Q & A: Psychologist Discusses Infants' Ability To Perform Math
Research by Karen Wynn, an assistant professor of psychology at the University of Arizona, concludes that even young infants can perform addition and subtraction of small numbers. The study, reported in the Aug. 27 issue of the journal Nature, involved 64 5-month-old infants. Ms. Wynn discussed her study with Assistant Editor Deborah L. Cohen.
Could you briefly describe the purpose of your study and research methods?
Previous research had shown that babies can distinguish small numbers; they can tell apart "twoness'' from "threeness'' and "oneness'' from "twoness'' and so on. The question was, "Do they have a numerical appreciation of them or understand the numerical relationship between these small numbers, or is it more perceptual?'' This study involved seeing whether infants are aware of these simple numerical relationships.
The methodology I used relies on a phenomenon that has been used over the past 15 or 20 years in studies of infants, and that is that infants tend to look longer at something they find surprising or unexpected.
What I did was to show infants an addition or subtraction--either with the correct outcome or ... an incorrect final number of objects--with the reasoning that if infants are able to compute these simple additions and subtractions, they will have an expectation of what the results should be and [thus] look longer at the incorrect results.
For example, in a one-plus-one situation, the babies sat on a table facing a display area sort of like a puppet stage. They would see a hand coming in from the side of a display placing a Mickey Mouse doll in the center of the display. Then a screen was placed in front ... hiding the doll. Then they would see a hand coming in a second time with another Mickey Mouse doll and then placing it out of sight behind the screen along with the first doll.
The question was, "Does the baby have the expectation of how many dolls should be there?'' Then we would remove the screen and show either the correct number of objects or an incorrect number, and then we would simply measure babies' looking time.
What we find is that babies look longer at an incorrect than a correct result. It was the same [principle] with subtraction. Only in this case [when one of two dolls is taken away] the babies look longer when there are two objects rather than one.
What we infer from this is that, since the babies are always looking longer at the incorrect results, they are able to determine the results of these simple additions and subtractions.
What do you think are the most important implications of your findings?
What it suggests to me is that we have some innate understanding of numbers that is built into us. Just the fact that infants are able to perform this at such an early age suggests that it may be innate.
Another [aspect] is that a wide range of studies on animals [has] shown this kind of ability to discriminate numbers, which suggests that an innate mental mechanism dedicated to determining number in the environment and to performing these simple rudimentary calculations may be part of our common cognitive structure.
How do you know that the babies' response means they understood the arithmetical concept underlying the change in quantity? Isn't it possible that they were simply responding to an unexpected change in the display?
The first experiment I did was a one-plus-one situation, resulting in one object or two. We found babies ... were surprised when they saw only one object, not two. The natural predisposition is for them to look longer at something new, but, in this case, they are looking longer at what the original situation was because they know the addition or subtraction should have altered the situation.
One interpretation is that they were expecting exactly two and computing the result; another is that they knew that if you add something there should be a change, but they didn't know how big or in what direction, more or less. The control I did for that was ... a one-plus-one situation that either resulted in two or three. In this case, both the results differ from the original number, so if they weren't computing the precise result, they should be equally happy to see two or three. But in this case ... they were surprised that there were three, not two. This shows to me a very specific expectation of exactly what that change should be numerically.
You stated in your study that these findings "may provide the foundations for the development of further arithmetical knowledge.'' What are the implications for students, teachers, and schools?
I'm not sure there are any implications for students, teachers, and schools--I would not expect so at this point. In general, this kind of research is aimed at laying out just what is the fundamental structure of human cognition. The more we know about ways in which the normal human mind functions, the better we will be able down the road to understand what's different about individuals whose mental functioning deviates from the norm and how to ultimately address their problems.