A new approach to an old math problem

The state looks to balance traditional and reform methods to improve learning.

Sunday, April 05, 2009

BY KRISTEN ALLOWAY

Star-Ledger Staff

The sixth-graders in Danielle Dragone's math class are learning how to calculate perimeters.

After a brief lecture, the kids at Central Middle School in Parsippany are out of their seats, using tape measures to find the perimeter of classroom objects: a poster, a book, a windowpane.

"Get to work," Dragone tells them. "Go measure things."

It's math as usual for Dragone and her students. But beyond New Jersey's quiet classrooms a battle is shaping up over the best way to teach mathematics to children.

In the midst of revamping its core curriculum standards for elementary and high schools, the state Department of Education has waded into the "math wars" -- a national debate over the best way to teach children mathematics.

As it has across the country for the last decade, the discussion has drawn in parents, math educators and mathematicians. In New Jersey, coalitions have been formed. Petitions have been signed.

What all sides agree on, however, is the urgency in improving kids performance in mathematics. The U.S. lags behind many Asian nations in math and science at a time when those skills are imperative to competing in the global economy.

"It's an area I believe as a nation we've got to address. It's what we're trying to do here in New Jersey," said Education Commissioner Lucille Davy, herself a former math teacher. "As a nation we need to produce children who follow math and science fields."

At one extreme in the debate is an approach called "reform math," which emphasizes conceptual learning -- or an understanding of why we do math the way we do.

Reform math also teaches students several different computational methods -- in addition to the traditional algorithms, such as long division -- with the goal of helping kids find one that works for them. It supports the use of calculators in early grades, and encourages student exploration -- such as using a tape measure to find the perimeter of routine objects -- under the theory it will help certain types of learners more easily grasp math concepts.

Critics argue reform math doesn't give kids enough basics and that different algorithms, or methods, confuse children. They understand the importance of conceptual learning but also want a return to some of the old ways -- things like lining numbers atop one another when it comes to multidigit multiplication. And they would ban calculators from classrooms until middle school.

NEW STANDARDS

To help strike a balance between the two approaches, the state has created a math task force, made up of 25 math educators, mathematicians and parents, who will meet this month to make recommendations for the state's new curriculum standards for both elementary and high schools. Standards are revised every five years for all subjects and grades.

For the past decade, the math curriculum standards have leaned toward reform math, Davy said. She wants the new ones to land in the middle.

"I think there was a movement away from children mastering the basics of math -- the basics of division, multiplication, the basics around percentages. We began to rely on calculators," Davy said. "We need to wind up with a balance."

Additionally, the state is pressing efforts to beef up the math curriculum in high school. The debate boiled over recently as state officials wrote and scrapped two drafts for new math standards. The first, nearly a year in the making, was too similar to what New Jersey has now, Davy said.

The second copied heavily from other states and drew the ire of many math teachers here. That draft prompted the creation of the Concerned Mathematics Educators of New Jersey, with more than 200 supporters, who worry the state will decrease the emphasis on the conceptual understanding of math.

Instead of presenting the new math standards to the state Board of Education in June as planned, the Department of Education has pushed the date to the fall.

New Jersey does well compared with other states on standardized tests in all grades. But that's not good enough, Davy said.

On the National Assessment of Educational Progress, the state's fourth-graders ranked higher than those in 46 other states and jurisdictions. New Jersey eighth-graders performed better than those in 35 states. Both rankings are from 2007, the most recent year for which statistics are available.

But the state continues to produce large percentages of kids who need remedial math when they arrive at college.

IN DEFENSE OF REFORM

Reform math advocates -- including many mathematicians and math educators -- argue kids need to go beyond memorizing facts and formulas to see how math applies to their lives. That deeper understanding helps prepare students for higher-level mathematics, they say.

"The traditional way of teaching math is to drill them until they memorize. That produced a lot of adults who hate math or don't understand math," said Cathy Liebars, a mathematician at the College of New Jersey and one of the founders of the Concerned Math Educators. "Kids don't just have to memorize things. They can learn basic facts while they are solving problems."

And calculators help students "when the focus is not on doing the computing but on how to figure out how to solve the problem," Liebars said. "Teachers help them understand when it is appropriate."

Opponents argue that approach -- which some call "fuzzy math" -- produces kids who have not mastered basic arithmetic and don't have instant recall of fundamental math facts. That leaves them ill-prepared for higher-level math, they say. Critics also worry that some reform curricula cover too many topics, instead of working more in-depth on fewer subjects.

"Reform math does not support or encourage the use of memorization of basic facts, including addition, subtraction, multiplication and division. That's a big problem," said Sarah-Kate Maskin of Ridgewood, a former elementary school teacher who helped start the New Jersey Coalition for World Class Math, a group of parents, educators and mathematicians at the other end of the debate. "If you have to think of a strategy (to multiply) nine times three, you're not going to get very far."

Critics also charge reform math places too much emphasis on the problem-solving process and not enough on getting the correct answer.

Hung-Hsi Wu, a mathematics professor at the University of California at Berkeley, who has assisted the Coalition for World Class Math, sees flaws with both methods.

But in reform math, "they were so intent on cultivating familiarity with the concepts ... they forgot about the end result," Wu said. "In mathematics, we want an answer. That's what happens in real life."

Both approaches have merit, according to the National Mathematics Advisory Panel, a group created in 2006 by then-President George W. Bush to study how to bolster math achievement.

The panel, which released its report last year, found that schools need to focus on basic skills, fractions and some geometry to prepare kids for algebra and higher-level math.

"You can't isolate computational fluency and conceptual understanding," said Sandra Stotsky, a professor at the University of Arkansas and a member of the national math advisory group. "The two must march together."

Davy said that is what she hopes to see in New Jersey's new math standards.

"I want kids to think about math and how math can be part of their everyday life," Davy said. "But kids also have to have enough precision to understand the answer does matter."

Kristen Alloway may be reached at kalloway@starledger.com.