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From: hrubin@pop.stat.purdue.edu (Herman Rubin)
Newsgroups: comp.edu,sci.math,sci.misc
Subject: Re: Subtle Math Questions
Message-ID: <11891@mentor.cc.purdue.edu>
Date: 5 May 91 13:36:34 GMT
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In article <1991May3.200312.10109@cci632.cci.com>, brs@cci632.cci.com (Brian Scherer) writes:

			.....................

> I wish to disagree on the point that math teachers do not learn much.
> I went to a college that was a teachers college and a science college.
> The only difference between the major in Math and the major in Math
> education was areas outside of the math department. Like english etc.
> The math ed people had to take courses in lesson preperation, 
> and the sych(sp) courses. The math courses were geared to the science
> arena and you had to have a B or better in them.

I have posted elsewhere on this topic.  The math courses now taught to
undergraduates rarely do anything appreciable towards understanding the
concepts.

> I would like to make a comment about the so-called teachers that
> teach at a college. Do you know that most never have to take any
> educational courses to be able to teach? Many do not know how
> to write lesson plans, have good examples (worked out ahead of time), 
> and really know how to present the material to the students. 

It is a very good thing that they have not had that (insert your own 
derogatory term).  Most of them have plenty of examples; too many of them
are not very good, I will agree.  The text usually has plenty of examples,
if the students can read :-).  Presenting the details of manipulations, which
is what is now stressed too often, is utterly deadly, and of little use.

How can concepts be taught?  By being carefully presented, and then by making
the students USE them in unusual situations until the light dawns.  The concept
of a proof cn be taught, but how to prove cannot be taught at all.  The idea of
using symbols can be taught, but how to formulate cannot; incorrect formulation
can be pointed out, and examples of correct formulation given, but giving rules
and buzz-words are more likely to cause harm.  These topics are important, not
how to compute sums and products, to solve formulated problems, to differentiate
and anti-differentiate.

> As an ex-secondary math teacher, who still teaches on the side, not only
> in the math arena, but in the computers (micro) and also for the bouy scouts
> I would guess that the whole area of education needs to be looked
> at and re-done.

I agree with the last sentence.  But redone from the point of learning, not
memorizing and passing examinations.  If you have faced a group of
undergraduates who have had the full two years of calculus, and cannot
use their calculus on a take-home exam in problems not that much different
from homework thoroughly discussed in class, I believe that you would agree
that their calculus was worthless.  We teach what can be forgotten after the
final, and examine accordingly.
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hrubin@l.cc.purdue.edu (Internet, bitnet)   {purdue,pur-ee}!l.cc!hrubin(UUCP)