Baby boomers with bad memories of learning “new math” in elementary school can be forgiven if they get an unpleasant feeling of deja vu when confronted with their children’s arithmetic homework. As Tom Lehrer sang:

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!

New math has grown old, but now there is new new math. It dominates the math curriculum in New York City schools and, like its predecessor, baffles parents and attracts controversy.

Earlier this month, the city announced that last year’s fourth graders scored far better on a state standardized math test than fourth graders the previous year. Most of the 2004-2005 fourth graders had had some of the new new math. But the results are unlikely to spur either side to call a truce in what some have called the math wars.

MATH CURRICULUM

For years, individual community school districts -- and sometimes even individual schools -- chose their own math curriculum. But after Mayor Michael Bloomberg won control of the school system in 2002, his Department of Education instituted uniform math and language arts curriculums in the vast majority of city schools.

Critics first attacked the idea of uniformity and then the Department of Education for the programs it chose.

The selection for the reading curriculum revived the decades old conflict between phonics -- in which students sound out words -- and so-called the whole language approach, where students learn to recognize words in books, often of their own choosing. To the chagrin of some, the city went with whole language, supplemented by phonics instruction.

Rote Calculations vs. Complete Math

A similar battle revolves around math. This bitter dispute pits proponents of a traditional approach where students eschew calculators and learn the fundamentals of rote calculations against advocates of what is called constructivist or complete math. In complete math, students learn concepts and several alternative ways of solving problems and try to incorporate problems from real-life experiences. This, its advocates say, helps students become mathematically functioning or “numerate.” The work can bewilder even a mathematically savvy parent whose mind boggles as their children discuss “strategies" for solving problems and, when subtracting, work their way from left to right (starting with, say, hundreds and moving to the tens and then ones) rather than the other way around, which is more traditional.

The city came down squarely on the side of reformers. It selected Everyday Math, a program developed at the University of Chicago in the 1980s. Almost three million students in grades kindergarten through six currently use it, according to its Web site. Thomas Loveless of the Brooking Institution has described it as “the most sensible” of the new new math programs and Everyday Mathematics has been endorsed by the National Science Foundation.

It also has attracted legions of critics. Some, including a number of mathematicians, have formed an organization called NYC HOLD (it is supposed to stand for Honest Open Logical Decisions on Mathematics Education Reform) to express concerns about the program. One member of its steering committee, mathematician Bastiann Braams, has written that Everyday Mathematics “offer[s] a hopelessly confusing potpourri of methods” for computation and, by introducing calculators to very young students “will contribute to the failure of many pupils to acquire proper facility with numbers and operations.”

But supporters counter that the traditional approach their critics remember so fondly did not work. To bolster their case, they note that U.S. students do not perform as well in math as their counterpoints elsewhere in the world. “In the field of children's learning of arithmetic, there is significant research to show that the force-feeding of computational procedures is harmful,” wrote Thomas C. O’Brien, a professor of education at Southern Illinois University. “But the critics continue to insist that arithmetic -- and knowledge in general -- is inert stuff to be transmitted and stored.”

Since neither Mayor Michael Bloomberg nor his school chancellor Joel Klein had any education experience to speak of, it is generally believed they relied on the advice of Diana Lam, then the number two person in the department, to select a program. As superintendent in San Antonio, Lam used Everyday Mathematics, and scores rose. After she left, though, the system dropped the program.

TEST SCORES

It would be nice -- and no doubt a relief to New Yorkers who simply want the city’s kids to get a good education -- if the test scores announced in late September could cast some light on this debate. Unfortunately, they don’t.

Some of last year’s fourth graders had more than a year and a half of Everyday Math when they took the test. But many others attend schools where the program had not yet been implemented.

Certainly the fourth grade scores seem like good news. New York City fourth graders saw their scores rise almost twice as sharply as did children in schools throughout the state as a whole with more than three-quarters of them meeting or exceeding state standards. And the scores for black and Hispanic fourth graders rose more than those for white students.

“If this isn’t good news, I don’t know what is,” Mayor Bloomberg said. Calling the scores “eye-popping,” the Daily News cheered, “clearly, something’s working.”

Many disagree, not all of them Democrats interested in unseating the mayor. These critics downplayed the significance of the results, seeing the cloud around the silver lining.

Eighth Grade Scores Declined

Many pointed to the poor eighth grade results. Scores for eighth graders declined by 1.6 points last year. The middle school version of Everyday Mathematics -- Impact Mathematics -- is being used, but the change came too late to affect last year’s eighth graders.

An analysis of the numbers by Public Advocate Betsy Gotbaum found that in 76 city schools, not a single eighth grader out of the more than 9,000 tested in those schools got the highest of the four grades on the test. (The tests are marked on a scale of one to four with four meaning that a child far exceeds the state standards.) In 39 of those schools, only 20 percent of kids met state standards. “Clearly, we need to invest more resources in our middle schools so that these students will be prepared to succeed in high school," Gotbaum said in a statement.

Election Year Statistics

Some questioned the validity of the scores, particularly in an election year. “New York State has historically overstated gains in the state,” Diane Ravitch, a professor of education at NYU, said in a radio interview.

“Double digit leaps should raise eyebrows” said Elizabeth Carson of HOLD, noting that large jumps in some individuals schools “cause us to be extremely cynical.” Problems could exist in how the text is scored, for example, she said.

And while math and reading scores may have gone up Ravitch said, all signs point to poorer student performance in other areas. “It’s not just a matter of having them [students] ready to take the test,” she said. “but having them able to read science and read history textbooks and make sense of them.”

Too Easy, Too Much Prepping, Taking Away From Other Subjects

Others, such as Clara Hemphill of Inside Schools, has said the test may be too easy . (You can judge for yourself by looking at test questions (in pdf format).

Even if the test scores are completely valid, it is difficult to use them to measure any single program among the many Bloomberg and Klein have instituted in the past three years. For better or worse, schools now spend more time on reading and math than they did previously -- and less on science, social students and the arts.

Schools have provided extra help to struggling students. “The remedial effort and the intensive effort for struggling students may be more effective than the core curriculum,” said Carson.

Again for better or worse, teachers and principals put a lot of emphasis on test preparation. Some schools offer supplemental classes or tutoring to help students bring up their scores. Students take practice tests and are told in no uncertain terms that the tests matter -- and matter a lot. For fourth graders, the test can pay a major role in determining what middle school the child will get into, spurring parents to hire tutors and buy test guides.

Is It Curriculums, Or Teachers?

Chancellor Joel Klein himself has said he is not sure how much difference a curriculum makes. “I think it’s a less filling/tastes great,” debate he told James Traub of the Times. “I don’t believe curriculums are the key to education. I believe teachers are.”

It will take years before we know what, if any effect Everyday Mathematics has on test scores -- and we may not know even then. Carson notes that the state is instituting new tests next year. That could make comparison between years -- and between the pre and post Bloomberg days -- largely meaningless.

BACK TO SCHOOL

The return to class for most of New York City 1.1 million public schools student proceeded calmly -- except for first-day jitters, anticipation and sometimes dread. The crises of previous years -- extreme teachers shortages or thousands of kids finding themselves without classes or even a school to attend -- appeared largely absent.

The city announced it would mark the new year by extending its new promotion policy, which requires a student to pass a standardized test, to seventh graders. The Department of Education said it had expanded gifted and talented programs to neighborhoods -- particularly poorer parts of the city -- that had had few if any such programs in the past. And it opened 53 new small high schools, at least one of which, Young Women's Leadership School in Queens, did not have a home. Sixteen charter schools, which are privately run but publicly funded, also began operation, including one run by the United Federation of Teachers.

But while teachers teach and students learn, controversies continue outside the classroom. Education has been, and will continue to be, a key issue in this year’s mayoral campaign. The state is still fighting a court order that it provide billions more dollars for education in the city.

And teachers and principals entered their third academic year without a contract. Teachers union president Randi Weingarten has called on the mayor to reach agreement with the union and has threatened to either endorse Fernando Ferrer or go out on strike if he doesn’t. The latter would be illegal -- and would certainly end the calm that marked the start of classes.