Alex’s Adventures in Numberland Read Online Free PDF Page B

instinctive, approximate sense. We do not count every person in every queue. We look at the queues and estimate which one has the fewest people in it.
    In fact, we use our imprecise approach to numbers constantly, even when using precise terminology. Ask someone how long it takes them to get to work and most often the answer will be a range, say, ‘Thirty-five, forty minutes.’ In fact, I have noticed that I am incapable of giving single-number answers to questions involving quantity. How many people were at the party? ‘Twenty, thirty…’ How long did you stay? ‘Three and a half, four hours…’ How many drinks did you have? ‘Four, five… ten …’ I used to think that I was just being indecisive. Now I’m not so sure. I prefer to think that I was drawing on my inner number sense, an intuitive, animal propensity to deal in approximations.
    Since the approximate number sense is essential for survival, it might be thought that all humans would have comparable abilities. In a 2008 paper, psychologists at Johns Hopkins University and the Kennedy Krieger Institute investigated whether or not this was the case among a group of 14-year-olds. The teenagers were shown varying numbers of yellow and blue dots together on a screen for 0.2 seconds, and asked only whether there were more blue or yellow dots. The results astonished the researchers, since the scores showed an unexectedly wide variation in performance. Some pupils could easily tell the difference between 9 blue dots and 10 yellow, but others had abilities comparable to those of infants – hardly even able to say if 5 yellow dots beat 3 blue.
    An even more startling finding became apparent when the teenagers’ dot-comparing scores were then compared to their maths scores since kindergarten. Researchers had previously assumed that the intuitive ability to discriminate amounts does not contribute much to how good a student is at tasks such as solving equations and drawing triangles. Yet this study found a strong correlation between a talent at reckoning and success in formal maths. The better one’s approximate number sense, it seems, the higher one’s chance of getting good grades. This might have serious consequences for education. If a flair for estimation fosters mathematical aptitude, maybe maths classes should be less about times tables and more about honing skills at comparing sets of dots.
     
     
    Stanislas Dehaene is perhaps the leading figure in the cross-disciplinary field of numerical cognition. He started off as a mathematician, and is now a neuroscientist, a professor at the Collège de France and one of the directors of NeuroSpin, a state-of-the-art research institute near Paris. Shortly after he published The Number Sense in 1997, he was having lunch in the canteen of Paris’s Science Museum with the Harvard development psychologist Elizabeth Spelke. There they sat down by chance next to Pierre Pica. Pica brought up his experiences with the Munduruku and, after excited discussions, the three decided to collaborate. The chance to study a community that doesn’t have counting was a wonderful opportunity for new research.
    Dehaene devised experiments for Pica to take to the Amazon, one of which was very simple: he wanted to know just what they understood by their number words. Back in the rainforest Pica assembled a group of volunteers and showed them varying numbers of dots on a screen, asking them to say aloud the number of dots they saw.
    The Munduruku numbers are:
     
     
one
     p g
two
     xep xep
three
     ebapug
four
     ebadipdip
five
     p g pogbi
     
     
    When there was one dot on the screen, the Munduruku said p g . When there were two, the said xep xep . But beyond two they were not precise. When three dots showed up, ebapug was said only about 80 percent of the time. The reaction to four dots was ebadipdip in only 70 percent of cases. When shown five dots, p g pogbi was the answer managed only 28 percent of