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The New Math: Kids Can Add and Subtract without Arithmetic

Knowing how to count lets kindergartners do arithmetic before they learn its rules
child and abacus



© ISTOCKPHOTO/DON BAYLEY
Young children can crudely add and subtract numbers before they have learned the rules of arithmetic, a new study finds. Researchers presented five- and six-year-old children with problems such as, "Sarah has 15 candies and she gets 19 more; John has 51 candies. Who has more?" To answer correctly, researchers say, the children must be harnessing an intuitive sense of how large different numbers are, which could help ease the pain of learning arithmetic.

Prior studies have shown that children as young as infants can judge simple mathematical relationships. When shown bunches of dots on a computer screen, for example, a preschool- or kindergarten-age child can tell that there are more dots combined in an image of 21 dots followed by one of 30 dots compared with a third 34-dot image.

A group including cognitive psychologist Elizabeth Spelke of Harvard University wondered if children could apply that ability, called nonsymbolic arithmetic, to Arabic numerals after learning to count but before they learned to add and subtract.

To find out, they gave several groups of children a laptop-based audiovisual test that asked whether one person had more or fewer candies or other objects than another person. The screen showed numbers to be added, such as 21 and 30, or subtracted, such as 64 and 13, followed by another number, such as 34, with which to compare the added or subtracted value.

The children answered correctly from 64 to 73 percent of the time, according to a report published online today by Nature. More affluent kids tested in the laboratory did better than their less well off peers tested in their classrooms, the group reports. The reason for the difference could be the testing environment, says Spelke, who adds that the important point is that kids from diverse backgrounds all showed the ability. "We never dreamed that you could simply give children the symbols and they will succeed," she says.

Consistent with the use of nonsymbolic arithmetic, their answers were more accurate the greater the difference was between the sum (or difference) of the first two numbers and the comparison number. Kids also did better when adding than when subtracting. (Subtraction requires a larger number than addition to arrive at the same comparison, and larger numbers have fuzzier sizes in nonsymbolic arithmetic, Spelke says.)

Spelke says the link between number symbols and nonsymbolic arithmetic might help kids learn math more easily. Teachers were skeptical of the experiment because arithmetic lessons easily frustrate children, but "the kids really loved these problems," she says. "It looks to us like a big part of the logic of addition and subtraction is already available to them."

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