CAMBRIDGE, Mass., Sept. 19, 2005 -- Psychologists at Harvard Universityhave found that five-year-olds are able to grasp numeric abstractionsand arithmetic concepts even without the formal education or languageto express this knowledge in words. The discovery of these inbornskills among preschoolers could point the way to new teachingtechniques, making arithmetic easier and more pleasant for elementaryschool children.
A paper describing the findings will be published in the Proceedings ofthe National Academy of Sciences and is now on the journal's web site.
"Teaching symbolic arithmetic is one of the primary tasks of the firstfour years of elementary education," says co-author Elizabeth S.Spelke, a professor of psychology in Harvard's Faculty of Arts andSciences. "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 basicunderstanding of this domain. I hope our work points the way toimproving mathematics education by building on this understanding."
Spelke and her colleagues asked 16 preschoolers to comparearrays of dots on a computer screen, or to merge two sets of dots andthen compare these with a third set. Even without the symbolicknowledge of arithmetic that formal schooling brings, thefive-year-olds could consistently tell which sets of dots were larger.Further successful comparisons between arrays of dots and soundsreinforced that the children understood the basic concept of amount.
These skills contrasted sharply with the preschoolers' ability tocomprehend symbolic arithmetic, as is taught in school. For instance,children were unable to answer verbal questions about numericaladdition, such as: "Suppose you have 15 marbles and your mom gives you10 more, while your sister has 20 marbles. Who has more marbles, you oryour sister?"
However, the children were able to solve this same problem when it waspresented in non-symbolic form, such as an array of 15 blue dots, thena second array of 10 blue dots, and finally a sequence of 20 tones.When asked whether there were more dots or tones, the youngsters wereable to give correct answers.
"A fundamental question for psychology is, 'Where do abstract numberconcepts come from?'" Spelke says. "Some have suggested they come fromhuman language or are constructed by children during formalinstruction; our studies provide evidence that children have abstractnumber concepts, and that they can operate on these concepts to performaddition, before they start school. We conclude that abstract numberconcepts do not depend either on language or on instruction."
Spelke's co-authors on the PNAS paper are Hilary Barth, Kristen La Montand Jennifer Lipton, all of Harvard's Department of Psychology. Thework was funded by the National Science Foundation, National Academy ofEducation and the Spencer Foundation.
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