Numbers in Mind

Babies' ballyhooed counting skills add up to controversy

In 1992, Karen Wynn’s numbers came in big. The numbers in question were tiny in an absolute sense, but they counted for a lot among investigators of child development. The reason: Wynn claimed to have exposed intuitive arithmetic skills of 5-month-old babies. The young psychologist, having received her doctorate in psychology just 2 years earlier, reported that infants show a facility for adding and

YOUR NUMBER’S UP. A baby sits on her father’s lap and gazes at one of a series of displays in a quantification study at Harvard University. Kirsten Condry

subtracting small numbers of items, on the order of 1 + 1 = 2 and 2 – 1 = 1. Her results appeared in a major scientific journal, attracted worldwide media coverage (SN: 8/29/92, p. 132), and inspired a wave of research into what she regards as infants’ seemingly innate “number sense.”

Now at Yale University, Wynn is more convinced than ever that babies, along with many nonhuman animals, carry an evolutionary legacy of basic number skills. She’s also aware, however, that a spirited debate has emerged about whether the line of research that she’s championed really taps into an inborn counting mechanism in the human brain.

Some scientists argue that babies use non-numerical visual cues, such as the area and length of the border around visible items, to make quantitative judgments. These handy perceptual features, which vary along with changes in item number, may eventually serve as building blocks when youngsters really learn to count, between ages 2 and 4, in these researchers’ view.

Or perhaps babies rely on an innate facility for making automatic distinctions of up to three or four items without counting them out, as some other scientists theorize. Calculation-free perception of small quantities could jump-start mathematical thinking in the preschool years.

These divergent explanations reflect a broad philosophical split among explorers of mental development. Researchers on one side hold that babies are born with the neural keys to unlock specific types of knowledge, including language use (SN: 5/3/97, p. 276: and face recognition (SN: 5/18/02, p. 307: Baby Facial: Infants monkey with face recognition). Across the gap stand scientists who regard learning as akin to a series of chemical reactions, in which a baby’s inborn motor and perceptual inclinations and natural desire for stimulation and contact mix together and precipitate new types of knowledge (SN: 3/20/99, p. 184).

These positions leave little room for compromise. Nonetheless, scientists who study infants’ number capabilities see themselves as engaged in a constructive dispute. “The debate about the foundations of numerical thinking has been incredibly productive over the past decade,” Wynn says. “Our science has become better as a result of it.”

Tots who total

If you want a baby to count, get a screen and two or three rubber Mickey Mouse dolls and then toy with the child’s curiosity. That’s the tactic Wynn took in her 1992 study.

In a “1 + 1” task, for example, 5-month-olds watched an experimenter place a doll on a table and then put a screen in front of it. The babies then observed the experimenter hide a second Mickey behind the screen. In a “2 – 1” task, infants saw the experimenter place two dolls on a table and then hide them with a screen, followed by the experimenter reaching behind the barrier and removing one doll in full view of the baby. Behind the screen, a second experimenter could remove or add dolls without the baby’s knowledge.

At that point in each task, the screen was removed. In three out of six repetitions of a task, an incorrect number of dolls appeared when the screen was removed, corresponding to “1 + 1 = 1” or perhaps “2 – 1 = 2.” The other trials concluded with a correct number of dolls.

Infants looked considerably longer at incorrect numbers of dolls. Since babies typically spend more time looking at new or surprising items than at familiar ones, Wynn concluded that her pint-size participants counted up how many toys were behind the screen and were intrigued by errant results.

This finding built on earlier evidence that, at about the same age, babies know that an object exists when it moves behind a barrier. Moreover, a 1980 study had indicated that 6-month-olds can discern when a small number of drumbeats matches the number of items shown in a picture.

Some researchers, however, doubt that babies actually manipulate numbers when confronted with small quantities such as those in Wynn’s addition and subtraction tasks. The infants’ impressive feats may rest on estimates of the total surface area of objects, not their number, report Harvard University psychologist Elizabeth S. Spelke and her colleagues Lisa Feigenson and Susan Carey in the Feb. 1 Cognitive Psychology.

In a variation of Wynn’s original study, 6-month-olds first looked at a small, irregularly shaped toy made of Lego pieces. A researcher then lowered a screen in front of the toy and openly placed a second, same-size Lego toy behind the screen.

When the screen was removed, infants showed little interest if they saw one large Lego toy that equaled the total area of the previous two small toys. If babies understand numbers, this incorrect result should have attracted their attention. However, the same babies looked longer if the raised screen revealed two large Lego toys–the correct number result that should have left them nonplussed–that covered twice the total area of the initial two toys.

Spelke says that in Wynn’s addition-and-subtraction study, infants looked longer at incorrect numbers of Mickey Mouse dolls because those displays also deviated from the dolls’ expected total surface area.

Since Wynn’s original experiments, she has devised other means of testing infants for number knowledge. A recent study directed by the Yale psychologist, slated to appear in Cognition, finds that 5-month-olds identify and count groups of dots that move in cohesive bunches across a computer screen. Half of 24 infants sat and watched a computer display in which each of two groups of three dime-size, red dots traveled a straight path from the bottom of the screen to the top. The rest viewed a display of four ascending groups of three dots each.

After tiring of these presentations, the infants saw alternating displays of two groups of four dots each and four groups of two dots each. Babies looked much longer at the display with the number of moving groups that they hadn’t seen before. The altered number of dots in each group didn’t seem to matter.

To make the task more difficult, each of the alternating groups contained eight dots. As a result, infants couldn’t distinguish on the basis of cues other than the number of groups, Wynn says. For instance, the total area of dots in each group and the total length of the borders around each group’s dots was the same in the two-group and four-group conditions.

Human infants share a numerical penchant with much of the animal kingdom, according to Wynn. Over the past 60 years, researchers have reported that creatures such as rats, birds, and monkeys (SN: 11/7/98, p. 296) display basic counting skills after training.

“Given that numerical abilities are present in so many animal species, it would be surprising if humans didn’t have a similar inborn capacity,” Wynn says.

Count us in

Babies show signs of being versatile counters. They can tally not just items and groups but also small numbers of actions and sounds, Wynn finds. In one experiment, half of a group of 6-month-olds watched a puppet jump up and down twice, then pause briefly before executing additional pairs of hops. The rest saw the same puppet perform three-jump sequences. Babies gradually lost interest in each routine and spent less time looking at the puppet’s capers.

In an ensuing session, the same infants saw the puppet switch between short sets of two jumps and three jumps. Novel numbers of jumps attracted much longer gazes from the babies, indicating to Wynn and her coworkers that the babies had monitored how many jumps occurred in each sequence.

Puppets also play a role in Wynn’s tests of sounds. After hearing sequences of either two or four sounds coming out of a speaker hidden in a puppet’s belly, 7-month-olds looked markedly longer at the puppet when it then emitted the sequence that they hadn’t previously heard. These data were presented by Wynn in April at the International Conference on Infant Studies in Toronto.

Big numbers don’t necessarily baffle babies, Spelke reports. In fact, infants’ numerical skills shine when they compare relatively large sets of items. Babies show particular skill at discerning one cluster of items from another if the number of items in each group differs by a 2:1 ratio, according to Spelke. In a study she conducted with psychologist Fei Xu of Northeastern University in Boston, 6-month-olds saw a succession of arrays of either 8 or 16 dots. From trial to trial, the positions and sizes of the dots changed. As a further perceptual precaution, arrays of 8 and 16 dots were equated for surface area and overall brightness.

Infants eventually lost interest in checking out dot clusters. In a subsequent session, though, they looked longer at novel-number displays when shown alternating arrays of 8 and 16 dots. In contrast, the same babies failed to discriminate 8 from 12–or 16 from 24–dots when tested in the same way.

Infants understand more than basic ratios, contends psychologist Elizabeth M. Brannon of Duke University in Durham, N.C. She finds that 11-month-olds distinguish between increasing and decreasing numbers of items in visual displays. In her experiment, babies first saw sequences of three displays portraying an ascending or descending number of blocks, such as 4 then 8 then 16 or 16 then 8 then 4. In subsequent tests, they saw alternating presentations of the previous block sequence and a sequence going in the opposite direction.

Novel sequences elicited longer looks from 11-month-olds but not from 9-month-olds, Brannon reports in the April Cognition. “Infants appreciate greater-than and less-than relations between numerical values before they’ve learned to speak,” she asserts.

Quantify this

Youngsters simply don’t have number knowledge until they’re preschoolers, argues Harvard’s Jerome Kagan. Babies operate in a perceptual world devoid of linguistic concepts such as number, in his opinion. Kagan argues that infants distinguish between a cup that’s three-quarters full and one that’s one-quarter full without possessing a concept of fractions, so they may show interest in unexpected clusters without counting up the items.

Real-life situations contain a range of perceptual cues to the quantity of visible items that are far simpler for infants and toddlers to use than a counting system, says psychologist Kelly S. Mix of Indiana University in Bloomington.

Consider a baby trying to choose between one plate of food or another. He or she may be swayed by the food’s total area, its edge length, its volume, the number of pieces, the ratio of food size to plate size, the time it took to dish the food up, or the rate at which food was dished.

“I think children build a concept of number out of basic perceptual abilities,” Mix says. “If babies really do use purely numerical knowledge in some situations, I’d want to know why they’re ignoring the many perceptual cues to quantity that are available.”

Infant quantification studies typically leave one or more crucial perceptual cues unaccounted for, contend Mix and her University of Chicago colleagues Janellen Huttenlocher and Susan C. Levine in the March Psychological Bulletin. Spelke’s finding that total surface area trumps counting for infants confirmed results reported by Mix and a colleague in 1999.

Aside from surface area, researchers have found that infants are sensitive to the rate, duration, and rhythm of sounds and visual events. These time-related cues could easily have influenced babies’ performance on Wynn’s jumping-puppet exercise, Mix says.

Infants use various perceptual cues to estimate the overall amount of something that appears to them as a solid mass, whether it’s a blob of whipped cream or a row of boxes, she theorizes. For sets of items–such as Wynn’s moving-dot entities–estimates of amount achieve rough accuracy from several characteristics, including contour length, area, and volume of items in each group.

A related theory posits that infants apply basic visual and spatial skills to numerical tasks. For instance, infants as well as many nonhuman animals may automatically distinguish among small numbers of items without having to count them, a process known as subitizing, says neuroscientist Tony J. Simon of Children’s Hospital of Philadelphia. When shown large sets of items, infants may notice quantitative differences only if the discrepancies are large enough, Simon proposes.

“Using current experimental methods, we can’t be sure we really know what infants know,” remarks psychologist Robert S. Siegler of Carnegie Mellon University in Pittsburgh, who studies how children learn math. For now, he favors Mix’s emphasis on the importance of perceptual cues to quantity during infancy.

Wynn differs but looks forward to the continuing debate. “Agreement in science is highly overrated,” she says.

Bruce Bower has written about the behavioral sciences for Science News since 1984. He writes about psychology, anthropology, archaeology and mental health issues.