December 22, 2001.
On January 1, 2002, Mike Bloomberg was going to take office as the new Mayor of New York City, succeeding Rudy Giuliani. Mr. Dennis Walcott, at that time President of the Urban League, was his designated Deputy Mayor for Policy, with responsibilities including Education. I thought it would be useful to offer the incoming Deputy Mayor some quiet advice. The letter was never acknowledged, and nine months later it does not appear that it had an effect on policy.
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: Mr. Dennis Walcott
Deputy Mayor for Policy (designate)
New York, NY 10007
Dear Mr. Walcott,
In your new position as deputy mayor for policy you will represent the mayor on Education. I realize that you know the NYC schools system very well as a parent, past member of the Board of Education, member of Sheldon Silver's advisory group on school governance and president of the Urban League, and as a physicist / mathematician at New York University with only a side interest in K-12 education I should be quite hesitant to offer you any advice or opinion. However, the situation is desperate.
One would think that curriculum has to be a key determinant for the success of a schools system, and one for which the difference between success and failure has pleasantly little correlation with fiscal burden. I have observed K-12 mathematics curriculum here rather closely and am seeing a philosophy and an implementation that is plain detrimental to the pupils' professional and educational prospects, as I will try to clarify in moment. What I have seen of local K-12 practices in science education only amplifies my sense of despair.
I urge you to recognize the pressing need for your new office to make its own assessment of curricular issues, acting independently of the Board of Education, the Schools' Chancellor, the Deputy Chancellor for Instruction and the entire schools and education bureacracy and relying instead on subject matter experts and trusted others outside the present system. You will find, I believe, that the NYC K-12 system has the opportunity to achieve enormous gains simply by adopting well established sound curricular practices. Unfortunately such positive change can, I believe as well, only come about under the influence of a full-press effort from the mayor's side in opposition to entrenched policies - an effort of a kind that one associates with the present mayor, although I don't believe that in his education policy struggles he ever focussed much on curriculum.
In mathematics curriculum, failure is ubiquitous throughout the K-12 system. This failure is part of broad movement away from a sound basic education, away from teaching, away from student mastery of skills and towards student ``exploration of concepts'' and what is insiduously called ``higher level thinking''. In a sad reflection of the nationwide character of this trend these failed curricula 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 6 x 6, 6 x 7, 6 x 8, 6 x 9, 7 x 7, 7 x 8, 7 x 9, 8 x 8, 8 x 9, 9 x 9. 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: [Bill Quirk] and [Mathematically Correct].
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 Board of Education and District curriculum specialists. With regard to CMP I quote from a review of 7th grade mathematics texts on the Mathematically Correct 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 [Adams]. 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) x (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, based primarily on my exposure to issues of mathematics education I believe that the NYC K-12 system is characterized by a failed curricular policy driven by a failed educational ideology. Large improvements in educational outcome are possible, but the present establishment appears to have a great deal of personal prestige invested in the roots of this failure. While an earlier NYC Schools' Chancellor (Mr.~Tony Alvarado) actively promoted the present failed curricular policies, the current Chancellor has, I am afraid, in effect committed himself to continuation of these policies by an attitude of neglect towards curricular failure for so long into his tenure. I am convinced that positive change will only come about through strong pressure from outside the educational system. It is especially important, I think, that there be a strong focus on curriculum from your office, even though under normal circumstances one would view this topic as entirely the domain of the educational authorities. They have demonstrated that their ideology stands in opposition to education.
Bastiaan J. Braams
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.