Professional development for
Mathematics Education reform in New York City

A letter to the New York City Board of Education, January, 2002, urging them to forego $9M in Federal moneys supporting fuzzy mathematics. The contracts that the Board were asked to approve supported teacher training for a variety of NCTM-based programs including TERC, Everyday Math, CMP, Math in Context, ARISE, IMP, Math Connections and Math Trailblazers. The Board decided to take the money.

Please see the Education Page of Bas Braams - Links, Articles, Essays, and Opinions on K-12 Education - and the NYC HOLD page for related matter.

to: Members, NYC Board of Education
by Facsimile and/or Email

Dear Members of the Board,

Before you at your meeting on Wednesday, January 23, are agenda items #1 and #2 to approve over $9M in contracts funding instructional and professional development programs in mathematics. The associated NCTM-based programs include, as I understand the resolutions, TERC, Everyday Math, CMP, Math in Context, ARISE, IMP, Math Connections and Math Trailblazers, and the associated contract partners include Marilyn Burns Education Associates Inc., the Mathematics in the City Project at CUNY, and the New Visions for Public Schools organization.

You would do better to throw $9M on a bonfire.

I write from the perspective of a physical and mathematical scientist who has paid attention to the mathematics curricula in the local schools and to national standards in mathematics and science education, and also as a citizen concerned about the enterprise of science and technology in this country.

The programs and organization that are to be supported under resolutions #1 and #2 support the failed ideology of constructivist mathematics teaching. Like its failed sibling, Whole Language for beginning literacy training, constructivist mathematics pedagogy stands in opposition to teaching, in opposition to education, and in opposition to student mastery of basic content and skills. It is a destructive and discredited philosophy, and the programs that are proposed for support represent its failed implementation. It is most unfortunate that the Chancellor's Office proposes this kind of ideological professional enhancement, which will only weaken education, rather than much needed professional enhancement focussed on improving teachers' mastery of subject matter.

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In the remainder of this letter I will provide more detailed criticism of some of the local mathematics curricula. I appreciate that this level of detail may seem to fall outside the Board's domain, belonging rather to the Chancellor's Office proper. I believe, however, that the Chancellor's Office is so deeply committed to the underlying failed ideology and failed practices that it is time for the Board to step in and critically review these curricular issues. I should also provide an alert that, in a sad reflection of the nationwide character of some underlying educational trends, the failed curricula promoted by the Chancellor's Office are often advertised as ``standards based'' or ``nationally validated''; indeed, these two phrases signal in practice an anti-educational and anti-intellectual character of the curriculum.

For the K-5 grades in NYC the most widespread of the anti-educational mathematics programs appears to be Investigations in Number, Data and Space, better known as TERC --- a prime example of the trend against content mastery and teaching. The program does not come with proper student textbooks (which only inhibit creativity), and the shelf-full of teacher material emphasizes discovery learning and student-developed algorithms. As a result, TERC fails completely to provide pupils with mastery of the basic arithmetic skills that are essential for the pupils' satisfactory performance in middle and high school science, mathematics and technical subjects, never mind their adequate functioning in the labor market. A mathematician colleague observed that in the entire set of TERC K-5 student materials only 20 computations require the use of the more difficult multiplications 6x6, 6x7, 6x8, 6x9, 7x7, 7x8, 7x9, 8x8, 8x9, 9x9. That is a concrete echo of the philosophy of TERC in which mastery of this third-grade material is not an important component of the K-5 education.

More detailed, devastating critical commentary on TERC may be found on two web sites: and

The anti-educational slant in NYC K-12 mathematics education continues in middle school, where CMP, or Connected Mathematics Program, appears to have earned strong backing from the Chancellor's and Districts' curriculum specialists. With regard to CMP I quote from a review of 7th grade mathematics texts on the web site,

"Mathematical Depth: There is very little mathematical content in this book. Students leaving this course will have no background in or facility with analytic or pre-algebra skills.
Quality of Presentation: This book is completely dedicated to a constructivist philosophy of learning, with heavy emphasis on discovery exercises and rejection of whole class teacher directed instruction. The introduction to Part 1 says ``Connected Mathematics was developed with the belief that calculators should be available and that students should decide when to use them.'' In one of the great understatements, the Guide to the Connected Mathematics Curriculum states, ``Students may not do as well on standardized tests assessing computational skills as students in classes that spend'' time practicing these skills.''
Quality of Student Work: Students are busy, but they are not productively busy. Most of their time is directed away from true understanding and useful skills."

For a different and in a way more striking, review of CMP I point to The authors of that review are clearly sympathetic to discovery learning and to the general philosophy of the CMP program (and I fault them for it), and yet they write (pages B-3 and B-4):

"The number strand is arguably the most basic and fundamental mathematics strand and much of the presentation in CMP is below the level articulated in the 2000 NCTM number standard for grades 6-8. Specifically we find that CMP students are not expected to compute fluently, flexibly and efficiently with fractions, decimals and percents as late as 8th grade. Standard algorithms for computations with fractions (e.g. (a/b)*(b/c) = a/c; (a/b)/(a/c) = c/b) are often not used.
Conversion of fractions to decimals is discussed only in simple cases such as for fractions with denominators of ten, and CMP lacks a discussion of repeating decimals. A discussion of long division is also missing. [...] Multiplication of fractions is discussed in 7th grade but mostly in simple cases.
We feel that CMPs overwhelming emphasis on conceptual development neglects standard computational methods and techniques."

At the high school level the saga of NYC K-12 mathematics education continues, now with the ARISE/COMAP and IMP curricula in the favored anti-educational spot. I have paid most attention to ARISE, mandated in my local District, but I believe that IMP is no better. The program seems to take great care to present mathematics as an imprecise science that does not offer exact answers to society's needs, and again it adheres to the philosophy of discovery learning. The mathematics content is diffuse, imprecise and meager, and it is a severe and wholly unreasonable challenge even for talented students to learn mathematics through this curriculum. I am afraid that it is in fact precisely these features that endear the program to the curriculum experts of the NYC schools system --- it appears not to be their goal that students learn mathematics, but only that they explore, discuss and articulate mathematical concepts.

* * *

In conclusion, I observe that the NYC K-12 system suffers from a failed educational ideology and a failed implementation in mathematics instruction, and the Chancellor's Office is deeply committed to the philosophical roots of this failure. It is time for the Board of Education to recognize failed ideology and failed curricula and to impose change towards proper teaching, proper education, and student and teacher mastery of subject matter content and of basic skills.

In connection with the matter immediately before you this Wednesday, I urge you to reject the Chancellor's request to fund the proposed programs for instructional and professional enhancement in mathematics.

Yours Sincerely,

Bas Braams

cc: Schools' Chancellor Harold O. Levy
Selected elected officials

Bastiaan J. Braams -
Courant Institute, New York University
251 Mercer Street, New York, NY 10012-1185

The opinions expressed in this page are strictly those of the page author. The contents of this page have not been reviewed or approved by New York University.