Fred Greenleaf

Professor of Mathematics

Courant Institute

New York University


Memo to NYU colleagues and District 2 parents



Spring, 2001


  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

website, which discusses the impact of these constructivist programs in

California 1990-1997 and their ultimate rejection by the State of California

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

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





   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.''