According to a study conducted at Harvard University, children as young as five years old are able to solve approximate addition and subtraction problems involving large numbers even before they have been taught basic mathematical concepts.
The study, conducted at Harvard by researchers from Harvard and the University of Nottingham, and published in the journal Nature, suggests that elementary education in mathematics might be improved if children's seemingly natural talent for approximate calculation were recognized and enhanced in a classroom setting.
One of the study's authors, Elizabeth Spelke, stated, "We've known for some time that adults, children, and even infants and non-human animals have a sense of number. We were surprised to see, however, that children spontaneously use their number sense when they're presented problems in symbolic arithmetic. These children haven't begun to be taught place value or exact addition facts," says Spelke. "Nevertheless, their natural sense of number gives them a way to think about arithmetic."
Researchers presented five-year-old children with a series of illustrated problems in the form of scenarios that involved the approximate addition and subtraction of symbolic numbers between five and 98. A subtraction question, for example, stated: "Sarah has 64 candies and gives 13 of them away, and John has 34 candies. Who has more?" The children performed well above chance on the tests and didn't have to resort to guessing. At the same time, the children were unable to provide an exact solution to the problems, showing that their performance with approximate numbers was not dependent on precise knowledge of the numbers.
Researcher Camilla Gilmore, a research fellow based in Nottingham's Learning Sciences Research Institute says: "Exact symbolic arithmetic takes years to learn and poses difficulties for many children. For this reason, teachers were concerned that our problems would frustrate the children, and they were amazed at the children's success and engagement. Our findings suggests new possible strategies for teaching primary mathematics and making it fun."