This article in Scientific American got my attention when I was searching to see if Scientific American has a kids magazine (I can't seem to find one…anyone know?)
Seems that they have done a study that shows that "young children can crudely add and subtract numbers before they have learned the rules of arithmetic":
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.
Looks like kids without formal instruction in arithmetic can still have a basic understanding of it. My favorite quote from the article was from cognitive psychologist Elizabeth Spelke of Harvard University:
"We never dreamed that you could simply give children the symbols and they will succeed," she says.
And my second favorite quote:
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."
Veeery interesting….I wonder if half the enjoyment was at being asked to try to figure it out for themselves rather then being told how to do it?