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Four years ago, federal officials launched an initiative to study the complex machinery of mathematics and science cognition, or in plain language, how students think, learn, and solve problems in those subjects.

Since then, that program has begun to exert its influence through the relatively modest but steady flow of public funding it provides for scholarly research, work that goes largely ignored by the public at large鈥攁nd even most educators鈥攂ut which, over time, can have broad influence in the classroom.

The federal center goes by the lengthy title of the Program on Mathematics and Science Cognition and Learning, Development and Disorders. It operates within the National Institute of Child Health and Human Development, the same federal entity that has generated much of the research that strongly influences federal reading policy today.

By federal standards, the math and science program has a small budget: It currently underwrites about 20 ongoing projects at an annual cost of some $7 million. But it is conducting its work at a time when federal officials, including the Bush administration, are calling for greater emphasis on research-based strategies in math instruction.

The central role of the NICHD program is to finance that research with public money鈥攔ather than generate it independently. Those studies, in turn, often end up in articles published in scholarly journals, which can shape the collective thinking of the education community.

鈥淚t takes a while to have an impact,鈥� said Daniel B. Berch, the director of the program. 鈥淵ou have to begin to make it evident to researchers in the field that [we] support this kind of work.鈥�

Even so, over the past few years the math- and science-cognition program鈥檚 grantees, many of whom also receive support from other federal agencies, have published about 50 articles in various journals, he estimates. One of the most widely circulated pieces was a 2004 paper that identified the potential benefits of 鈥渄irect instruction,鈥� or more straightforward presentation of facts from teachers to students, on students鈥� scientific reasoning and judgment. That study, whose primary author was David Klahr, a psychology professor at Carnegie Mellon University in Pittsburgh, compared that teaching approach with 鈥渄iscovery learning,鈥� a more hands-on classroom method. (鈥淣CLB Could Alter Science Teaching,鈥� Nov. 10, 2004.)

Other studies backed by the NICHD math and science program have probed such disparate topics as how students with various disabilities learn math; whether gender differences affect student learning; and how children develop math skills such as estimation, number sense, and mastery of basic arithmetic facts.

Building a Base

Some of those topics touch long-standing debates about how math and science should be taught. But Mr. Berch says while his program鈥檚 work could eventually influence classroom instruction, its impact is indirect: Those decisions are ultimately left to school officials and policymakers, he says.

鈥淵ou don鈥檛 [craft] a curriculum out of one study,鈥� Mr. Berch said in an interview from his office in a National Institutes of Health building in Rockville, Md., in suburban Washington. His program is trying to promote sustained research rather than one-shot examinations of how students learn. 鈥淲e want to make it more cumulative,鈥� Mr. Berch said.

To that end, most of the projects supported by the NICHD program are being conducted over a three- to five-year period. Most grant recipients receive between $250,000 and $500,000 in direct funding, plus additional costs, on average, he estimates.

Math-Panel Influence

Mr. Berch said he was asked by G. Reid Lyon, the influential and controversial former chief of the NICHD鈥檚 child-health and -behavior branch, to lead the math- and science-cognition program. The reading research supported by the NICHD has had a strong influence on the types of instruction in that subject that the federal government supports, most notably through the $1 billion-a-year Reading First grant program, which requires the use of research-based instructional strategies in that subject.

Critics have accused the NICHD of favoring research that supports phonics, a teaching method rooted in associations between sounds and letters, at the expense of other approaches.

Similar philosophical divides exist over how to teach math. The 鈥渕ath wars鈥� have pitted those who call for stronger teaching of basic number facts and foundational skills against those who worry that such an approach will result in too much rote memorization and drill, and not enough problem-solving.

Over the past year, improving math and science education has become a major focus among federal officials, who worry that the nation is not turning out enough students who can fill highly skilled jobs.

Earlier this year, the Bush administration announced a series of steps aimed at improving how math is taught, including the formation of the National Mathematics Advisory Panel, a group of 17 experts charged with identifying what research says about how to teach that subject.

The NICHD program would seem well positioned to provide that research. Mr. Berch serves as one of the panel鈥檚 six nonvoting members. And two cognitive psychologists whose work has been funded through his program鈥擠avid C. Geary of the University of Missouri-Columbia, and Robert S. Siegler of Carnegie Mellon University鈥攚ere also named to the panel. Mr. Berch said he offered advice to Department of Education officials about who might serve, but had no say in the final selection.

Area of Need?

Mr. Geary believes the math panel can help make educators aware of the research emerging from the NICHD program. NICHD support for reading 鈥渞eally clarified where instruction should be focused,鈥� Mr. Geary said, by examining 鈥渢he processes of reading. I think the same applies to math and science.鈥�

Jere Confrey, a professor of mathematics education at Washington University in St. Louis, agreed that knowing more about students鈥� cognitive skills in math and science is important. But she also saw a more urgent need for studies on instruction in those subjects, and how to prepare teachers to work with students of different abilities. Ms. Confrey led a panel of the congressionally chartered National Research Council that produced a report in 2004 on how to judge the effectiveness of math curricula. (鈥淣RC Urges Multiple Studies For Math Curricula,鈥� May 26, 2004.)

鈥淲e have more problems in instruction than pure cognitive research,鈥� Ms. Confrey said. 鈥淐ognition has to be fostered by effective and rich classroom discussion.鈥�

Like Ms. Confrey, James Hiebert, a professor of education at the University of Delaware in Newark, questioned whether the NICHD math and science program would favor research on basic math skills rather than problem-solving ability.

鈥淚t鈥檚 easier to investigate cognition in simple-skill learning than in conceptual understanding,鈥� Mr. Hiebert said. 鈥淪ometimes research tends to be skewed toward basic fact learning.鈥�

But after hearing a description of various math projects supported by the NICHD program, in distinct areas such as estimation, number sense, and mastery of arithmetic facts, Mr. Hiebert added that he could detect no ideological bias in the program鈥檚 work.

Mr. Berch said his only concern is funding useful research on cognition and learning disabilities, not weighing in on ideological disputes.

鈥淲e are not taking sides with respect to the math wars,鈥� he maintained.

In the 1970s and 1980s, cognitive research on how students solve arithmetic proved extremely valuable and shaped classroom pedagogy and curricula for years to come, Mr. Hiebert said. Today鈥檚 research could prove similarly important, he said.

鈥淥ne of the problems we have in math is we don鈥檛 understand the learning processes well enough to know [which] instructional strategies might be preferred,鈥� Mr. Hiebert said. Valuable research 鈥渆ventually finds its way into the system, even if the effect is so indirect that it鈥檚 hard to trace it back to the original source.鈥�