November 9, 2005
ON EDUCATION
'Innovative' Math, but Can You Count?
By SAMUEL G. FREEDMAN
PENFIELD, N.Y.

LAST spring, when he was only a sophomore, Jim Munch received a plaque honoring him as top scorer on the high school math team here. He went on to earn the highest mark possible, a 5, on an Advanced Placement exam in calculus. His ambition is to become a theoretical mathematician.

So Jim might have seemed the veritable symbol for the new math curriculum installed over the last seven years in this ambitious, educated suburb of Rochester. Since seventh grade, he had been taking the "constructivist" or "inquiry" program, so named because it emphasizes pupils' constructing their own knowledge through a process of reasoning.

Jim, however, placed the credit elsewhere. His parents, an engineer and an educator, covertly tutored him in traditional math. Several teachers, in the privacy of their own classrooms, contravened the official curriculum to teach the problem-solving formulas that constructivist math denigrates as mindless memorization.

"My whole experience in math the last few years has been a struggle against the program," Jim said recently. "Whatever I've achieved, I've achieved in spite of it. Kids do not do better learning math themselves. There's a reason we go to school, which is that there's someone smarter than us with something to teach us."

Such experiences and emotions have burst into public discussion and no small amount of rancor in the last eight months in Penfield. This community of 35,000 has become one of the most obvious fronts in the nationwide math wars, which have flared from California to Pittsburgh to the former District 2 on the Upper East Side of Manhattan, pitting progressives against traditionalists, with nothing less than America's educational and economic competitiveness at stake.

In these places and others, groups of parents have condemned constructivist math for playing down such basic computational tools as borrowing, carrying, place value, algorithms, multiplication tables and long division, while often introducing calculators into the classroom as early as first or second grade. Such criticism has run headlong into the celebration of constructivism by the National Council of Teachers of Mathematics and such leading teacher-training institutions as the Bank Street College of Education.

The strife has taken on a particular intensity here in Penfield, perhaps, because the town includes an unusually large share of engineers and scientists, because of the proximity of companies like Xerox, Kodak and Bausch & Lomb. Skilled themselves in math, they have refused to accept the premise that innovation means improvement, and in their own households they have seen evidence to the contrary.

For Joe Hoover, the epiphany came two years ago when he took his daughter, Kathryn, then in sixth grade, to lunch at McDonald's and realized she could not compute the correct change for their meal from a $20 bill.

For Claudia Lioy, it was seeing her daughter, Iris, then in third grade, plodding through a multiplication problem by counting 23 groups of four apples. When Mrs. Lioy pleaded with Iris's teacher simply to show the class a times table, the teacher replied, "But that's drill-and-kill."

For Ben Lee, it was having his teenage daughter, Olivia trying to answer probability problems by a method called "guess and check" - until he pulled out his own 10th-grade math book to instruct her about the appropriate formula.

"I don't mind having kids appreciate what they learn," said Mr. Lee, an engineer who now works as a purchasing agent for Kodak. "But it's crazy to make a kid spend a night trying to solve a problem with these rudimentary and feeble tools."

By last spring, these parents had discovered one another and their common exasperation with constructivist math. Jim Munch's father, Bill, a software developer at Kodak, drew up a petition asking the Penfield schools to offer pupils the option of taking traditional math. Nearly 700 residents signed it. Last June, the Board of Education turned down the request.

Not surprising, school officials here paint a wildly different picture of the new math curriculum than do the critical parents. They point to a slip in Penfield's scores on standardized math tests and Regents exams in the late 1990's as a catalyst for changing the program. They also note that since the introduction of the constructivist curriculums - Investigations for elementary school, Connected Math for junior high, Core Plus for high school - those scores have risen gradually but steadily.

In a broad sense, Penfield can be a hard place to make the indictment against constructivism stick. The high school sends 90 percent of its graduates to two-year or four-year colleges, and the mean SAT score stands at 1117 (with 562 on math). In the battle of anecdotes, school officials assembled their own array of parents to praise the new curriculum when this columnist visited Penfield last week.

Susan Gray, the superintendent, attributed the criticism of the math program to "helicopter parents" who are accustomed to being deeply involved in all aspects of their children's lives. "Because the pedagogy has changed, the parents who knew the old ways didn't know how to help their children," she said. "They didn't have the knowledge and skills to support their children at home. There's a security in memorization of math facts, and that security is gone now."

YET many of the dissident parents have extensive math backgrounds and thus the ability to criticize the curriculum. It is also true that most of them tolerated the constructivist program for its first several years, until bitter experience drove them into rebellion.

Mary Rapp, the assistant superintendent, acknowledged the legitimacy of some complaints. In response, she said, Penfield has begun supplementing the constructivist classes with lessons in computation. Nearly 300 pupils in the district are now receiving remedial classes. A group of teachers worked last summer to revise the math syllabus in the high school in a somewhat more conventional direction. As a result, the district has had to petition the state for a postponement in the Math A Regents exam, from early 2006 to June.

Still, in the math wars, tweaking around the edges does not settle the issue. The dispute is fundamental. To its advocates, constructivist math applies the subject to the real world, builds critical thinking and rescues classes from numbing repetition.

But to those parents in Penfield and elsewhere - who have children in junior high unable to do long division or multiply two-column numbers, who pay for private tutors or sessions at traditionalist learning centers like Kumon, who wonder why there are so many calculators and so few textbooks - the words of a recent graduate to the Board of Education ring tragically true.

"My biggest fear about going to college," Samantha Meek said at a meeting last spring, "is attending introductory math courses How am I going to be able to explain to my professors that I do not understand what they are talking about, that I do not have the same math background as the rest of the students, and that I cannot do mental math and can barely do it with pencil and paper?"

E-mail: sgfreedman@nytimes.com

WHY TERC? Asks a 9 year old, Who Questions the Value of 'Fuzzy Math' For Her Future Academic Goals

"Constructivist" Math: Why Johnny Can't Add

Constructivism in the Classroom

Understanding the Shallow Learning Expectations Promoted by the NCTM's Math "Standards" and NCTM "Math Reform"

Dr. Alice Christie's Constructivist Math Page

Glosssery of Science Education Terms

Slippery Rock University in Pennsylvania teaches teachers how to teach constructivism