From: lady@uhunix.uhcc.Hawaii.Edu (Lee Lady)
Subject: Re: Is Math Hard?
Followup-To: sci.math,misc.education
Summary: A little bit of history of the New Math.  
Keywords:  The New Math
Organization: University of Hawaii (Mathematics Dept)
Date: Mon, 9 Nov 1992 10:37:53 GMT

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.  And I'm no rocket scientist.
>>Unions, intersections, subsets, and such stuff that turns out to be a bit
>>similar to and gates and or gates in logic design.
>
>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.

Certainly that was a major factor.  But my personal opinion is that the
new math was wrong in its conception.  It was a program designed by
mathematicians who had no understanding of how people actually learn
mathematics.  (Of course at that time, no one else did either.  And to a
large extent that's still true now.)  What these mathematicians
understood was how they themselves thought about mathematics.  This 
way of thinking was something they themselves had learned after long
struggles and they thought that future students could short-circuit
that struggle.  I think that this was a mistake on their part.

(The new math came along along a little while after mathematicians got
the bright idea that calculus books ought to be oriented around epsilon
and delta.  This was also about the time that I as a sophomore showed up
for my first day of Matrix Theory and had Evar Nering announce that he
would not be using the usual text by Franz Hohn but instead would be
giving us a set of dittoed notes of his own and that instead of
teaching us Matrix Theory he would be teaching something called Linear
Algebra.  His dittoed notes later came out as a book and if you look at
the original edition of Nering's book you'll get some idea of what that
course was like.)

Before the New Math there was SMSG -- the School Mathematics Study Group
-- who reworked the high school curriculum and produced a set of
textbooks which were supposed to be models for textbook publishers to
start from.  A lot of the SMSG material was rather nice.  They made the
real numbers an integral part of the geometry course.  On the other hand,
they placed an importance on the Hilbert axioms for geometry that I think
tended to turn it into a bunch of uninteresting formalisms that many
students would not be able to relate to.  For instance, as I remember 
they spent quite a bit of time on the notion of betweenness for points on
a line.  

In the algebra text, there was a total absence of word problems since
they asserted that word problems were irrelevant to mathematical thinking
and were an anachronism in the mathematics curriculum.  


I believe that the new math began with the Madison Project, organized by
a mathematician named Robert Davis at the University of Wisconsin.  He
stressed what was called the Discovery Method and his people seemed to be
fairly successful in teaching experimental elementary school classes.
(This was before there was general awareness that experimental classes
are *always* successful, not matter what the approach.)  

After that, publishers produced a lot of textbooks which prominently
claimed to use the Discovery Method.  But mostly they seemed to miss the
whole point.  They would simply give a lot of exercises with vague
instructions where it was impossible to figure out what was wanted.  (I
saw several of these books because I had a daughter in elementary
school.)  

I assume that Robert Davis was teaching nice middle-class students with
well educated parents.  Much later, after the new math was in full, um,
flower, there was a program called Project Seed (not to be confused with
other programs of various sorts having the same name) directed by a Berkeley
numerical analyst named, I believe, Friedman.  Project Seed sent
mathematics faculty and graduate students into ghetto schools 
teaching algebra to elementary school students.  

I observed a couple of Project Seed classes since I was thinking of
becoming involved in the program myself.  My friend who was teaching the
class was teaching not only algebra but also spelling and anything the
students seemed to need to know.  It seemed to me that the students were
responding mainly to his enthusiasm and were willing to let him
teach them anything they wanted to.  (Their regular teacher, however, was
by no means inept or indifferent.  When I saw the kids she had to deal
with, I was rather impressed with her.)  

I think the biggest failure of the new math was in not realizing that
there's a whole lot more to changing the school curriculum than just
coming up with some good ideas and trying them out in experimental
programs.  The developers had no concept of how to work with the system.
They put much too little effort into finding ways of educating teachers
and convincing the teachers that the new approach had real value.  And
they gave no thought to how to deal with textbook publishers and the
very competitive high-stake game of selling textbooks to boards of
education.  

Most of all, though, the new math proponents were never successful in
explaining what the new math was about.  Most people believed that the
point of the new math was in the subject matter.  I think that 98% of the
people in the country believed that the topics in the new math were
recent mathematical discoveries.  Sets.  Modular arithmetic.  Representing
numbers in other bases.  (This was a time when in the popular culture the
binary number system was regarded as roughly as difficult to understand
as the theory of relativity.)  All this stuff was apparently very
important, since mathematicians said it was, but most people had a hard
time seeing quite why.  ("So now that mathematicians have invented sets,
does that mean that numbers are obsolete?"  "Oh, so you're a graduate
student in math.  Have they completely switched over to the new math in
universities now, or do they still teach things like calculus?")  

The proponents of the new math never managed to convey the point that it
wasn't about subject matter, it was about a different approach to
teaching, a different attitude.  And so basically, except for a few
experimental programs, there never was any new math in the schools.  

--
It is a poor sort of skepticism which merely delights in challenging
those claims which conflict with one's own belief system.  
                                                          --Bogus quote 
lady@uhunix.uhcc.hawaii.edu         lady@uhunix.bitnet
Newsgroups: sci.math,alt.politics.kibo