CAMBRIDGE, Mass., Sept. 19, 2005 -- Psychologists at Harvard University have found that five-year-olds are able to grasp numeric abstractions and arithmetic concepts even without the formal education or language to express this knowledge in words. The discovery of these inborn skills among preschoolers could point the way to new teaching techniques, making arithmetic easier and more pleasant for elementary school children.
A paper describing the findings will be published in the Proceedings of the National Academy of Sciences and is now on the journal's web site.
"Teaching symbolic arithmetic is one of the primary tasks of the first four years of elementary education," says co-author Elizabeth S. Spelke, a professor of psychology in Harvard's Faculty of Arts and Sciences. "Some children have enormous trouble mastering this skill, and most children find symbolic arithmetic challenging and, at times, confusing. Our studies say, however, that children already have a basic understanding of this domain. I hope our work points the way to improving mathematics education by building on this understanding."
Spelke and her colleagues asked 16 preschoolers to compare arrays of dots on a computer screen, or to merge two sets of dots and then compare these with a third set. Even without the symbolic knowledge of arithmetic that formal schooling brings, the five-year-olds could consistently tell which sets of dots were larger. Further successful comparisons between arrays of dots and sounds reinforced that the children understood the basic concept of amount.
These skills contrasted sharply with the preschoolers' ability to comprehend symbolic arithmetic, as is taught in school. For instance, children were unable to answer verbal questions about numerical addition, such as: "Suppose you have 15 marbles and your mom gives you 10 more, while your sister has 20 marbles. Who has more marbles, you or your sister?"
However, the children were able to solve this same problem when it was presented in non-symbolic form, such as an array of 15 blue dots, then a second array of 10 blue dots, and finally a sequence of 20 tones. When asked whether there were more dots or tones, the youngsters were able to give correct answers.
"A fundamental question for psychology is, 'Where do abstract number concepts come from?'" Spelke says. "Some have suggested they come from human language or are constructed by children during formal instruction; our studies provide evidence that children have abstract number concepts, and that they can operate on these concepts to perform addition, before they start school. We conclude that abstract number concepts do not depend either on language or on instruction."
Spelke's co-authors on the PNAS paper are Hilary Barth, Kristen La Mont and Jennifer Lipton, all of Harvard's Department of Psychology. The work was funded by the National Science Foundation, National Academy of Education and the Spencer Foundation.
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