When she was a graduate student at Johns Hopkins University, Jinjing Jenny Wang kept wondering: How do children learn to count?
It's so basic, "but when you think about the problem, it is really difficult," she said. "There is no number in this world we can see and touch. There's no 'three-ness' in the world that is perceivable."
Linguists, philosophers and scientists have puzzled over this, Wang said. She knew that decades of research had established that children typically don't fully understand numbers until they are preschoolers, but she wondered what they knew before then. "How do they know these words are associated with numbers - or quantities in the world?" she asked.
What she and Lisa Feigenson, a cognitive scientist at Johns Hopkins, learned from experiments is revelatory: Babies are able to understand something important about numbers long before they can say them out loud. The researchers discovered that children as young as 14 months old are capable of recognizing that counting is related to quantity - even if they're still a few years away from truly understanding what "one, two, three" means.
The findings are one more piece in the puzzle showing how an infant's mind develops something fundamentally human: the ability to engage in complex, abstract thinking. And the results are surprising, because earlier research has shown that although young children often can say the numbers from 1 to 10, they don't truly understand what the numbers mean until they're about 4 years old.
"A lot of kids can repeat the numbers in sequence," Feigenson said. But it seems that early on, they are probably reciting, the way younger children can remember phrases such as, "Eeny, meeny, miny, moe," and "Mary had a little lamb."
"This work is really groundbreaking," said Sara Cordes, an associate professor of psychology at Boston College who was an editor for Developmental Science, which just published the findings. "It suggests that infants are linking the count routine to an understanding of numbers much earlier than we had thought before."
When Wang proposed testing whether babies know what counting is, Feigenson told her, "Jenny, you're crazy, they obviously won't." She tried to talk Wang out of it.
After all, most children, if asked to hand over a set number of toys, can't reliably do that until about age 4. It's not until then that they really understand that words like "three" and "five" represent a precise quantity.
But Wang had done so much good work in her lab, with her dissertation well underway, Feigenson said, that she eventually agreed to the study. "Live and learn," Feigenson thought.
The design of the experiment was simple: They played a hide-and-seek game with babies. Researchers showed 14- and 18-month-old babies four toys and hid them in a box. The babies couldn't see inside, but they could reach in to pull out toys.
Researchers showed the babies the little dogs or cars, and counted out loud as they dropped them into the box, saying, "Look! One, two, three, four-four dogs!"
Other times, they didn't count, but said, "This, this, this and this - these dogs!" as they dropped them into the box.
When they didn't use number words, the babies often became distracted after a researcher pulled out a single toy, as though they had no expectation there were more toys in the box.
When the researchers did count, the babies expected more toys would come out and would reach into the box to find them. They didn't know the precise number, but could remember the approximate number, reaching for about the right number of toys.
Feigenson said the early results indicated "it clearly worked - the babies are responding to counting. I thought, 'That's not right.' We ran four more studies, with different conditions."
They tried replacing the counting numbers in the script with names, labeling the toys Sophie, Katie, Annie, Mary, before dropping them into the box. And the babies responded as they had without numbers - which is to say, not reaching for multiple toys. "That made us think we're actually finding something about babies' understanding about counting instead of just a way to improve their memory," said Wang, now a postdoctoral student who will become an assistant professor at Rutgers University.
"My intuition was totally wrong," Feigenson said, not for the first time, even after 16 years as a professor at Hopkins specializing in the development of numeric ability in children. "It's great fun that the science continues to surprise me."
Wang said the research doesn't upend previous findings; scientists don't think a 1-year-old can understand what "five" truly is. But it shows babies understand something about counting before they understand the number words, recognizing they are signaling quantity.
In Feigenson's Laboratory for Child Development, researchers study the origins of thoughts - how people learn, how much of humans' capacity to understand intricate ideas is innate, and how much is gleaned through their environment and social and educational cues. When babies see a block, do they understand the block will still be there after they blink? Do they understand it's solid? That if you drop it, it will fall?
"Our research would fall flat really fast if babies didn't enjoy the experiments," Feigenson said, because the only way to motivate an infant is to make an experience fun.
Still, the work has its challenges, such as subjects falling fast asleep mid-experiment or starting to wail. "They cry, they're hungry, they need to take a break - they drop their pacifier on the ground," Feigenson said. Every scientist faces tribulations in the lab, she said. "The baby scientists just have funnier tribulations."
The counting study leads to a lot of other questions. Wang wonders how important the social aspects of the counting routine are to learning. Feigenson asked what it is about counting that signals to a baby that the words are about quantity, and whether early counting affects later ability to think about math. They have been running studies testing whether babies respond to counting in a foreign language, and plan to test whether babies will respond to irregular counting, such as "1, 4, 2, 3."
Wang, whose first baby is due any moment, is already wondering about her daughter. "I don't think I can stop thinking" about the science as a new mom, she said. "I'll be trying to figure out what she is thinking."