Professor of Mathematics
Memo to NYU colleagues and District 2 parents
Teacher responses to the Math Programs being implemented in District 2
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.
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
. 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 8th 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
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
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
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.''