Psychologists at Harvard University have found that preschoolers are able to grasp numeric abstractions and arithmetic concepts without formal education or the language to express this knowledge in words. Scientists conclude that these skills are inborn. The discovery could lead to the development of new teaching techniques that would make arithmetic easier and more pleasant for grade school children.
"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 continues, "A fundamental question for psychology is, 'Where do abstract number concepts come from?' 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."
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.
Co-authors on the PNAS paper are Hilary Barth, Kristen La Mont and Jennifer Lipton, all of Harvard's Department of Psychology.
Glenn Doman's book How to Teach Your Baby Math gives detailed instructions on using dot cards. You can download Math Diamonds and use them in the same way that you would use dots.