.  Mathematics is supposed to
be strictly logical.  For example, we might know "A implies B"
because we have derived it, step by step, starting from the
axioms.  To repeat: math is validated by formality and rigor.

Some physics results are validated by logic, but others are
validated by observation.  For instance we might say "the moon
(as seen from earth) subtends half a degree" because we have
observed it to be so.  More generally physics (and natural
science in general) depends on a complex lattice of facts,
based on observations linked together by logic.  My point for
today is that physics is allowed to use observations and other
tricks that are not properly part of mathematics.  So in this
sense physics is broader.

But when we move from the essence of mathematics to the
applications of mathematics, physics is too narrow.  Math has
all sorts of applications outside physics.

There are many other reasons why math ought to be thought
of as not identical to physics.

============

I've seen schools where the math teachers were in cahoots
with the science teachers.  They introduced matrices in math
class, and the next week they were doing photon polarization
in physics class.  Ditto for vectors, derivatives, Green
functions, group theory, etc. etc.

I've also seen schools where they couldn't get their act
together.  I vividly remember a particular example: the
eigenvalue expansion for the Green function.  The math
professor said it was "icky" and too applied, and refused
to cover the topic, saying "wait until it comes up in a
nice physical context; they'll cover it there."  Well, a
week later it came up in E&M class, and the professor
"assumed" (in defiance of the facts) that everybody knew
it, and refused to cover it, saying it wasn't his job to
teach basic, general techniques of mathematical physics.
He didn't want to derail his schedule.

Guess which school gets more donations from alumni who
(a) are successful and (b) remember the school fondly.