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Numbers and Our Divided Brain

New research suggests that humans use one area of the brain for calculations and another for estimations. If proven, the work could lead to refinements in the way math is taught.


Probing humanity's uncanny knack for numbers, an international research team has unveiled evidence that the human brain handles mathematics in two distinct ways: One part of the brain does calculating, another does estimating.

The findings not only illuminate the fundamental nature of mathematical reasoning, but may lead to improvements in how basic arithmetic is taught, even to children with severe learning disabilities, according to the scientists based at the Service Hospitalier Frederic Joliot in Orsay, France, and the Massachusetts Institute of Technology.

In a series of behavioral and brain-imaging studies published last week in Science, the researchers pinpointed where in the brain such numerical abilities reside. They were able to show how different modes of thought weave together in the tapestry of mathematical reasoning.

The scientists demonstrated that the regions of the brain involved in exact arithmetical calculations such as addition or multiplication are also involved in joining words to make a sentence.

In contrast, the ability to muse more generally about the approximate relationships between numbers falls to a part of the brain more involved in spatial skills.

Cognitive neuroscientist Brian Butterworth at University College London, author of "The Mathematical Brain," called the new research "a virtuoso performance."

The work draws attention to growing efforts to fathom the roles played by neural anatomy and learning in forging such a unique human mental ability.

"The development of higher mathematics is surely one of the crowning cognitive achievements of our species, which no other animal even approaches," said MIT cognitive psychologist Elizabeth Spelke, who conducted the studies with psychologist Stanislas Dehaene in France. "What gives rise to this achievement?"

To answer that, the scientists probed the biology of numbers.

The ancient followers of the Greek mathematician Pythagoras, who is credited with codifying many of the principles of geometry, were so enthralled by the natural order revealed through arithmetical operations that they believed numbers to be the basic elements of the universe.

Certainly, the new research shows them to be an elemental property of the mind.

By the Numbers

Indeed, the neural circuits that allow human beings to count on their fingers also allow them to balance their checkbooks, calculate the engineering of cathedrals and unravel the numerical fabric of space and time.

"The whole area of mathematical cognition is tremendously important, though it is only just becoming recognized as such, because the ability of humans to use numbers has been one of the keys to raising us, if you will, from the Stone Age to the phone age," Butterworth said.

Many animals share with humans an inborn instinct for approximate numbers--the ability to intuitively sense quantities such as the "twoness" of one's hands or the "fiveness" of the fingers on each. But only human beings have taken the additional mental leaps to create the more formal, ordered structures of mathematical calculation. Human infants appear to display an innate number sense as early as 5 months of age.

"This . . . sense might be the foundation on which our ability to understand numbers is based," said the Paris-based Dehaene, who led the research team.

Until recently, however, researchers who wanted to understand the actual neural processes at work were limited to studies of people whose brains had been damaged in ways that impaired their ability to calculate. The roster of those with number disorders includes stroke patients who can subtract but not multiply, or who can recite strings of numbers flawlessly but cannot add or subtract them.

"I've seen patients who lack this number sense, this intuition of quantity," Dehaene said. "They can't do 3 minus 1 or tell you what is between 2 and 4. They can learn to recite '4 times 7 is 28.' However, they never really grasp what it means, and they fail to apply this knowledge appropriately."

To investigate the biological basis of arithmetic, Dehaene, Spelke and their colleagues tested how volunteers fluent in Russian and English solved a series of arithmetic problems designed to pinpoint mathematical modes of thought.

Volunteers who were taught in one language and then tested in another took a full second longer to perform the calculation than when they performed both tasks in the same language.

But that time lag occurred only when the problem involved an exact calculation. When tested on approximate math problems, there was no language-dependent delay.

The distinction persisted even when the bilingual volunteers were tested on complex mathematical operations, such as addition in a number base other than base 10 and the approximation of logarithms and square roots.

Dehaene's team then used two different brain imaging techniques to track which brain regions were activated in each kind of task.

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