December 17, 2002

Chancellor Joel Klein

Office of the Chancellor

New York City Department of Education

52 Chambers Street

New York, NY 10007

Dear Chancellor Klein,

We are Chairs and administrators of mathematics at New York City colleges and universities and are writing to express our concern about K-12 mathematics curricula that have recently been implemented in New York City. These curricula, based on the 1989 Standards [1] of the National Council of Teachers of Mathematics (NCTM), were adopted by the Board of Education under your predecessors, despite the fact that they had been strongly criticized in a 1997 open letter [2] addressed to then Secretary of Education Richard Riley and signed by 200 academics, including Nobel Prize and Fields Medal winners, representing a wide spectrum of mathematics and science departments at U.S. institutions.

More recently, the Spring 2001 Commission on Mathematics Education [3], chaired by CUNY Chancellor Matthew Goldstein, stated in its draft report: "the NCTM standards do not contain the rigor, algorithmic approach, formal methods, and logical reasoning which are required [of] students who will go on to become scientists, engineers, mathematicians, computer scientists, physicians, and educators of mathematics." We fully concur.

In New York City, curriculum developers, BOE officials, and schools of education for decades experimented with K-12 math curricula without impacting the distressingly large proportion of high school graduates whose deficient math skills exclude them from the careers listed above and many others as well. Omitted from these efforts were representatives of university mathematics and science faculty who, at the very least, should have been consulted for their views on the type of mathematics instruction needed by college-bound students. We are now asking to participate actively in curriculum reform efforts, and one purpose of this letter is to offer our views on necessary structural change in those efforts and to explain how we can be of assistance.

More specifically, we wish to underscore our concern that a decision by the Working Group on Numeracy to continue support for defective curricula will profoundly damage the career opportunities of New York City children, the viability of mathematics and science programs at many CUNY colleges, and the economic infrastructure of New York City, which is increasingly technology-based and so dependent upon the supply of mathematically competent students entering the workforce. Because we are not represented on it, we are writing to ensure that the working group, as well as Dr. Lam and yourself, are aware of the following issues that have often distorted discussions of mathematics education.

* Our disagreement with the driving principles of curricula such as TERC, CMP, ARISE, and IMP is principally about what is taught: they are content-poor. However, that lack of content is in turn forced by a pedagogical model that is defective in multiple ways.

* Claims, that 1989 NCTM-Standards based curricula foster critical thinking skills and higher order thinking, are rhetorical constructs for the profoundly dangerous perception that concrete and pictorial representations are a substitute for basic algebraic skills.

* We are not advocates of any specific New York City curricula or style of pedagogy that preceded the introduction of NCTM Standards-based curricula.

* We do advocate experimenting with curricula that have achieved good results in the United States and outstanding results in Singapore, whose English-language mathematics curriculum has propelled students to first place in international comparisons.

* We are prepared to explain in detail why certain education research studies cited nationally and locally, particularly in District 2, in support of NCTM-Standards based curricula are, in a word, deceptive. Whether or not the deception is intentional, close examination of these studies reveals:

- study and control groups were improperly matched with respect to critical parameters;
- the failure to track the effect of outside tutoring invalidates claims of improved performance;
- there was a disastrous slide in year to year performance of student cohorts in some District 2 schools with heavily minority student demographics;
- an enormous financial and administrative investment in teacher training yielded at best a marginal improvement that was educationally insignificant;
- and the testing instruments used in some cases were so poorly constructed that they did not measure critical basic skills.

We do not wish to harp on the errors of the past. We wish to offer our support for the Children First Initiative and believe we can provide constructive assistance in many ways. As you know, CUNY, NYU and other mathematics departments are hoping to participate in a new NSF initiative, which is of critical import in the present discussion because it seeks to support collaborations between university mathematics departments and K-12 school districts. Such an effort can be effective only if it is informed by co-operation and collaboration between ourselves and DOE mathematics education officials, including especially the members of the Working Group on Numeracy.

In conclusion, we wish to emphasize the need for active collaboration between CUNY mathematics departments and the DOE. About 60 percent of the CUNY entering class is comprised of graduates of the public school system. In turn, the City University produces about 40 percent of the teaching workforce. The past failures of mathematics education in New York City are coming full circle, as evidenced by observations of K-6 teachers who don't know whether the numerator of a fraction is above or below the fraction line and who think that 1/4 is larger than 1/3 because 4 is greater than 3.

For the sake of New York City's children, first and foremost, we want such spectacular failures to become a memory of the distant past. We are anxious to participate actively in the work of the Children First initiative and await your response.

References

[1] Curriculum and evaluation standards for school mathematics, National Council of Teachers of Mathematics, Reston, VA., 1989, pp. 21, 73, 127.

[2] An open letter to United States Secretary of Education Richard Riley, Washington Post, November 18, 1999, available at www.mathematicallycorrect.com/riley.htm.

[3] Report of the panel on mathematics education in New York City schools, Board of Education of the City of New York, Press release N-141, May 30, 2001, available at www.nycenet.edu/news/press/00-01/.

Sincerely yours,

Prof. Sylvain Cappell - Chair of Faculty Appointments and
Promotions

Courant Institute of Mathematical Sciences (NYU)

Prof. Robert Feinerman - Chair - Dept. of Mathematics and Computer
Science

Lehman College (CUNY)

Prof. Wallace Goldberg - Chair - Dept. Of Mathematics

Queens College (CUNY)

Prof. Warren Gordon - Chair - Dept. Of Mathematics

Baruch College (CUNY)

Prof. Ed Grossman - Chair - Dept. Of Mathematics

City College (CUNY)

Prof. Erwin Lutwak - Chair - Dept. Of Mathematics

Polytechnic University of New York

Prof. Charles Newman - Acting Director

Courant Institute of Mathematical Sciences (NYU)

Prof. George Shapiro - Chair - Dept. Of Mathematics

Brooklyn College (CUNY)

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