One school that has adopted a new approach to math–one that combines procedural knowledge with conceptual knowledge–is the Garfield Elementary School in Revere, Mass. Three-quarters of Garfield’s students receive free or reduced-price lunches, and many are the children of recent immigrants.

Three years ago, Garfield started using Singapore Math, a curriculum modeled on that country’s official program and now used in about 300 school systems in the United States. Many school systems and parents regard Singapore Math as an antidote for “reform math” programs that focus less on basic problem solving and more on conceptual problems as a result of earlier recommendations from the National Council of Teachers of Mathematics.

According to preliminary results, the percentage of Garfield students failing the math portion of the fourth-grade state achievement test fell from 23 percent in 2005 to 7 percent last year. Those rated advanced or proficient rose to 43 percent from 40 percent. Recently, a fourth-grade class at Garfield opened its lesson with Singapore’s “mental math,” a 10-minute warm-up requiring students to recall facts and solve computation questions without pencil and paper.

“In your heads, take the denominator of the fraction three-quarters, take the next odd number that follows that number. Add to that number, the number of ounces in a cup. What is nine less than that number?” asked teacher Janis Halloran. A sea of hands shot up. (The answer: four.)

Halloran then moved on to simple pencil-and-paper algebra problems. “The sum of two numbers is 63,” one problem reads. “The smaller number is half the bigger number. What is the smaller number? What is the bigger number?” (The answers: 21 and 42.)

In this class, the students didn’t use the lettered variables that are so prevalent in standard algebraic equations. Instead, they arrived at answers using Cuisenaire rods, sticks of varying colors and lengths that they manipulate into patterns on the tops of their desks. The children use the rods to learn about the relationship between multiplication and geometry. The goal: a visceral and deep understanding of math concepts.

“It just makes everything easier for you,” said fifth-grader Jailene Paz.

The Singapore Math curriculum differs from so-called “reform math” programs, which often ask students to “discover” on their own the way to perform multiplication and division and other operations, and have come to be known as “constructivist” math.

One reform math program, “Investigations in Numbers, Data, and Space,” is used in some 800 school systems and has become a lightning rod for critics. TERC, a Cambridge, Mass., nonprofit organization, developed that program, and Pearson Scott Foresman, a unit of Pearson Education, distributes it to schools.

Ken Mayer, a spokesman for TERC, says many parents have a misconception that Investigations doesn’t value computation. He says many school systems, such as Boston’s, have seen gains in test scores using the program. “Fluency with number facts is critical,” he says.

Polle Zellweger and her husband, both computer scientists, moved to Bellevue, Wash., two years ago so their two children could attend its highly regarded public schools, but they grew suspicious of the school’s Investigations program. Last summer, they had both children take a California grade-level achievement test, and both answered only about 70 percent of the questions correctly. Zellweger and her husband started tutoring their children an hour a day to catch up.

Eric McDowell, who oversees Bellevue’s math curriculum, says parents misunderstand Investigations. McDowell says schools supplement the program with more traditional drilling in the basics, and students end up flourishing. “It’s not an either-or situation,” he says.

In the Alpine School District in Utah, parent Oak Norton, an accountant, has gathered petitions from 1,000 families to protest the use of Investigations. His complaints began more than two years ago, when he discovered at a parent conference that his oldest child, then in third grade, wasn’t being taught the multiplication tables.

Barry Graff, a top Alpine administrator, says the system has added more traditional computation exercises and plans to give each school a choice between Investigations or a more conventional approach. Graff, who says Alpine test scores tend to be at or above state averages, expects critics to keep up the attacks.

“Other than the war in Iraq, I don’t think there’s anything more controversial to bring up than math,” he says. “The debate will drive us eventually to be in the right place.”

–From wire service reports