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math and the brain

It is not a typical math test. The elementary school students lie as still as they can in a brain scanner while they answer questions for University of Western Ontario neuroscientist Daniel Ansari. "Which number is larger, 7 or 1? What about 9 or 8?"

Dr. Ansari and his colleagues study neurological deficits that make it so hard for some children to learn arithmetic, the subtle differences between the brains of children who struggle with the most basic calculations and those who excel.

They want to find new ways to identify and help the five per cent of children who have a learning disability called developmental dyscalculia, which makes it difficult to master addition, subtraction, multiplication and division. But their work has broader implications as well. Dr. Ansari, a world leader in the study of the brain and math, wants to understand how children learn arithmetic, what can go wrong, and how teachers and parents can intervene to help.

He hopes to collaborate with educators on new approaches and teaching techniques that could help preschoolers and elementary students strengthen the foundation needed for higher level skills.

His focus is on the seemingly simple ability to understand what numbers mean, to get that "five," for example, can mean five houses, five balls or five mittens and how this is different from four. There is compelling evidence that children who score low on standardized arithmetic tests have difficulty with this; they find it harder to identify which of two numbers is larger.

"We have learned so much about language and learning to read. The same thing needs to happen with math," said Dr. Ansari, who notes that for every 14 studies on how children learn to read, only one is done on how they grasp math. Dyscalculia is as prevalent as dyslexia, a learning disorder that makes it hard for children to master reading, Dr. Ansari said. But parents, teachers and educational professionals have far less awareness about it.

Western cultures place much more emphasis on reading and literacy than numeracy and mathematics, he said. For years, being good at math was seen as a reflection of overall intelligence and not related to specific brain circuitry.

That started to change in the 1990s, when researchers such as French mathematician and neuroscientist Stanislas Dehaene published preliminary findings on brain organization underlying numeracy and arithmetic.

Arithmetic is a branch of mathematics that involves addition, subtraction, multiplication and division - the basic calculation operations, said Dr. Ansari. Mathematics is broader, and includes geometry, calculus and other branches. People with dyscalculia have difficulty with arithmetic, which may affect how well they do in other areas of math.

The disorder can be devastating, said Brian Butterworth, an expert on the dyscalculia who works at University College London in the U.K. Children who have it are often mocked by the peers and seen as stupid.

It is not that they can't say that 7 is larger than 1, Dr. Ansari said, but it takes them much longer to come up with an answer and they tend to make more mistakes than their peers.

They also tend to have trouble recognizing whether one image has more dots or pieces of fruit in it than another.

"There is not a complete break down, but the system is much weaker," Dr. Ansari said.

"This system, our ability to represent magnitudes, is really the building block of everything else. With reading, we know linking letters with speech sounds is a prerequisite for becoming a fluent reader," he said.

"We think it is much the same in the domain of mathematics. The building block is being able to recognize and rapidly process numerical magnitudes, whether in symbolic form, like Arabic numerals, or non-symbolic, an array of dots or fruits."

The researchers are also interested in other deficits related to learning arithmetic, and how they may be related to problems associated with dyslexia.

Mapping the numerical meaning of a number, like five, onto its symbol, 5, can be a challenge for some children with dyscalculia, much like mapping sounds onto letters is hard for some youngsters with dyslexia. Dr. Ansari wants to know whether common brain mechanisms are involved in difficulties in arithmetic and reading.

He and his colleagues have a number of experiments under way. In 2007, he and graduate student Stephanie Bugden began tracking 25 students. The children are now nine or 10 and about to begin their second round of math tests in a magnetic resonance imaging scanner. They vary in their mathematical abilities from well below to above-average, but they all perform well in other subjects and score within the normal range on intelligence tests.

While the children answer questions about which number is larger, the scientists measure their brain activity in regions that have been shown to be important to doing arithmetic. (See sidebar.) They are also able to measure the physical size of math-related brain regions and the strength of the connections between these areas and other parts of the brain.

There is no guarantee that learning more about brain deficits related to arithmetic will lead to better teaching techniques, or ways to help children who have severe or moderate difficulties with arithmetic.

Researchers don't need a detailed brain map to develop and test teaching approaches and tools, like playing board games or using number lines. (See sidebar) But it could shape new approaches, lead to a more sophisticated screening tool to identify children with dyscalculia and help scientists assess whether new interventions change brain function.

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