The research is the first using brain scans to look at ability to learn math and brain structure or function.
The study also looked at differences between how children and adults learn math, and it could help researchers understand the origins of math-learning disabilities. The study was published online April 29 in Proceedings of the National Academy of Sciences.
"We can actually predict how much a child is going to learn during eight weeks of math tutoring based on measures of brain structure and connectivity," said Vinod Menon, the study's senior author and a professor of psychiatry and behavioral sciences at Stanford's Department of Psychiatry and Behavioral Sciences.
The results are a significant step toward the development of targeted learning programs, said the study's lead author, Kaustubh Supekar, postdoctoral scholar in psychiatry and behavioral sciences.
The researchers focused on third-grade students. Children at that age — 8 and 9 — are at a critical stage for acquiring basic arithmetic skills, the scientists said. The study's 24 third-graders received 15 to 20 hours of individualized math tutoring over eight weeks, including lessons on new concepts.
Children also practiced math skills with an emphasis on speed. The sessions were tailored to each child's level of understanding.
Before tutoring began, the children were given standard assessments, including tests of IQ, working memory, reading and math problem-solving. The children's arithmetic performance was tested before and after the eight weeks. And all children had magnetic-resonance-imaging scans performed on their brains.
Because the children also learned math at school, which could have influenced the study results, the study included a control group of 16 third-grade children who didn't receive tutoring but had the same testing and brain scans.
All 24 children who received tutoring improved their arithmetic performance, the researchers discovered. The accuracy and speed of their problem solving improved 67 percent on average. But individual gains varied widely, ranging from 8 percent to 198 percent. The children who did not receive tutoring did not show any change in arithmetic performance during the study.
When the researchers analyzed the children's brain scans, they found that the amount of gray matter in three areas predicted ability to benefit from math tutoring.
A larger hippocampus, considered one of the brain's most important memory centers, was the best predictor of improvement with tutoring.
Connections between the hippocampus and several other brain regions, especially the prefrontal cortex and basal ganglia, also predicted the degree of benefit from tutoring. These regions are important for forming long-term memories, the researchers said.
"The part of the brain that is recruited in memories for places and events also plays a pivotal role in determining how much and how well a child learns math," Supekar said.
None of the students' assessment scores, such as IQ or tests of working memory, could predict how much an individual child would benefit from tutoring.
Researchers noted that the hippocampus and other brain regions highlighted in the study differed from those previously found to aid adults in learning math. When solving math problems, adults rely on other brain regions that are specialized for representing complex visual objects and processing spatial information.
The tutoring approach used in the study was also a factor in students' improved performance, the scientists found. Tutoring included repeating problems in a sped-up fashion. Once kids are able to pull up answers to basic arithmetic problems automatically from memory, their brains can tackle more complex problems.
"Memory resources provided by the hippocampal system create a scaffold for learning math in the developing brain. Our findings suggest that, while conceptual knowledge about numbers is necessary for math learning, repeated, sped practice and testing of simple number combinations is also needed to encode facts and encourage children's reliance on retrieval — the most efficient strategy for answering simple arithmetic problems," Menon said.
The researchers will next compare brain structure and wiring in children with and without math learning disabilities. They want to analyze how brain wiring changes in response to tutoring and examine whether lower-performing children's brains can be exercised to help them learn math.
Other Stanford co-authors included social science research assistants Anna Swigart and Caitlin Tenison; and postdoctoral scholars Dietsje Jolles and Miriam Rosenberg-Lee. A researcher at Vanderbilt University also collaborated on the work. The research was funded by the National Institute of Child Health and Human Development.
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