A head for figures

it has been noted that some patients with strokes or brain damage have severe difficulty with language and exact calculations, while their ability to estimate remains intact. Now, a team of French and us researchers has obtained first-hand evidence to prove that two very different modes of brain activity underlie our inborn capacity for mathematics. Besides shedding light on the cognitive basis for one of the hallmark talents of humans, the findings may help psychologists and educators develop new ways to teach arithmetic to children who struggle with numbers.

Children in countries like India, who are taught in English and not their mother tongue, might benefit from this research. Teaching mathematics is assuming more importance across the world, with Japan leading the race to make its children strong in mathematics.

So, how do people do mental mathematics? Do we need to a have a sense of two eyes and 10 fingers for numerical work? A Swiss psychologist had argued that the ability to do maths with fingers emerges around the age of five years and requires the development of logic skills, such as transient reasoning and putting two sets of objects into one-to-one correspondence. In fact, it has been recognised that infants as young as six months can detect changes in the number of objects in a visual array.

Scientists have long wondered about the extent to which language is required for maths. Despite their lack of language skills, even monkeys and five-month-old infants have some ability to understand numbers. They gape in surprise when they see someone put two dolls behind a screen and then raise the screen to reveal only one doll. Also, the brain centres that process numbers seem to be different for exact and approximate calculations.

Mathematicians, describing what happens in their heads, have long offered clues that at least two modes of thinking -- one based on a non-verbal, visual-spatial sense of quantity, the other on language-related symbols -- work together when the human brain processes numbers. Albert Einstein, for example, was not alone in insisting that numerical ideas came to him in certain "images, more or less clear, that I can reproduce and recombine at will". In contrast, other mathematicians have reported their dependence on verbal representations of numbers.

Studies on patients with damaged brains have suggested a similar distinction: some patients can subtract (which is a non-verbal, quantity-based operation) but not multiply (which is a rote verbal operation) and vice versa. The study led by the French cognitive neuroscientist Stanislas Dehaene and cognitive psychologist Elizabeth Spelke of the Massachusetts Institute of Technology not only confirms the two-mode theory but locates where in the brain such activity takes place ( Science , Vol 284, No 7).

The researchers asked volunteers fluent in both Russian and English to solve a series of problems after schooling them in the necessary math. One group was schooled in Russian, the other in English. If they learned the math in English and were tested in Russian or vice versa , the volunteers needed up to a full second more to solve the problem, but only when the problem involved exact calculation; for example, does 53 plus 68 equal 121 or 127? When tested on an approximate math problem, such as is 53 plus 68 closer to 120 or 150, the bilingual volunteers experienced no language-dependence lag. "I was amazed that the dissociation could be so sharp," says Dehaene. "After all, we presented our subjects with tasks that are superficially extremely similar. Our brains really solve these two tasks in quite different ways."

The language-related distinction continued to show up even when researchers trained and tested the bilingual volunteers in more complex mathematical operations, such as addition in a base other than 10 and the approximation of logarithms and square roots. Dehaene's team then used functional brain imaging techniques to track which regions of the brain were operating in each task. Exact calculations lit up the volunteers' left frontal lobe, an area of the brain known to make associations between words. But mathematical estimation involved the left and right parietal lobes, a bilateral neural network responsible for visual and spatial representations and also for finger control.

It is also quite intriguing that both monkeys and human infants unfamiliar with language can numerically distinguish among small groups of objects. This raises the possibility that the innately grasped non-verbal sense of quantity, which humans share with other primates, may be a crucial partner to the symbolic mode of mathematical thought unique to humans, which allowed Einstein to capture the universe in an equation.

Dehaene cautioned that these findings cannot be used to pinpoint children who are "naturally" better or worse at mathematics. The results might lead to the development of better teaching methods. Moreover, "even children with severe language problems can and should learn to develop their non-verbal number sense through non-symbolic quantity manipulations," scientists suggest.

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