**NYC HOLD Honest Open
Logical Debate on math reform**

**Are
our school’s math programs adequate?**

** Experimental mathematics programs and their
consequences**

**New York**** ****University**** ****Law**** ****School**

**New York City**

**June 6, 2001**

**opening
remarks**

Fred Greenleaf

Professor of
Mathematics

Courant Institute of
Mathematical Sciences

I would just like to introduce myself, so members of
the audience will know the issues I have been concerned with when we come to
the Q/A period. During the past year I have spent quite a bit of time

Examining curricular materials for various
NCTM-based middle and

high
school programs -- CMP, ARISE, and to some extent the IMP

program
which is slated to go into effect throughout the

in Fall
2000.

Conducting
numerous discussions and interviews with teachers

in
District 2 and elsewhere in NYC

Participated in many discussions with colleagues at the Courant
Institute

who have
become concerned about the NCTM based math programs being

introduced
in NYC schools.

Tonight I would like to comment on some of the flaws
I see in these constructivist programs.

1. I've had
a lot of experience with curriculum development, and that

includes serious efforts on programs for entering
freshmen who are

not necessarily going to be math majors. Whether
we're talking about

core programs in math and science literacy for
liberal arts majors, or

regular math courses for science majors, business
majors, and premed students, I have found that the single greatest obstacle to success
for entering college students -- even in
courses for non-majors -- is lack of *proficiency*
in algebra. That means: being able to DO it, not just talk about it.

Most NCTM based programs I reviewed strongly downplay
symbolic manipulation skills (which lie at the heart of real mathematics) in
favor of ad hoc ``visualization'' techniques, and lengthy unguided projects in
which students are supposed to ``discover math principles for themselves''. Now
there is something to be said for including in a math curriculum some projects
in which students are encouraged to ``learn by discovery'' -- I have often done
this the courses I have developed. The problem is that most NCTM based programs
being suggested for use in NYC are quite extreme in their emphasis on the
process of “discovery'', at the expense of mastery of basic content and
proficiency in basic skills. The NCTM based programs are quite unbalanced in
their emphasis, and as a result are totally inadequate as preparation for
eventual college level courses.

In a recently completed review of math programs being
implemented in NYC, the Levy Commission conceded that the high school programs,
such as those being implemented throughout the Bronx in Fall 2000, were not an
adequate preparation for college level work, and went on to suggest that “choice''
be allowed beginning in grade 9, so college bound students might take courses
with stronger content.

THAT IS TOO
LATE! The underpinnings of proficiency in algebra are

laid in
middle school, and even at the elementary level. For example,

learning to
work with fractions, *as fractions*, is
the precursor to algebra

It is not
enough to deal with them as numbers punched up on a calculator, or

by comparing
lengths of paper strips

Doors will be closed to students who aspire to
college level work unless students are allowed to elect courses with stronger
content, *beginning in middle school at
the latest*, but preferably throughout the early grades.

Next I would like to comment on the view from the
trenches: what do teachers think? In my interviews I found many math teachers
willing to speak, as long as their anonymity was assured. I spoke to teachers
at the elementary, middle and high school levels. Many complained that the NCTM
based courses tend to be quite “dumbed down''. Here are some quotes:

``I've been
teaching math for a long time, and am struck by how much less

math
actually gets covered under the new programs, compared to what got

accomplished
just a few years ago''

``Weaker
students may benefit from these programs, but the effect on the

stronger
students is going to be disastrous.”

“The only
ones who will really benefit from these programs are the

Kaplan
tutorial centers -- for them it will be a godsend!''

One teacher described an hour-long training session
in which kids colored an array of numbers. She asked the trainer, what was the
point of spending so much time on this? What math concepts did it lead to? The
reply:

`”Concepts
don't matter. What counts is how the kids feel about it.''

I can't think of a better illustration of what the
phrase ``dumbed down'' might mean.

Skilled teachers' hands are being tied by overzealous
administrators and NSF-funded ``trainers'', who know about pedagogy but have
very little knowledge of math CONTENT. Indeed some of the more zealous proponents
of these constructivist programs have claimed that one doesn't really need to
be proficient in content in the early grades, one simply has to know how to
teach. Experienced math teachers are chastised -- even threatened with
reprisals -- if they deviate from the mandated constructivist scripts. As one
teacher put it:

``There is
no longer any classroom autonomy. Teachers are being treated

as if
expertise in one's subject, and personal teaching skills, are

irrelevant.
Everyone is being forced to work from the same fairly

ridiculous
script.''

This atmosphere of micromanagement and intimidation
is alienating many of the experienced teachers. Older, experienced teachers are
contemplating

early retirement; younger ones look to other
locations where ability to

teach math content is appreciated, and probably
better paid.

The constructivist philosophy is flawed at its core.
Educationists posit that really meaningful learning takes place when students teach
each other in small peer-led group discussions, with teachers confined to roles
as mere “facilitators'' of this process. It is absurd to expect students to
invent major portions of math on their own, through extensive time consuming
group projects. Discovery based learning has a valid place in the classroom,
but the constructivist programs are extremely biased in this direction, and
progress is very slow. In fact, many teachers report that:

``In our
school, using program xxx, no teacher has ever managed to cover

more than
60\% of the year's material.''

The District replies ``We never expected to cover all
of it''. Yet the District has repeatedly failed to offer guidance on *which* 60% is to be covered. Furthermore,
if these curricula are to provide an adequate preparation for the State Regents
exams, one would have to cover *all* of
the course materials, and that is impossible.

It is time to acknowledge the serious flaws in the NCTM
based programs

being promoted so zealously in District 2, so we can
get on with the task of creating programs of math preparation adequate for
today's world. What we really need are programs with some sense of balance,
created with the involvement of mathematicians as well as educators.