Newsgroups: comp.edu
Path: utzoo!utgpu!news-server.csri.toronto.edu!rpi!zaphod.mps.ohio-state.edu!van-bc!balden
From: balden@wimsey.bc.ca (Bruce Balden)
Subject: Re: Preparation of mathematics teachers
Organization: Computer Signal Corporation
Date: Sun, 05 May 1991 16:21:59 GMT
Message-ID: <1991May05.162159.5499@wimsey.bc.ca>
References: <1991May1.192513.11714@watmath.waterloo.edu> <1991May2.195751.22316@psych.toronto.edu> <11890@mentor.cc.purdue.edu>

In article <11890@mentor.cc.purdue.edu> hrubin@pop.stat.purdue.edu (Herman Rubin) writes:
>In article <1991May2.195751.22316@psych.toronto.edu>, grant@psych.toronto.edu (Stuart Grant) writes:
>> In article <1991May02.171317.751@wimsey.bc.ca> balden@wimsey.bc.ca (Bruce Balden) writes:
>> >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
>Most students getting regular BAs in mathematics are little better.
>Even the kindergarten teacher should understand induction.  Even the first grade
>teacher should be able to teach the very important use of symbols for precise
>expression.  All junior high school and high school teaching of mathematics 
>should be by those who understand proofs, and teach them, and can even
>occasionally produce them.
>
>> >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.
>The items I have mentioned above are the foundations.  It does no good to know
>how to manipulate if you do not know when.  This is what led to the "new math",
> [Good stuff omitted for space]
>understand.  At the present time, it is possible for someone to go through
>all the courses, and even get a MS in mathematics education, taking the special
>graduate courses on top of a standard BA, and never do other than manipulate.
>
>Teach the children to reason BEFORE they are brainwashed into believing that
>mathematics consists of manipulation.
>-- 
"BRAINWASHED" is the operative word here.

I think we are headed to the notion that schools should not be quite so
isolated from the world at large.  At one time, it was thought that a 
"reasonably educated person" could teach all youngsters well and that
slighlty more specialized people (secondary school subject teachers) could
handle the adolescents.  

The problem has been a consistent misappreciation of the intrinsic value
of science and mathematics and its identification with the intellectual
elite.  The result is that an entire generation of people are out there 
in the school system, especially the elementary school system, with bizarre,
erroneous, and destructive ideas not so much about mathematical concepts
themselves, but about its place and usefulness in the world.  As such, they
mould their charges in their own images, which, by nature of their callings
do not favour the subject at hand.

In my original posting, I tried to make clear that the scientists themselves
are by no means innocent of this crime.  Science has been by nature an elitist
and exclusive endeavour and it suited the scientists of earlier generations
just fine to keep the pool of people who understood it quite small.

It is only in the post-Sputnik age that we have figured out that it is 
desirable for science to have a wider penetration.

However, given that the well is poisoned, we cannot give up.  We must recognize
that the mission is the rescue both the subject itself and its twisted 
representation in the elementary school system from the nineteenth century
mindset.

As far as I can tell, the only way to achieve this is to adopt the methods
of school athletics programs: involve members of the community.  This has
many political and other problems, but I believe there is a substantial
community of scientists in the community at large willing to help out the
school system.

Of course, doing this requires some structure.  Guidelines and materials
have to be prepared.  Cooperative mechanism that don't give school officials
problems have to be arranged.  

The premise here is students MUST be able to see the subject at work in the
REAL world, in the hands of ordinary people before that will attach much
importance to it.  

The elementary school situation is a little more extreme: here, I think
that the First Grade teacher's personal attitudes to the subject can
definitely poison the student's mind.  A more positive role model
is urgently required here.

In the secondary school, the teacher there is isolated from the world.  
Even though he be execellently prepared, he falls behind because he
is not part of the technical world ("those who can do, those who can't ...")
Therefore, I do not start with the presumption that he needs help from
the outside world, but that he needs to be a part of the outside world.
In other words, there needs to be a mechanism for teachers to participate
in the world at large and for other professionals to teach in the schools.
Keeping the worlds at such a distance invites a great gap between the
school's vision of the subject and reality.

As a simple, early step in accomplishing something positive,
n the great tradition of NetLand, I propose the provision of a
NetNews link to every high school in America.  WE here in NetLand
can field questions from high-schoolers and others on what the subject
is really used for.  

Of course, sci.math would probably need dividing into many other 
geographically limited subgroups, but that is the price of success.

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