From: hrubin@pop.stat.purdue.edu (Herman Rubin)
Subject: Re: Is Math Hard?
Organization: Purdue University Statistics Department
Date: Mon, 16 Nov 1992 17:31:24 GMT

In article <1992Nov11.195326.25846@ariel.ec.usf.edu> mccolm@darwin.math.usf.edu. (Gregory McColm) writes:
>In article <Bx9uy1.LB0@mentor.cc.purdue.edu> hrubin@mentor.cc.purdue.edu (Herman Rubin) writes:
>>In article <1992Nov5.180244.27364@athena.mit.edu> jamess@athena.mit.edu (John A Mess) writes:

>>>In article <Bx79Lo.LG1@mentor.cc.purdue.edu> hrubin@pop.stat.purdue.edu (Herman Rubin) writes:
>>>>In article <1992Nov4.044300.15766@cbfsb.cb.att.com> wa2ise@cbnewsb.cb.att.com (robert.f.casey) writes:
>>>>>In 5th grade, we did set theory (at least the simple stuff).  At the time,
>>>>>I couldn't believe that we were doing such easy stuff instead of hard
>>>>>long division and such.  But it seemed that the teacher and the rest of
>>>>>the class had a hard time figuring it out....

>>>>From the experiences when people who had an understanding of mathematics
>>>>taught it, most of the children could get some grasp of the subject.  But
>>>>failure of the attempts to teach the teachers was what killed the new math.
>>>>Teachers who can only teach rote can only do harm to those who want more.


>The look-say method of teaching children how to read is merely 
>the most notorious example of the Educational establishment 
>running amok.  The New Math was another. 

On the reading I agree.  But the New Math was an attempt, which in my
opinion was not the best way to do it, to remedy the observation that
learning to carry out arithmetic manipulations conveyed no understanding. 
That is still the case, even in those countries which have the best 
schools.  Now I do not think that they did things in the best way, but
it was reasonably successful when those who understood the number system
taught it.  The teachers could not learn that.

The problem is that 
>professors of education (who are largely responsible for these 
>disasters) are as isolated from the "real" world as other 
>professors.  Just as many mathematicians know only their own 
>mini-field --- and no applications --- many education professors 
>know only THEIR minifield, etc.  Many professors of education 
>have about as much experience in teaching preCollege children 
>as many computer science professors have programming computers.  

Mathematicians are much better at knowing applications than you seem
to think.  Also, they know a fair amount of mathematics.  But the 
professors of education claim that they know how to teach a subject
without knowing anything about the subject.  

It makes no difference whether or not they have taught children.  They
have no idea of what is worth learning.  They have studied the learning

of nonsense syllables, and proclaim that that is the way to go, etc.
>Being part of the problem myself, I'm shouldn't berate others, 
>but when we try to reform the world, we should keep an eye on 
>how practical our proposals are.  Keep in mind that ALL reforms 
>will be imposed on the schools by ignorant school boards, corrupt 

This is why we need a strong voucher system, so that those who want
otherwise can do otherwise.  

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

>When I was in High School, I was at the alleged 7th best HS in 
>California.  I encountered History teachers who didn't know 
>History, Science teachers who didn't know science, etc.  I do 
>believe that many teachers simply do not know their subject.  
>The problem is so huge that I am not sure what to do about it.
>Certainly the problem will remain so long as teachers are 
>underpayed.

Scholars of history must decide it someone knows history.  Scientific
scholars must decide if someone knows science.  Those who understand
a subject must be the ones to decide if a teacher knows enough of the
subject to teach.  

They must also not be under pressure to certify enough teachers to 
handle the classes.  It is only if the public learns that the teachers
are incompetent that they will ever do anything about it.  And with a
voucher system, an individual school can do something even if the 
majority does not care enough.  In fact, the only reason a voucher
system can be installed quickly is that most people do not care enough.

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

>An appalling amount of preCollege education still works this
>way.  Its easier to teach & then use multiple choice exams.

What can happen if the teachers know nothing else?
>>[...]
>>I have occasionally taught courses taken by prospective mathematics teachers.
>>Many of my colleagues teach those candidates more often.  They all would like
>>to be able to flunk most of them.  So they have had calculus; but they can 
>>only do routine, and not even that well.  Does an undergraduate who has taken
>>two full years of calculus have time to forget it?  I have had 16 out of 21
>>[...]

>I am more concerned about future teachers who don't seem to 
>like math.  They can do the problems, sure, but they regard 
>math as some dreadful chore.  I'm sure that they're going 
>to communicate these feelings to their students.

This is due to a lack of understanding.  All they know is how to do
routine problems, which really is nothing more than a chore.  What 
do you expect?  The New Math was an unsuccessful attempt to change
that aspect.  

I do not even know if the following can be carried out for the prospective
teachers.  INSIST that they have facility at using mathematical notation
to formulate (not solve) word problems of substantial complexity.  This
knowledge is what is needed to apply mathematics, and is comparable to
writing sentences and paragraphs in the vernacular.
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hrubin@snap.stat.purdue.edu (Internet, bitnet)  
{purdue,pur-ee}!snap.stat!hrubin(UUCP)
Newsgroups: sci.math