The Human Capacity For Mathematics

Capacity Relies On Two Modes Of Thought, As Reported In 7 May 1999 SCIENCE

Washington, DC -- A team of French and U.S. researchers has obtained the first hard evidence that two very different modes of brain activity underlie our inborn capacity for mathematics. Besides shedding light on the cognitive basis for one of humanity's hallmark talents, the researchers' findings may help psychologists and educators develop new ways to teach arithmetic to children who struggle with numbers. The findings appear in the 7 May 1999 issue of Science.

Mathematicians describing what happens in their heads have long offered clues that at least two modes of thinking -- one based on a nonverbal, visual-spatial sense of quantity, the other on language-related symbols -- work together while 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 of brain-damaged patients have suggested a similar distinction: some patients can subtract (a nonverbal, quantity-based operation) but not multiply (a rote verbal operation), and vice versa. The new study, lead by cognitive neuroscientist Stanislas Dehaene of INSERM 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 mental activity takes place.

The researchers asked volunteers fluent in both Russian and English to solve a series of problems after first 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 -- as well as 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 -- is 53 plus 68 closer to 120 or 150? -- the bilingual volunteers experienced no such language-dependent lag in their answers.

"I was amazed that the dissociation could be so sharp," said 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 brain regions were operating in each kind of 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.

As it happens, finger counting is an almost universal early stage in a child's learning of exact arithmetic. Also intriguing is that both preverbal human infants and monkeys can numerically distinguish among small groups of objects. This raises the possibility that the innately grasped nonverbal sense of quantity, which humans share with other primates, may be a crucial partner to the symbolic mode of mathematical thought, unique to humans, that allowed Einstein to capture the universe in an equation.

Dehaene cautioned that these findings can't be used to pinpoint which children are "naturally" better or worse at mathematics. Many studies, he said, have indicated that "the impact of education is probably much greater than any initial difference" in innate ability. To that end, the results might lead to the development of better teaching methods. What's more, "even children with severe language problems can and should learn to develop their nonverbal number sense through nonsymbolic quantity manipulations." Putting his money where his mouth is, Dehaene said that he will devote some of his recently awarded $1 million McDonnell Foundation grant to the study of "dyscalculic" children and adults.

International in scope, the weekly peer-reviewed journal Science is published by the American Association for the Advancement of Science in Washington, DC.

ORDER ARTICLE #19: "Sources of Mathematical Thinking: Behavioral and Brain-Imaging Evidence," by Stanislas Dehaene, Philippe Pinel, and Ruxandra Stanescu at INSERM and Service Hospitalier Frédéric Joliot in Orsay, France; and Elizabeth Spelke and Sanna Tsivkin at the Massachusetts Institute of Technology in Cambridge, MA. CONTACT: Stanislas Dehaene at 33-169-867-873 (phone), 33-169-867-816 (fax), or dehaene@shfj.cea.fr (available for interviews beginning 4 May).

There is also a related Perspective in this issue of Science by Brian Butterworth of University College London.

ORDER ARTICLE #3: "A Head for Figures," by B. Butterworth at University College London in London, UK. CONTACT: Brian Butterworth at 44-171-391-1150 (phone), or b.butterworth@ucla.ac.uk.

For copies of the two articles, please email scipak@aaas.org, or call 202-326-6440.