Testimony at School Mathematics Education Hearing of NYC Council Education Committee, November 5, 2003

City Council Education Committee Meeting
November 5th, 2003

Testimony of (Prof.) Stanley Ocken
The City College of City University of New York


1. New York City K-12 mathematics education is in chaos.

2. The DOE has chosen to adopt as a uniform curriculum Everyday Mathematics, an expensive and complex program that under the best circumstances has been shown to provide only slight improvement in the performance of third, fourth, and fifth-grade students.

3. The most optimistic extrapolation of that improvement will not raise the mathematics competence of most New York City high school graduates to the level required by the entry-level mathematics courses offered in New York City's senior colleges.


My name is Stanley Ocken. I am Professor of Mathematics at the City College of CUNY. I will begin by commenting on misleading testimony offered earlier at today's hearing. Referring to a large-scale study ("the ARC Tri-State Study") of three reform curricula:

Professor Fosnot asserted that the study results demonstrated "significantly higher" test scores for the reform students vs.the control group. In this context, the word "significant" is universally understood to mean "large" or "important" or "of significant consequence." In fact, the ARC Study drew no such conclusion. Rather, its Executive Summary stated

"The reform students consistently outperformed the comparison students: All significant differences favored the reform students; no significant difference favored the comparison students"

The term "significant" in this statement is an abbreviation for the purely technical term "statistically significant." It means only that the sample was sufficiently large to ensure reliability of the test results. In no way does it characterize the magnitude or importance of the improvement in scores shown by the test group.

I view it as unfortunate that the ARC study chose to use abbreviated terminology, given the tremendous potential for misinterpretation. In fact, the study does not state that the difference in scores is of any educational significance whatsoever, for it would be entirely inappropriate for an unbiased statistical report to do so.

In fact, the difference in scores was extremely modest. The ARC Executive Summary, posted on the Web at http://everydaymath.uchicago.edu/educators/tristate_student_achievement_study. pdf and involving over 100,000 students, reports

The average score of the Reform students was 66.8%
The average score of the Control students was 65.0%

My observation: if the test contained 55 questions, then, on average:

To apply these results to New York City mathematics education, one must understand that the mathematical competence of most New York City high schoool graduates is appalling. The vast majority haven't mastered the very minimal mathematics required for entrance to a senior college of CUNY. Even worse, of those who do, the vast majority are unprepared for college level mathematics. Finally, of those who enroll in college math courses, a large portion drop or fail.

The disturbing assertions of the previous paragraph would be changed not a whit if the preparation of New York City high school graduates were to show the slight improvement shown by the Reform students in the ARC Study. In my view, the results of the ARC study are of no use whatsoever in setting educational policy in New York City.

New York City high schools are graduating an appallingly large percentage of students who cannot correctly perform the most basic operations with fractions, decimals, and percents. Ample evidence for this statement is provided by the results of the CUNY Skills Assessment Test (SKAT). Students gain entrance to a senior college if they correctly answer 25 questions on a test that contains 20 questions on 8th grade or lower level arithmetic (fractions, decimals, percents, and a bit more) and an additional 20 questions on basic algebra and graphing techniques. Only a minority of high school graduates score at that level. Even worse, this cutoff is drawn at a level of mathematics competence far below that required for placement into the lowest level mathematics course at CCNY, and, I suspect, at the other senior colleges.

While the underlying causes of the above stated failures are complex, one treatable cause is the total lack of co-ordination among assessments used in the K-16 educational continuum. Specifically, the New York State 4th grade, 8th grade, and Regents A assessments are astonishingly free of the sorts of questions needed to measure student achievement in basic skills involving fractions, decimals, percents, and elementary algebra.

The impact of the chaos in K-12 mathematics education cannot be overstated, particularly with respect to the aspirations of ESL students, whose entrance into the job market has in the past been facilitated by mathematical, as opposed to linguistic, competence. All students deserve a shot a careers in science, engineering, business, medicine, secondary mathematics education, and many others, all of which require at least one semester of college calculus.

I will always remember a conversation with an education school colleague who, when asked to estimate the portion of college students taking calculus, came up with an answer of "about one percent." In fact, in September 2000, the number of U. S. senior college students enrolled in first year calculus was over forty per cent of the number of students registering as entering students in those institutions.

K-12 educators should prepare their students for success, not failure. Unfortunately, much of the "reform" movement is moving in the wrong direction. In influential circles, including those with decision making power at the DOE, the reigning buzzwords are "higher order thinking", "focus on real-life problems" , and "conceptual understanding. " These are Mom-and-apple-pie disiderata, but in the context of mathematics education discussions, they should be recognized as disingenuous code phrases that in practice signal abandonment of fluent and automatic symbol manipulation skills as the most critical goal of college preparatory mathematics.

I urge the City Council Education Committee to exercise its influence and authority by moving New York City DOE policy away from that potentially disastrous perspective.


1. The DOE should immediately reconsider its choice of curricula and use as criteria for adoption: appropriate emphasis on basic skills development, simplicity of implementation, and appeal to teachers. The adoption process should be public. In particular, teachers must be free to voice their opinions without fear of retribution.

2. Integration of K-16 mathematics education into a seamless curriculum, a principal recommendation of the Year 2000 Math Commission chaired by CUNY Chancellor and mathematician Matthew Goldstein, should be a primary focus of DOE policy. Accordingly, decisions on K-12 curriculum should be made only with the full voice of CUNY and other university mathematics faculty who are nominated by the chairs of CUNY mathematics departments.

3. Individual student performance should be tracked throughout K-16 in order to measure the performance of the K-12 school system. There will be pressure for meaningful improvement only when there is clear documentation of the miniscule success rate of those students who begin elementary school in New York City and finish by passing a CUNY math course.

4. New York City should impose its own assessments, relevant to the needs of all students, with appropriate emphasis on the needs of those who are college bound. Those assessments should be aligned with grade-appropriate materials on the CUNY mathematics entrance test. The DOE should publicize student peformance, or lack thereof, on these assessments and use that data to pressure New York State to revise its 4th grade, 8th grade, and Regents Exams to align with the needs of college-bound students.

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