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25th June

First Published in The New York Sun, June 25, 2004

By Andrew Wolf

Hooray for new math, New-hoo-hoo-math, It won’t do you a bit of good to review math. It’s so simple, So very simple, That only a child can do it! o sang the satirist (and college mathematics professor) Tom Lehrer.The new math he was referring to was the kind of math taught to me at J.H.S. 79 in the Bronx by my seventh-grade math teacher, Helen Kaufman.

There was no attempt to salvage our selfesteem other than the satisfaction we got from getting exactly the right answer. Mrs. Kaufman stretched our thinking about numbers by teaching us to solve problems in base-eight, rather than the familiar base-10 or decimal system. Mr. Lehrer offers a fine definition of this system: “Base eight is just like base ten really — if you’re missing two fingers.”
Most of us got it, without sacrificing any body parts.
This teaching has served me well, right up to this day. When I did it in school it was painful, often downright unpleasant. If given a choice at the time, I would have skipped it all. Fortunately, no one cared what I thought. School is often about learning those things you don’t think are important right now, but with maturity and hindsight recognize as essential.

We’ve strayed from that ideal with today’s constructivist, or fuzzy, math. Pupils today must “solve problems,” often working collectively in groups to “construct” their own methods and answers. Even the wrong answer is okay. To facilitate this type of teaching, math problems on standardized tests now typically use small numbers to enable the child to develop his own methodology.

That’s why I’m so skeptical about the recently released standardized test scores for math. This testing problem is not a reflection on Chancellor Klein, other than the fact that he has promoted the spread of this ersatz type of math instruction. The truth is that there have been questions of confidence with the results of these math tests for several years.

Consider that math scores on last year’s fourth-grade state-administered test (this year’s test results are not yet available) rose to 66.7% on grade level from 52% between 2002 and 2003. Impressive. But when those same children, this year’s fifth-graders, took this year’s city test, only 38.5% scored at grade level. Did they become stupid in one year? Or do we need to re-evaluate both our curriculum choices and our testing procedures?

I offer the following challenge. Take a reasonable sample of New York City students today, perhaps 10% picked at random, and administer the same math tests we used 10 or 15 years ago, before the system was dumbed down with fuzzy math. I predict that the results won’t be pretty.

Complicating all this is that the fuzzy math program that the Department of Education is implementing in the lower grades is “Everyday Math,” published by McGraw-Hill. But the same firm is also the one that provides the city with the math tests. In other words, McGraw-Hill will be testing the efficacy of the programs it is selling to us. I’m sure all concerned are honest and above board. But the inherent conflict in this should be apparent.

A teacher from Washington Irving High School sent me an e-mail a few days ago with distressing news regarding the results of the “Math A” Regents examination.

The state education department is bending over backward to make the idea of testing for the mastery of subject matter a cruel joke. They are concerned that precious few high school students will meet the new requirement of passing five Regents exams to earn their diplomas. So they are redefining “passing.”
My correspondent tells me that there are 84 questions on this test, and the passing grade is an already dumbed-down 55. So how many questions must a student answer correctly in order to pass? You say 47? Wrong.

The state education department has decreed that answering just 28 questions correctly earns you a 55 and a passing grade, even though that is only a real score of 33.3%. Can this get worse? Yes, it can.

Sixty of the questions on the test are multiple choice. Merely making random guesses will earn the average student 15 of the 28 correct answers needed to pass. Another 13 right answers and it’s on to Math B. Basically,a student who is able to correctly answer 13 questions, just 15% of the test, and making random guesses on the balance, can pass the test.

I favor taking the testing function away from the city and state education departments and putting it in the hands of an independent board of professionals. Insulated from the political fallout of failure, such an entity could return integrity to the system and could demand that a passing grade once again mean something. This would ensure that the accountability we are looking for from the mayor and governor is real and not some kind of politically inspired new math.

© 2004 The New York Sun, One, SL, LLC. All rights reserved.

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