This article appeared as an op-ed in the New York Sun, Thu Feb 6, 2003. The editors pulled out the following to catch attention: "Joel Klein would do well to reverse himself and listen to the advice about successful curricula that mathematicians and others have provided to him and his staff."

Related Web references: Chancellor Joel I. Klein's "Children First" New Standard Curriculum for NYC Public Schools # Reviews of UCSMP Everyday Mathematics # The Many Ways of Arithmetic in UCSMP Everyday Mathematics # Spiraling through UCSMP Everyday Mathematics # BJB Essays and Opinions # New York City HOLD # Mathematically Correct.

Thanks to Elizabeth Carson, David Klein, and Martha Schwartz for their advice about this article.

Klein's Math Problems

By Bas Braams

The New York Sun

Thursday February 6, 2003

On January 21, following a period of secretive planning, Schools Chancellor Klein and Deputy Chancellor Lam announced a new standard curriculum for reading and writing and mathematics in New York City public schools. The standard curriculum will apply to all but about 200 of the 1,200 public schools, and will be introduced for reading and writing this coming fall, and for elementary school mathematics in fall 2003 or fall 2004 at the discretion of the schools.

Many were quick to applaud the action of the chancellor for bringing order into chaos, but the curricula he chose have serious defects. Of particular concern is the announced elementary school mathematics program, Everyday Mathematics, sometimes also called Chicago Math.

Everyday Mathematics requires massive fixes at the most basic level. The program does not teach the standard procedures at all for subtraction and division, and offers a hopelessly confusing potpourri of methods for all the four elementary operations (addition, subtraction, multiplication, and division). The program has pedagogical features (notably, rapidly jumping around over different topics without staying focused long enough for pupils to achieve mastery) that appear to make it all but unworkable as intended. It introduces calculators as early as kindergarten, and this will contribute to the failure of many pupils to acquire proper facility with numbers and operations.

The administration has responded to these failures by selecting also the Math Steps basic skills supplementation program and by allowing an additional year for teacher training before the new program must be used in the schools. But this is an absurd strategy. Mr. Klein is under no obligation to suffer the defects of Everyday Mathematics.

In choosing Everyday Mathematics, a program twice rejected in the thorough and careful California textbook adoption process, Mr. Klein ignored offers of assistance and advice from mathematicians and scientists from New York City universities and from across the country. Some valuable information that they have provided on school mathematics programs is available at the Web pages of New York City HOLD (www.nychold.com), an organization of parents, mathematicians, educators, and others concerned with K-12 mathematics education in New York City.

To see the defects of Everyday Mathematics, one need only examine its treatment of paper-and-pencil subtraction of two multi-digit numbers.

Most adults will have learned to write the smaller number below the larger one, lined up at the right, and write down the result of the subtraction right to left, doing whatever "borrowing" is needed mentally. This is not taught in Everyday Mathematics. Instead, the Everyday Mathematics pupil is exposed to five different subtraction methods, each of them viewed as suitable for the same task. The gymnastics employed to avoid simple methods is truly breathtaking.

There is in Everyday Mathematics a "trade first" variant of the traditional method: Borrow first in all columns where it is needed, recording the intermediate results, and then do the subtractions. There is a "counting up method": count up from the smaller to the larger number, first by ones, then tens, and so on, and then the odd remainder, and then in a second pass, add up the addends. (Example: If we do 425 - 48 then the second stage involves adding up 2 + 50 + 300 + 25 to obtain 377.) The third standard method is left to right subtraction, the way one might well do the problem mentally, but carried out with paper and pencil. The fourth approach is a "partial differences method": subtract in each column separately, keeping track of the sign if a borrow would be needed, and then combine the results by mental arithmetic. Finally there is the "same change rule": change both numbers by the same amount so that the smaller number ends in one or more zeroes and the problem is easier. Addition, multiplication, and division likewise have multiple standard methods in Everyday Mathematics, and in all of this, true fluency in the basic operations appears not to be an aim of the program.

One can well imagine how a pupil who already has excellent mastery of arithmetic can enjoy seeing and understanding how the multiple methods of Everyday Mathematics all lead to the same correct result. The danger of this profusion of methods for pupils who are not so comfortable with the basics is also easily imagined. These pupils, and some teachers and parents as well, will be hopelessly confused. Combine that with the easy tolerance of calculators in Everyday Mathematics and one can foresee that entire classrooms will throw up their hands and rely on the calculator for arithmetic, never to achieve the facility with number and operation that they'll need to advance beyond the grade school level.

Everyday Mathematics combines the very defective treatment of basic arithmetic with some quite sophisticated content elsewhere, resulting in a strange mixed bag that ought never have been selected for city-wide use in the elementary schools. Mr. Klein would do well to reverse himself and listen to the advice about successful curricula that mathematicians and others have provided to him and his staff. As one example, I would suggest that the chancellor look hard at the documented results of the Saxon Math curriculum. He can start by perusing the input provided by New York City HOLD to the Chair of the Children First Numeracy Working Group and available through the NYC HOLD Web pages.

Mr. Braams is a research associate professor in the department of mathematics at New York University.

(Please note as well: Reviews of UCSMP Everyday Mathematics # The Many Ways of Arithmetic in UCSMP Everyday Mathematics # Spiraling through UCSMP Everyday Mathematics # New York City HOLD # Chancellor Joel I. Klein's "Children First" New Standard Curriculum for NYC Public Schools # Links, Articles, Essays, and Opinions on K-12 Education.)

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