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Mathematical unknowns

THERE'S A new four-letter word among some elementary school teachers in Boston: "TERC." Mere mention of the math curriculum from kindergarten through Grade 5, which was created by the nonprofit Technical Education Research Center in Cambridge, was enough to bring a collective groan from more than 100 Boston Teachers Union representatives who gathered at a recent weekend retreat on Cape Cod.

The alternative curriculum is not only cumbersome, charges the union's president, Richard Stutman, but also contributes to the achievement gap between white and minority students. That charge is almost sure to escalate the math wars between educators who favor traditional pencil-and-paper arithmetic and reformers such as the creators of TERC who propose to teach children to "reason mathematically."

Emphasis on traditional algorithms such as long addition would seem essential to a later understanding of advanced math. In Asia, where students outperform their American counterparts, teachers drill math facts and repeatedly demonstrate math skills. The goal is to create automatic and accurate responses that allow students to move up to the next layer of math knowledge.

TERC and other so-called "constructivist" teaching methods deemphasize standard computational skills, focusing instead on group learning that encourages students to make connections between mathematical ideas.

Memorizing single procedures is not considered especially useful. Instead, games and props are used to assist students to develop multiple strategies to solve problems. For example, TERC asks students to develop a deeper understanding of the meaning of fractions but not necessarily how to multiply them quickly.

A call for a debate

TERC was first introduced in Boston a decade ago, but the School Department implemented it across the board only a year ago. Stutman is calling for a debate on that decision. It's a reasonable demand.

Boston school officials need to determine whether their choice of curriculum is impeding the ability of minority students to compete academically. TERC is used in more than 2,000 elementary schools across the nation, including some in Boston suburbs. But families with higher incomes are often in a better position to supplement constructivist teaching methods with private tutors.

Boston teachers try to compensate when they see disturbing trends, such as declining minority enrollment at the city's elite Boston Latin School. The Independent School Entrance Examination required for admission to Latin favors elementary school students with strong computational skills. Boston teachers, therefore, jettison TERC when it comes time for them to prep their students and ready them to compete for seats with private and parochial school students. When the chips are down, said Stutman, Boston's teachers employ "ABT" -- "Anything But TERC." But it's still a catch-up game.

Testing confusion

Testing policies of the state Department of Education only add to the confusion. The math section on the fourth grade Massachusetts Comprehensive Assessment System exam is based largely on constructivist concepts, according to Chris Coxon, the deputy superintendent for teaching and learning in the Boston schools. But the high-stakes 10th grade test, he says, now focuses more heavily on traditional computational skills. As a result, Boston was forced to change its high school math curriculum last year, precisely at the time it was ramping up TERC in the elementary grades.

Coxon wants to see a happy medium in the math curriculum. But he recognizes studies arguing that minority students from low-income homes perform better in carefully structured traditional classrooms. Clearly, many minority youngsters are struggling under the current system. In Boston, 37 percent of fourth-graders failed the math portion of the most recent MCAS test. For white students the failure rate was 16 percent.

State education officials readily admit that they need to know more about the math curriculums that are in use across Massachusetts. They are designing a survey to determine how many systems rely on the constructivist math approaches and how those students fare on assessment tests. That information should help to advance the debate in Boston.

Susan Jo Russell, a curriculum specialist with TERC in Cambridge, cites other studies showing that elementary students -- including low-income pupils -- who are taught in the constructivist style outperform counterparts on standardized tests. But success, she advises, depends greatly on the level of commitment of teachers and professional development programs to support them.

"A curriculum is only a tool," she says. "It can be implemented well or poorly."

Proponents of both the traditional and constructivist approaches agree that it takes more time, training, and money for teachers to acquire competence in constructivist techniques. The question is whether it's worth the investment. Time is especially constrained in Boston, where the goal is often to help underperforming students advance by more than one grade level in a single academic year.

Stutman's complaint has resonance. Boston teachers cope with a lot regarding the academic, social, and health demands of their students. And few parents of Boston students can afford to supplement TERC with private tutors. More research is needed, but it might simply be the case that the city's educators and students can no longer afford the luxury of a high-maintenance math curriculum.

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