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From: me@csri.toronto.edu (Daniel R. Simon)
Subject: Re: Subtle Math Questions
Message-ID: <1991May4.132542.21078@jarvis.csri.toronto.edu>
Organization: CSRI, University of Toronto
References: <1991May2.195751.22316@psych.toronto.edu> <1991May3.124454.12758@watdragon.waterloo.edu>
Date: 4 May 91 17:25:42 GMT
Lines: 51

In article <1991May3.124454.12758@watdragon.waterloo.edu> mcramer@watdragon.waterloo.edu (Mert Cramer) writes:
>The notion that, within the present framework, any change in maths instruction
>will make a difference is naive. An informative discussion of the development
>(or not) of maths skills in pre-school children is in a BBC documentary called
>"Four plus four equals the wings of a bird". Among the points it makes:
>1. For most people math is something you do at a desk and has no relivance to
>   life problems.
>2. The formal method of teaching math makes the subject which the student
>   encounters which is NOT concrete (numbers apply to anything) hard to
>   visualize.

Both of these points, as far as I can tell, apply equally well to absolutely
any discipline that involves the least bit of abstraction.  In most other
disciplines, of course, developing the skills of abstraction is understood by 
everyone to be one of the key goals of teaching the subject, whereas 
mathematics teachers instead face constant skepticism from others about the 
value of learning the abstractions they teach.

>3. The teaching of math concepts by exploration rather than by lecture is
>   a more effective technique.

[......]

>One the major points in the film is that the curiosity about math and numbers
>is largly destroyed by the usual techniques of promary teaching. You might say
>that anyone who has an interest in math by the time they get to university
>has survived in spite of all formal education has tried to do to them.

I, for one, would like to challenge, based on my personal experience, the 
common perception that the "usual techniques" for teaching mathematics, or
any other subjects, are anything like what most people seem to think they are.  
When I look back casually on my elementary school years, I remember (oddly 
enough, given that I was raised in the sixties and seventies) exactly the same 
kind of interest-destroying tedium described above, not just in math class, but
in every single one of the subjects I studied.  On the other hand, if I 
reminisce with a little more care, I can vaguely remember that a huge fraction
of my in-school time was subject to a virtually uninterrupted stream of 
attempts to make my education more "creative" and entertaining, most of which 
left me with feelings of enjoyment and enthusiasm, and virtually nothing else.  
My clearest memories by far are of learning "the old-fashioned way" through 
conventional, structured lessons, which imprinted their material in my brain 
much more effectively than the myriad "projects" and "activities" which (I seem
to remember) delighted me at the time, but whose purpose now escapes me 
entirely.

Am I really unique in having had such a diverting and unproductive time in 
public school?


"There *is* confusion worse than death"		Daniel R. Simon
			     -Tennyson		(me@theory.toronto.edu)