Babies of fourteen to eighteen months old, who cannot form the words “one,” two, or “three,” can understand the concept of counting anyway, Johns Hopkins University researchers concluded after a recent study. Jenny Wang and Lisa Feigenson wanted to test whether the counting books for babies and counting rhymes for toddlers had a measurable impact:
To find out, Feigenson and first author Jenny Wang, a former graduate student at Johns Hopkins who is slated to become an assistant professor at Rutgers University, worked with sixteen infants between 14 and 18 months old. The babies watched as toys, little dogs or cars, were hidden in a box that they couldn’t see inside of, but could reach into.
Sometimes the researchers counted each toy aloud as they dropped them into the box, saying, “Look! One, two, three, four — four dogs!” Other times the researchers simply dropped each toy into the box, saying, “This, this, this and this — these dogs.”
Without counting, the babies had a hard time remembering that the box held four things. They tended to become distracted after the researchers pulled just one out — as if there was nothing else to see. But when the toys were counted, the babies clearly expected more than one to be pulled from the box. They didn’t remember the exact but they did remember the approximate number.
“When we counted the toys for the babies before we hid them, the babies were much better at remembering how many toys there were,” Wang said. “As a researcher these results were really surprising. And our results are the first to show that very young infants have a sense that when other people are counting it is tied to the rough dimension of quantity in the world.”Johns Hopkins University, “Babies understand counting years earlier than believed” at ScienceDaily (October 24, 2019)
The question under study was not whether the infants understood the exact numbers (they didn’t) but whether they understood that the researchers were, in fact, counting things:
In a subsequent experiment, researchers let the babies retrieve three toys before their searching response was measured. Even with counting, the babies seemed less interested in exploring the box in this scenario, “suggesting that infants represented the counted arrays imprecisely,” the study authors write. Still, the results of the initial experiment indicate babies comprehend that numbers signal quantity, sometimes before they are even able to say, “one,” “two” and “three.” Indeed, when the researchers tried labelling the toys with names instead of numbers ( “Look! This is Sophie, Katie, Annie, Mary!”), the young study subjects did not look for additional toys after two were retrieved, reacting the same way they did when numbers were not used.Brigit Katz, “Babies May Understand Counting Before They Fully Understand Numbers” at Smithsonian.com
Approximate number sense is more important in early childhood development than we may realize:
As Wang explained, something about the process of counting helps young children mentally alter how they look at a series of objects. Normally, a toddler tries to hold each individual item in her limited working memory. But watching an adult count the items seems to trigger the baby to view them as a set, and she switches to using the approximate number sense—one of the earliest math skills to develop, which allows someone to roughly compare groups of items and understand, for example, that eight items is more than five items. In the study, toddlers were able to distinguish four objects from six and continue to look for more hidden ones, but they did not differentiate three hidden objects from four, suggesting that they were relying more on estimates of the numbers rather that specifics.Sarah D. Sparks, “Infants Recognize Counting Long Before They Can Say, ‘1, 2, 3’” at Education Week
Wang added that numbers, unlike pets or treats, are abstractions. We must grasp them mentally as well as experientially. In fact, when they become very large, we can only grasp them mentally.
Wang and Feigenson hope to go on to study whether there is a relationship between early rough counting exercises of this type and later numerical skills.
The paper, “Infants recognize counting as numerically relevant” by Jenny Wang and Lisa Feigenson in Developmental Science, requires a subscription.
Note: The chiliagon is sometimes used to demonstrate the abstract nature of numbers. It is a mathematical figure with one thousand sides. It can be understood in principle as an abstraction but cannot really be pictured.