After almost a decade of conflicts, the new year may provide a turning point in the debate over how to teach mathematics.
Prospects that the Bush administration will put the topic in the spotlight, along with forthcoming research, may shed light on the controversy over how to teach the discipline’s basic skills and concepts. And that combination could push adversaries toward a consensus leading to a unified approach to instruction, some educators say.
“There are a large number of areas where people could in fact sign on together,” said Uri Treisman, the director of the Dana Center and a professor of mathematics at the University of Texas at Austin. He points to a recent successful attempt by a group made up of members with differing philosophies to agree on the content of middle school math.
But the long-running and often emotional debate could continue over issues both big and small. The U.S. Department of Education’s choice of those who favor the traditional approach in math instruction to head a $400,000 math education enterprise, some say, is a signal that common ground may be hard to find.
The grant is addressing some of the issues centering on math teachers’ knowledge of the field—one of the key points the Bush administration plans to speak to in a math initiative it plans to kick off this year. (“Bush to Push for Math and Science Upgrade,” Nov. 20, 2002.)
“My real worry is that what’s going to happen is the Bush administration is going to control the dialogue,” said W. Gary Martin, an associate professor of mathematics at Auburn University in Alabama and a supporter of new curricula influenced by the NCTM. “I wish we could get down to the real issues, but there’s so much posturing going on, you don’t know what people’s real agendas are.”
In 1989, the National Council of Teachers of Mathematics helped launch a movement to define what students should know in basic subjects when it published its first set of content standards. Following, in part, the NCTM’s lead, groups representing history, English, science, and other subjects began to set standards for their respective fields.
While the math standards were hailed as a model for other disciplines, by the mid-1990s some mathematicians began to criticize them and to lead drives to discredit them. The critics—often described as traditionalists because of their emphasis on the basics—say the NCTM’s approach doesn’t give students the proficiency they need in performing mathematical functions and fails to prepare them for high-level math.
The battle over math instruction has been waged in recent years as states such as California and Massachusetts have set standards. It also flared in 1999 when mathematicians and scientists urged then-Secretary of Education Richard W. Riley to overrule a Department of Education panel’s endorsement of curriculum influenced by the NCTM.
A typical dividing line between the two sides is over the use of calculators in elementary school classrooms. The NCTM suggests that young children can learn mathematical concepts with the help of calculators, allowing them to focus on mathematical reasoning. Although the NCTM says that calculators should not preclude teaching of basic skills, traditionalists say the instruments distract students from mastering basic operations.
But in the past year, Mr. Treisman and others say, the debate has shown signs of calming down. For example, the Washington-based group Achieve recently published a draft of what math knowledge and skills students should have by the end of 8th grade. The set of so-called expectations was the product of a panel that had diverse views on how math should be taught, said Mr. Treisman, a member of the Achieve panel.
The drafting process was often difficult, he said, but the outcome is proof that differing sides can come to agreement.
“We came up with a document that everyone around the table was comfortable with,” said Matthew D. Gandal, the vice president of Achieve, a partnership of governors and business leaders that pushes for state policies to improve student achievement. “It shows that it’s possible.”
The process succeeded, Mr. Gandal added, because the participants spent hours arguing about what to put into the document and hashing out their differences.
While the Achieve project represents an example of how compromise is possible, research is starting to emerge that demonstrates the effect of curricula influenced by NCTM standards.
Late last year, a federally subsidized research project released preliminary findings suggesting that curricula based on the NCTM’s conceptual framework had resulted in increased student test scores.
Researchers examined scores in three states where large proportions of schools used three elementary curricula developed under a National Science Foundation program to put the NCTM’s standards into a curriculum format. The study compared the scores of students who learned under the NSF curricula with children of similar demographic backgrounds who learned under other curricula. It found that the students using the new curricula scored better across the board.
“Students using the programs we studied consistently outperformed other students,” said Sheila Sconiers, the director of the Alternatives for Rebuilding Curricula, the NSF-financed project that conducted the study. The difference “may not be huge in absolute terms, but it’s [statistically significant]. We’re sure it’s not by chance.”
According to the NCTM’s leader, the report verifies that the organization’s standards can be successfully turned into classroom materials that improve students’ achievement, debunking critics’ claims that the standards aren’t demanding enough to produce high achievement levels.
“This is research that should not be ignored,” said Johnny Lott, the president of the 100,000-member group and a professor of mathematics education at the University of Montana- Missoula. “What this suggests is that what was proposed in the NCTM standards ... has possibly been incorporated into a successful set of curricular materials that work in practice to produce higher achievement in students.”
Still, some NCTM opponents say that the research may have too many holes to show definitively that the curricula were successful. The study doesn’t specify which curriculum students in the control group learned under, according to Wayne W. Bishop, a mathematics professor at California State University-Los Angeles and one of the most vocal critics of the NCTM and the curricula based on its standards.
What’s more, he said, the study doesn’t specify that students from the control group had had at least two years in the same school, as students in the group using the NSF-backed program did. Students who are transient are less likely to receive tutoring and other help that may improve their test scores, Mr. Bishop noted.
Ms. Sconiers, however, said that the study’s statisticians were able to control for factors such as students’ longevity in a school, and the NSF-backed programs still yielded higher-performance than others.
But Mr. Treisman, who calls himself a centrist in the debate, said the study is persuasive enough that some NCTM critics recognize that the math teachers’ approach might work in certain situations.
Because the new style of curriculum requires teachers to practice new ways of teaching, the study recommends that such courses of study might work well in districts with experienced teachers who stay in their jobs for a long time. In schools with high teacher turnover, however, a more structured curriculum that new teachers can learn quickly would probably be a better fit, Mr. Treisman said.
“The question is, in which district, with what configurations, is one curriculum more likely to lead to positive impact,” he said.
Those are the questions many people hope will define the debate this year, instead of the polarization that has characterized it. Over the past several years, test data have indicated that math achievement is improving in the United States, although it still lags behind that in other countries, according to Linda P. Rosen, a consultant to math and technology education projects. She was an aide to Mr. Riley when he was secretary of education.
For example, Ms. Rosen said, a 1999 study found that 8th graders in several U.S. school districts serving wealthy areas scored as high as those in the best countries of the world on the Third International Mathematics and Science Study—Repeat. In the same study, inner- city U.S. districts ranked at the lowest international levels.
Other data suggest, Ms. Rosen said, that girls’ SAT scores are higher than ever, and that gaps between minority and white students on the National Assessment of Educational Progress are shrinking.
“There are lots of little bubbles out there that deserve scaling up,” Ms. Rosen said. “What we have to figure out is what are the circumstances [leading to math achievement], and what do we have to do to get those circumstances.”