A new study shows the different thinking involved in "how much" versus "how many."

Neuroscientists at University College London and Caltech identified the region of the brain active in performing basic mathematical concepts such as counting and arithmetic. Their findings could eventually help educators teach math more effectively and identify students with learning disabilities.

The study, published earlier this week in the Proceedings of the National Academy of Sciences, also explains how our minds differentiate between “how many” objects we see or “how much” of something is in a particular space.

To understand the two different modes of evaluating amounts, imagine picking the shortest checkout line at the grocery store. You could count the number of shoppers in each, in which case you’d be thinking discretely, in terms of numerosity. However, if you were a hurried shopper, you would probably take a quick glance over each line and pick the one that seemed the shortest, thinking in terms of continuous quantity.

In the past decade, brain scans have identified the region of the brain that allows us to conceive of numbers—an area known as the intraparietal sulcus (IPS), which is located towards the top and back of the brain and across both lobes—but scientists have had trouble isolating more specific networks within that area.

“Up until now, no one’s been able to discover this because it’s very hard to distinguish between a response of ‘how many’ and one of ‘how much,’” said Brian Butterworth, professor of cognitive neuropsychology at University College London and co-author of the study. “Even with numerals, we’re not sure how they’re being interpreted by the brain.”

To differentiate between the two thought processes, the team showed test subjects a series of separate, discrete blue and green squares on a screen and asked them to assess how many of each color there were. They then ran a continuous spectrum of blue and green regions and had subjects estimate how much of each they had seen.

They found different regions of the IPS were activated by each stimulus, and that the ability to evaluate “how many” appears to be innate. The new study supports previous findings on infant mathematical abilities.

“It looks as though the system responsible for numerosity is present from birth and plays an important role in learning arithmetic,” said Butterworth. “When a child learns to count and learns arithmetic, the child is learning using discrete objects in a set. When you’re adding two squares and five squares, it’s two sets of discrete objects being combined into a new set.”

Randy Gallistel, professor of psychology and co-director of the Rutgers University Center for Cognitive Research said the study could help explain how mathematical abilities evolved in humans and clarify how we think about numbers.

“This is quite an interesting piece of work relating to the history of mathematics,” he said. “It focuses on an issue that has been central to the development of mathematical thought since the Greeks, that is, the distinction between discrete and continuous quantities.”

Originally published March 10, 2006

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