Parents whose children are struggling with math often view intense tutoring as the best way to help them master crucial skills, but a new study released on Monday suggests that for some kids even that is a lost cause.

According to the research, the size of one key brain structure and the connections between it and other regions can help identify the 8- and 9-year olds who will hardly benefit from one-on-one math instruction.

"We could predict how much a child learned from the tutoring based on measures of brain structure and connectivity," said Vinod Menon, a professor of psychiatry and behavioral sciences at Stanford University School of Medicine, who led the research.

The study, published in the online edition of Proceedings of the National Academy of Sciences, is the first to use brain imaging to look for a connection between brain attributes and the ability to learn arithmetic. But despite its publication in a well-respected journal, the research immediately drew criticism.

Jonathan Moreno, professor of medical ethics at the University of Pennsylvania, fears that some parents and teachers might "give up now" on a math-challenged child. "If it gets into the popular consciousness that it's wise to have your kid's brain checked out" before making decisions about academic options, he said, "that raises huge issues."

Menon and his fellow scientists agree that their research shouldn't lead to hasty conclusions. They are exploring whether any interventions might change the brain in such a way that children who struggle with math can benefit more from tutoring.

Just as learning to juggle increases the amount of gray matter in the area of adult brains that is responsible for spatial attention, said Menon, maybe something could pump up regions relevant to learning arithmetic before a child begins math tutoring.

Until then, he said "it's conceivable" that parents will interpret the new study as saying some kids cannot benefit from math tutoring, "and give up before even trying. How this plays out is far from clear."

Mental math

The study was conceived as a way to understand why some children benefit more than others from math instruction, said study co-author Lynn Fuchs, professor of special education at Vanderbilt University and an expert on ways to improve reading and math skills in students with learning disabilities.

For the research, the scientists first ran several tests on 24 third-graders to measure their IQ, working memory and reading and math ability. The children also underwent brain imaging. Structural MRI (magnetic resonance imaging) revealed the size and shape of various regions, while functional MRIs revealed connections among them.

Then the children received 22 one-on-one tutoring sessions, spread over eight weeks, for eight to nine hours per week. The tutoring emphasized number knowledge (principles like 5 + 4 = 4 + 5, and that many pairs of numbers add up to, say, 9) and fast-paced mental math ("quick, what is 6 + 9?").

After the tutoring, the children all improved in their arithmetic ability, solving more problems correctly and more quickly. But the amount of improvement varied enormously, from 8 percent to 198 percent.

None of the measures - pre-tutoring IQ score, working memory and math skills - predicted how much a child would improve.

But when the scientists compared each child's improvement with his or her pre-tutoring brain images, two connections jumped out. The volume of gray matter (neurons) in the right hippocampus, one of the twin structures crucial for forming memories, varied by about 10 percent in the children, Stanford's Menon said. The strength of the wiring between the hippocampus and the prefrontal cortex and the basal ganglia varied by about 15 percent. Both predicted how much a child's math skills improved with tutoring, the scientists reported.

The prefrontal cortex, behind the forehead, "is important for cognitive control, which plays a role in the formation of long-term memories," Menon said. The basal ganglia, tucked under the brain's outer surface, "is involved in habit formation and procedural memory," such as how to add numbers.

"Children with a larger right hippocampus and greater connectivity between the hippocampus and these two structures improved their arithmetic problem-solving skills more," said Menon.

These brain features explained 25 percent to 55 percent of the variation in improvement after math tutoring, he said. That, of course, leaves almost half of the difference among children to be explained by other factors.

Among the concerns raised about the study is its size. It enrolled only two dozen children, on a par with many neuroimaging studies but quite small for research that might influence people's behavior, said psychologist Scott Lilienfeld of Emory University.

"This is very, very preliminary evidence that brain measurements might tell you something that psychological measurements don't," said Lilienfeld, co-author with psychiatrist Sally Satel of an upcoming book, "Brainwashed: The Seductive Appeal of Mindless Neuroscience," that critiques some uses of neuroimaging. "It's important to see if the findings hold up in a second sample, and if other labs corroborate this."

Because brain images seem more rigorous than psychological measures, he said, there is a risk that parents and educators will interpret the study as definitive evidence that some children are doomed to be innumerate.

"Caution has to be the watchword here," he said.