Fred Greenleaf

Professor of Mathematics

Courant Institute

Memo to NYU colleagues and District 2
parents

TEACHER INTERVIEWS

Spring, 2001

Teacher responses to the Math Programs being implemented in District 2

xxxx

This is a summary of my interviews
with District 2 math teachers conducted

between March- December, 2000.
Identities of schools and teachers have been deleted

at the request of the interview subjects.

At a District 2 meeting in April, 2000
I spoke to a few teachers from different

schools and noted that implementation and administration
attitudes toward

the constructivist programs being implemented in District 2
seem to

vary greatly from school to school. I thought it would be
useful to hear

first hand comments from teachers at several schools to
assess the feelings

of experienced math teachers toward these programs.

xxxx

INTERVIEW SET #1. These interviews
involved several math teachers at a

large middle school (xxx) where use of CMP is currently
mandated. This

program is now in force throughout grades 6-8; this is also the
first year

that students entering (xxx) from other District 2 schools
received most of their training

with the TERC math program(K-5).

From the comments of teachers at (xxx)
it seems that the administration at

this school is one of the most doctrinaire, insisting that
all teachers

adhere strictly to the CMP materials and methods. Not all do,
despite this

directive, especially the older teachers who are retiring soon. I
was

impressed by the teachers; (xxx) seems to have a large cadre of
knowledgeable

and experienced teachers at the present time. This will
soon change. Out of

(xxx) math
teachers, about 2/3 are planning to retire over the next several

years. I have discovered through other avenues that the
school administration

seems bent on replacing them with people committed to the CPM
philosophy.

The situation at (xxx) is as extreme
as the worst case rumors suggested.

. One policy memo to teachers states that ``the CMP materials are

all that students need, and no supplementary
materials should be used as

they will only impede progress through the CMP
modules.'' Teachers were

outraged by this policy: In English or Science
classes use of multiple

sources and discussion of various points of
view would be viewed as sound

pedagogy.

. One teacher was criticized, by an Asst. Principle who happened to drop

into class, for having "non-CMP
topics" showing on the blackboard.

. At least one teacher (retiring this year) told the Principal that his

job was ``not to teach CMP, it was to teach
Mathematics.'' He is one

of the few who gave his students supplementary
textbooks, and assignments

from
them, so they could get some practice at skills and some exposure to

a more coherent view of some of the CMP topics.
The younger teachers

seem afraid to do this, in fear of reprisals
from school administrators

committed to these programs.

. In this school, teachers, no matter how experienced, are directed to
act

only as ``facilitators'' for the inquiry-based
learning activities of the

CMP modules, and are ordered not to ``instruct''. Students are supposed to

discover everything for themselves through
project activities.

I had heard reports that in the CMP
(and TERC) programs

1. Students did not have texts to work with at home

2. Students were not given homework

3. Students were given no work designed to develop and reinforce

basic computational and algebraic skills.

At (xxx) students DO get a booklet for
each module, which they can take home.

They do get homework assignments, but
only from these booklets; assignments

continue project work and have NO skills component.
Supplementary texts and

assignments providing reasonable emphasis on skills are provided by
a few

teachers, but only at the risk of being ``not in compliance''
with directives

from the Principal's Office.

Module booklets (8 in all) are taken
from the students when each module

is finished, allowing students no further opportunity to
review topics

previously covered. The teachers felt this was a particularly
stupid policy.

Regarding supplementary materials, the
one book I saw (used by one teacher)

looked quite good, with an intelligent balance between basic
skills and

inquiry based projects. This text (Middle Grades Mathematics:
An Interactive

Approach, Prentice-Hall) was clearly
organized to give students an overview

of what they were learning in the project exercises, and
extensive practice

developing basic computational and algebraic skills -- aspects of
mathematical

training that are sorely lacking in the CMP modules.

Most of the teachers were unfamiliar
with the Singapore Curriculum, which I mentioned as being used by some District
2 parents to supplement CMP; they were quite interested in learning more about
them. About

half of those at the meeting knew about the
www.mathematicallycorrect.com

website, which discusses the impact of these constructivist
programs in

in 1997. The rest were eager to check it out.

All the teachers were extremely
frustrated by the philosophy of the school

administration, which if followed would completely tie their hands and

prevent them from exercising their experience and knowledge of
the subject.

They felt that inquiry based learning
has its place as a component of the

curriculum, but that the CMP program is completely one-sided in
its emphasis.

Here are some
of the point the teachers made:

. Weaker students tend to respond favorably to CMP, but the better
students

are bored by it. It is, however, part of the
CMP philosophy that

the CMP program is all that is needed for ALL
students.

. A problem not anticipated by the creators of CMP: In their heavy

emphasis on verbal problems, discussion, and
writing, they neglect to

observe thatfor
many students in NYC schools, English is not their

first language. These students tend to find the
CMP projects hopelessly

confusing, since many of which are worded in
ways that assume strong

verbal skills. (Eg a verbal
problem with 4 parts to it.) These students

often do very well in more standard programs.
In fact, at (xxx) math

scores have traditionally been quite a bit
higher than language scores

on schoolwide tests.

. Heavy emphasis on ``learning by discovery'' makes for very slow
progress

toward the topics carefully outlined in the NY
State Standards. (I have

a copy of this document, which anyone is free
to borrow. It is very clear

about what should be achieved at what grade
levels, and has illustrative

examples; the topics listed seem eminently
sensible to me.) In fact,

I was told that teachers are finding it impossible to complete the

present CMP modules in one academic year,
because it takes so long for

students to get through the projects. Thus,
students are already falling

behind the CMP schedule, in addition to falling
hopelessly behind in

progress toward the topics set forth in the NY
State Standards.

In fact, in the 6th grade program:

No teacher at (xxx) has ever managed
to cover more than 5 of the

8 modules that make up the year's
program in CMP!

Of course students then enter 7th grade way behind the goals set for

that year's CMP program, and teachers are left
to deal as best they can

with the resulting train wreck.

CMP materials in their present form
place little emphasis on development

of basic skills, and teachers feel that students will
indeed be at a

great disadvantage when they encounter standardized testing.
There

are several tests of great importance to parents:

1. In the autumn of the 8^{th} grade, students take the exams for
admission to the

specialized high schools (Stuyvesant, etc).
This is their only chance.

Those exams demand math skills that are not stressed at all in CMP.

2. At grade 10.5 all students take Regents A. The nature of this test

is indicated in some detail in the NY State
Standards. My own comparison

of the NY State Standards and the material for
same grade levels

in the CMP program is really alarming: the CMP
material is quite

dumbed down -- more than a grade level behind
on many topics specified

in the NYS Standards; other NYS Standards
topics are ignored completely.

3. At grade 11.5 or so, college bound students take the Regents B. Their

success in this exam will depend on the nature
of the ARISE program

(another constructivist program) being phased in grade 9. I have

a complete copy of the ARISE texts in my office
and have been looking through them

At the present time I can report that it is way too limited for
college-bound students

who intend to
take Calculus, though it might not be a bad program for students

who intend to avoid math in their college
careers. The book has

some similarities with Quantitative Reasoning,
though it is more

incoherent, does not go as deep, and is less
demanding.

As with CMP, the ARISE program is being imposed as the ONLY

math option. The better students will find it
boring,

unfocused, and lacking coverage of important
topics; they will be

badly served by it, in the name of an ideology
that insists there

can be a single perfect program suitable for
all students.

4. All college bound students will of course have to take the math

component of the SAT tests, which will have an
impact on whether

they get into the colleges of their choice. The
last time I looked,

the SAT requires quantitative skills that have really
been played down

in the present versions of CMP (and ARISE and
TERC).

The teachers also noted:

. Science teachers at (xxx) are upset by what is lacking in CMP.

The science curriculum is based on the NY State Math Standards; students

from CMP seem unable to do anything they are
expected to have covered.

They have very weak computational and algebra skills, and are unaware of

many NYS Standards topics (such as scientific
notation) which are not

coherently covered in CMP, and are certainly
not emphasized to the level

that would make students proficient. Science
teachers are doing what they

can to fill in missing skills, but this should
not be necessary and

detracts from the teaching of science topics.

. This is the first year students entering 6th grade at (xxx)

have been steeped in the TERC Program (K-5th
grade). Teachers complained

bitterly that these incoming students can't do
much of anything: add,

divide, deal with fractions, you name it. This
was NOT previously the

case, and to the teachers the difference is
quite dramatic. It is another

reason teachers find it hard to finish the CMP
modules; they have to

spend time bringing students up to the level of
being able to do the CMP

projects.

All in all, what I heard from the
teachers sounds pretty depressing. I hope

this summary will be helpful to everyone, and that the next
meetings with

other schools can be arranged with more advance notice.

INTERVIEW SET #2. This note records observations by a teacher
(xxx), from

another District 2 school, who has taught math for many years
at grade

levels 2,4,6. xxx has been working
with the TERC materials for the last 4 years,

and has been through several training sessions. The school is one with above

average students.

This teacher made the following
points.

1. xxx sees
some merit in the group learning approach; certain students

respond well to group activities and develop an interest in the
subject.

However, xxx also feels that the TERC
curriculum is weak and horribly

one-sided, and that it can only be successful

if substantially augmented with materials directed toward
basic math

skills and more math content that would put the group
activities in

a meaningful context. xxx felt
that many of the TERC projects

had little math content and involved mostly meaningless
games.

2. The principal at this school is
covertly in favor of supplementation,

but is apprehensive about letting outsiders know that this
is going on.

The general policy seems to be ``Don't
ask, don't tell.'' Or, as

one colleague of xxx put it: ``If you're going to do
something involving

algorithms next week, you'd better block the door and cover the
windows''.

Teacher xxx was, at another time,
chastized at a TERC training session

for attempting to mention non-TERC stuff.

3. xxx agrees
with teachers interviewed at other schools (where CMP was

used) that progress through all the group work mandated by
TERC was painfully

slow. No one in this school ever got through more than 6 of
the designated

11 units of the grade 4 TERC program,
and many only managed to do 5.

At some District School Board meetings
Lucy West (head of the Math Office

leading the effort to install contructivist programs throughout
District 2)

has challenged this criticism by arguing that some schools
allocate less

time to math than others, and suggested that maybe I've been
talking to the wrong schools.

That is certainly not so in this
school, which spends 1.5 hours every day on

math. In fact, so much time is spent on math and literacy
there is little time

for social studies or anything else.

4. xxx also
finds it very difficult to adapt the TERC program to the diverse

needs of students in her class and (covertly) tries to keep
the

brighter kids from getting bored by giving them extra
assignments and

references for outside reading. xxx does
this at some risk; there could be

considerable trouble if word leaked out.

5. The thing that xxx,
and many other math teachers at her school most

resent is that teachers are now being controlled in all
aspects of their

activity. 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. The atmosphere being created by Lucy West's trainers
and school administrators

is alienating many of the experienced teachers (toward
whom the TERC advocates

generally show contempt), and is inducing younger teachers to
look toward

other locations where ability to teach math is actually
appreciated, and

probably better paid too.

Attempts by TERC trainers to control
and micromanage teacher actions in

class runs very deep. Certain words, such as ``algorithm''
are to be avoided;

in some settings teachers are being told to use the exact
script provided by

trainers, without deviation. For instance, it is considered
deviant for a

teacher to write out the setup for a multiplication problem in
vertical

form:

48

x 13

____

?

That smacks of ``algorithms''!
Teachers are required to write it horizontally

as 48 x 13 = ? , so
it fits with the ``friendly numbers''" trial and

error methods being promoted by TERC proponents. God forbid
that a teacher

should actually teach the standard addition or multiplication
algorithms

(as xxx did)!

6. xxx feels
that everything in the TERC curriculum has been seriously

``dumbed down''. xxx
has been teaching math at various levels for a long time,

and is struck by how much less math actually gets covered
under the

new program as compared to what got accomplished just a few
years ago.

Yes, xxx says, the weaker students may
benefit a bit from TERC, but the effect

on mid- and higher-level students is going to be
disastrous.

To illustrate the inanity (xxx's
words) of some TERC projects,

xxx recounted a recent training session in which the
trainer spent 2.5 hours

demonstrating how to work with a group of students discussing

``how many ways can you figure out $63
\times 16$ using manipulatives.''

xxx noted that the trainer seemed completely unaware that
most kids in the

group of 30 students ceased paying attention after about the
first 30 minutes.

It was BORING beyond belief, yet the
trainer hadn't a clue.

7. xxx finds
the approach of TERC proponents quite anti-intellectual.

After another prolonged training
session in which 4th graders spent many hours

coloring an array of numbers to illustrate connections between
the entries,

xxx asked the trainer: ``I don't see the point of spending
so much time on

all this. What math concepts does it illustrate or lead
to?'' The response:

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

What better definition could you find
for the notion of ``dumbed down''?

8. To sum up: xxx felt that one of the
insidious effects of these programs was the

impact on teacher morale, mentioned above. Though the program
may have some

benefit for the weakest kids, for the
rest, the impact will be

disastrous in the long run. Finally, xxx notes that: ``The only one who will

really benefit from these programs are the Stanley Kaplan
training

centers -- for them it will be a godsend.''