Path: utzoo!utgpu!news-server.csri.toronto.edu!rpi!zaphod.mps.ohio-state.edu!unix.cis.pitt.edu!dtate
From: dtate@unix.cis.pitt.edu (David M Tate)
Newsgroups: comp.edu
Subject: Re: Subtle Math Questions
Message-ID: <124567@unix.cis.pitt.edu>
Date: 6 May 91 14:21:33 GMT
References: <1991Apr24.142835.26475@mccc.edu> <1991May3.200312.10109@cci632.cci.com> <11891@mentor.cc.purdue.edu>
Organization: University of Pittsburgh
Lines: 41

In article <11891@mentor.cc.purdue.edu> hrubin@pop.stat.purdue.edu (Herman Rubin) writes:
>
>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;

What makes you say these things?  I teach how to prove; I teach formulation.
Yes, it's difficult as hell, but that doesn't mean you shouldn't even bother
to try.

>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[...]

You equate "teaching" with "giving rules and buzz-words"!?  No wonder you 
think it's impossible.

Today is the first day of summer classes here at Pitt.  This afternoon, I'll
be teaching a required sophomore course which, if it had a name, would be 
called something like "Problem formulation and modelling".  The whole point
of the course is to teach the Art of Problem Formulation and "Solution" (with
the scare quotes emphasized).  It's about all those things you say can't be
taught.  I've taught this course once before, with striking improvement in the
students' skills.  Of course, I'd rather get at them in high school, but it's
the best we can do...

Of course, from reading your previous postings I know that you do not really
think of teaching in the cynical terms you have used here.  So I'm curious:
why can't we teach the Art of Modelling the same way we teach other Arts?  I
took violin lessons for years; they weren't just "rules and buzz-words".

(Of course, this requires that the instructor be an artists of sorts himself,
 and not a mere technician...)


-- 
       David M. Tate        | "Your telegram has been sent, sir.  You should be
  dtate@unix.cis.pitt.edu   |  receiving it in about an hour.  We've sent your
          Motto:            |  bags ahead to your hotel.  Where will you be
  Gramen artificiosum odi   |  staying?"		--Firesign Theater.