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From: balden@wimsey.bc.ca (Bruce Balden)
Subject: Re: Subtle Math Questions
Organization: Computer Signal Corporation
Date: Thu, 02 May 1991 17:13:17 GMT
Message-ID: <1991May02.171317.751@wimsey.bc.ca>
References: <1991Apr24.142835.26475@mccc.edu> <1991May1.192513.11714@watmath.waterloo.edu> <1991May2.133856.8338@psych.toronto.edu>

In article <1991May2.133856.8338@psych.toronto.edu> grant@psych.toronto.edu (Stuart Grant) writes:
>>>I think you'll find that the majority of primary and secondary school
>>>math teachers do not get their math education from a college's math
>>>department in "regular" math courses but either from a regular college's
>I agree that watered down courses in which students are not expected to learn
>are not much use to anyone. However, I don't think that this is 
>the biggest problem with the math instruction in primary and secondary
>schools. _Any_ math course taught at a college or university will be at  
>least as sophisticated as what teachers will be teaching in primary and
>secondary schools. Not knowing how to do differential equations is not
>the greatest problem math teachers have.

Nevertheless, the good teacher of mathematics will have a deep appreciation
of the way mathematics is actually used in the world at large and not just
a good understanding of a traditional list of arithmetical and algebraic
algorithms and formulas.  The student who sees his mathematics teacher as
inadequate, not only in the internal mechanics of the subject, but in
success in making the subject relevant to the world at large, will correctly
reason (YES, students are capable of reasoning) that this person has nothing
of importance to tell him.  Just as the coach of the football team is
normally expected to be a good athlete well beyond the capabilities of
the average high-school athlete, so should a high-school or even elementary
school mathematics teacher be a source of inspiration.  

Currently, of course, we cannot attract people with the requisite combination
of people and technical skills into the school system, particularly at the
lower levels.

Of course, the mathematics community itself is not immune to criticism in this
regard.  Take the college level, at which I have some experience.  The
"sexy" subject, regarded as the principal goal of a good engineering and
science student is Calculus, which, in my experience, is one of the most
bizarre and arcane subjects students ever encounter, being obsessed with
complex derivative and integral calculations of dubious value.

The dreary subject, reserved for "slow" student and non-specialists, is
"Finite Mathematics".  In my opinion, the topics in this course are far
more relevant to the ordinary experiences of people than first year calculus.

It is true of course, that if you want to extend these techniques and ideas
much further, then you have to drag in a LOT of mathematical machinery, 
especially linear algebra, but there is no motivation to do so otherwise.

Therefore, when the average second year student encounters linear algebra,
he finds it a dry, if not extremely difficult subject and quickly forgets
everything about the subject twenty minutes after the final exam.  I have
myself answered many net queries which would be quite unnecessary if
these courses had any habit of sinking in.

Let's face the basic truth:

People in general lose interest in mathematics at an early age because
the parts of the subject that they see are INTRINSICALLY uninteresting and 
unimportant.  Even a slow student can figure out that his bank president
doesn't know the fine points of long division.



-- 
DISCLAIMER: Opinions expressed are my own, not those of my employer.
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*	Bruce E. Balden	    		Computer Signal Corporation Canada    *
*	Thaumaturgist			225B Evergreen Drive		      *