Penn linguist determines tipping point for children learning to count

Once a child has learned to count to the number 73, he or she can count as high as 100 and continue to infinity, according to research from Charles Yang, an associate professor in the Department of Linguistics in the School of Arts & Sciences and director of undergraduate studies at the Institute for Research in Cognitive Science.

Yang studies how children learn language. Until recently, his work focused on exceptions to rules, like past tense or plural, for example, when adding “-ed” or “-s” doesn’t apply to words, such as “think” and “thought” or “ox” and “oxen.” After attending a conference about numerical cognition, he started contemplating how children learn to count.

“The first 10 words are completely unhelpful. They won’t tell you anything about how numbers are forming. They are just arbitrary sounds,” Yang explains. The words “one,” “two,” “three,” “four,” “five,” “six,” “seven,” “eight,” “nine,” and “ten” follow no logical rule, making the series itself hard to learn, and patterns ungeneralizable.

Children absorbing language subconsciously need such rules, so based on how the first 10 numbers sound, 11 spoken aloud should read “one-teen,” much like 14 becomes a combination of the words “four” and “teen.” There are 17 such outliers—1 through 10, plus 11, 12, 13, 15, 20, 30, and 50. For those numbers, memorization becomes the sole educational mechanism.

“The more exceptions a rule has, the longer it takes the brain to process words that follow this rule,” Yang says. “A child’s brain is looking for a more efficient way of organizing and processing linguistic information.”

Figuring out how many irregular numbers existed allowed Yang, a computer scientist by training, to determine how high a child would have to count to fully develop the concept of numbers over time. He turned to a formula he had discovered for his other language work, a simple equation based on the number of exceptions to a rule. He has a book on the subject coming out soon.  

“I was stunned to discover the equation predicted [a threshold at] 73,” he says. Yang calls this the tipping point. It corroborated research from the 1980s that had revealed that counting to the low 70s predicted further counting skill. Here, finally, was a potential reason why, suggesting the human ability with numbers may be language-based.

Interestingly, a number system’s complexity determines where that threshold lies. For example, the Chinese classification has fewer irregularities than counting in English—meaning fewer outliers to memorize—so children counting in that system can reach 100 by the time they are 4-and-a-half—a full year earlier than American English learners.

Conversely, there’s a greater delay with children learning to count in languages like Tamil, with its more complex system.

Yang has just scratched the surface in this field. He’ll soon start collaborating with Elizabeth Brannon, the Edmund J. and Louise W. Kahn Term Chair in the Natural Sciences in the Department of Psychology, who specializes in numerical cognition, among other areas.

In addition, Yang plans to assess broader uses for his equation in language decision-making processes and beyond.

Counting 73