We may think we learn all the math we know in school, but new findings indicate this might not be true. A study of preschool children suggests that some basic arithmetic skills are innate.
When typical preschoolers are presented with a math problem--such as, "If you have 20 apples and then get 10 more, how many will you have total?"--they don't have a clue. That's because the answer requires symbolic arithmetic tricks that must be taught. However, even infants are known to have an internal counting system up to the number 4, and for larger sets of objects, they can estimate. For example, they can tell that one set includes more objects than another, as long as the sets aren't too close in size. But can preschool children perform mathematical operations on those sets, such as addition? Common wisdom says they can't, but the question has been difficult to address experimentally.
To quiz preschoolers on their innate math skills, a team led by Elizabeth Spelke, a psychologist at Harvard University in Cambridge, Massachusetts, presented 16 five year-olds with a computer game. In one part of the game, a cluster of between 10 and 58 blue dots appeared and then hid behind a box. Then, another cluster of blue dots appeared before joining the others behind the box. Finally, the children were shown a cluster of red dots outside the box and had to guess if there were more red than blue dots in total. In another experiment, a series of beeps revealed the number of hidden dots rather than showing them. Because these dots cannot be seen, says Spelke, answering correctly requires "arithmetic in the deeper sense" of combining abstract sets of numbers.
Their test results wouldn't get them into the Massachusetts Institute of Technology, but the children did tell the researchers the right answer about two thirds of the time--significantly better than random guessing. The study, reported online this week in Proceedings of the National Academy of Sciences, suggests that early math education could take advantage of this innate talent, says Spelke.
The findings are "exciting," says Stanislas Dehaene, a cognitive scientist at the National Institute for Medical Research in Orsay, France, who obtained similar results testing Amazonian people who do not have language for numbers larger than 5 (ScienceNOW 19 August, 2004) It shows that we're born with "computational abilities," he says.