If a 6-month-old can distinguish between 20 dots and 10 dots, she’s more likely to be a good at math in preschool. That’s the conclusion of a new study, which finds that part of our proficiency at addition and subtraction may simply be something we’re born with.
Researchers have long wondered where our math skills come from. Are they innate, or should we credit studying and good teachers—or some combination of the two? “Math ability is a very complex concept, and there are a lot of actors that play into it,” says Ariel Starr, a graduate student in psychology and neuroscience at Duke University in Durham, North Carolina.
One of those actors appears to be the approximate number system, or the intuitive capacity to discern between groups of objects of varying magnitudes. We share this talent with numerous other animals, including rats, monkeys, birds, and fish. Some of those animals, for example, can match the number of sounds they hear to the number of objects they see, while others can watch handlers place different numbers of food items into buckets, and then choose the bucket with the most food. For ancient humans, this skill would have been an asset, Starr explains, by helping a group of humans determine if predators outnumbered them, for example.
Researchers suspect that this intuitive number sense may play into humanity’s unique ability to use symbols to do math. While both a monkey and a human can look at photos of 20 and 30 dots and then choose a photo of 50 dots to represent that total value, only a human can add the symbolic Arabic numerals for 20 and 30 together to get 50.
Past studies have investigated intuitive number sense in humans ranging in age from preschoolers to college students. Some researchers asked those study participants to take math tests and judge approximate numbers on the spot, while others compared a participant’s current intuitive number sense to their past standardized math test scores. Those people who are best at math, researchers found, also tend to be good at approximating numbers. But these tests presented a chicken-or-egg situation: Does excelling at math sharpen a person’s ability to approximate numbers, or are people who are good at approximating numbers most likely to go on to excel at math?
Now, a new study published online today in the Proceedings of the National Academy of Sciences clarifies the direction of that relationship. The study confirms that a child’s ability to approximate numbers seems to act as a foundation for developing math skills later in life.
To get around some of the caveats with earlier work, the researchers turned to infants who had not yet learned to talk or manipulate numbers. Starting with babies “is really critical because a lot of math-related education happens informally through parents, society, and in preschool,” says Michele Mazzocco, a professor in the Institute of Child Development at the University of Minnesota in Minneapolis who was not involved in the study. In other words, infants provide a relatively clean slate for judging how intuitive number sense later relates to math abilities. “This is a very important contribution,” she says.
Starr and her colleagues recruited 48 6-month-old infants to briefly join them in the lab. The researchers showed the babies opposing images of two sets of dots that flashed before them on a screen. One side of the screen always contained 10 dots, which were arranged in various patterns. The other side alternated between 10 and 20 dots, also arranged in various patterns. The team tracked the infants’ gaze—a common method for judging infant cognition—to see which set of dots they preferred to watch. Babies prefer to look at new things to old things, so the pattern of dots that flashed between arrays of 10 and 20 should appear more interesting to infants because the dots were changing not just in position, but in number. Both screens changed dot position simultaneously, so in theory, the flashing pattern changes were equally distracting. If an infant indicated that she picked up on the difference in dot numbers by preferentially staring at the 10- and 20-dot side of the screen, the researchers concluded that her intuitive number sense was at work.
To see how, if at all, the infants’ intuitive number sense related to their math ability later in life, 3 years later, the researchers invited those same babies to return to the lab. The team asked the children to complete a set of standardized tests that measure math ability, intuitive number sense, understanding of number words, and general intelligence. The researchers tested whether children knew what Arabic numerals meant, for example, and asked them to solve word problems such as, “If Johnnie has one cookie and them his mom gives him three more cookies, how many cookies does he have?” They also asked the children to complete visual arithmetic problems, such as showing them an image of two tokens, replacing that image with another depicting three tokens and then asking them how many tokens exist in total. To account for differences in general intelligence, the kids completed standardized verbal and nonverbal tests such as tasks that required them to fill-in-the-blanks for missing words in sentences and choose between images of objects missing from photos.
Children who performed in the top 50% of the math achievement test had a significantly higher intuitive number sense in infancy than those who performed in the bottom 50%, the authors found. This relationship held true even when the researchers controlled for general intelligence. However, although differences between the children’s scores were large and the relationship between intuitive ability and math ability was significant, it did not explain all of the statistical model’s variation. “It’s not like 90% of children’s scores were explained by infant scores,” says Elizabeth Brannon, a cognitive scientist at Duke University and senior author of the paper. This is not surprising, she says, because prior research indicates that “there are tons and tons of things that influence how well someone does at math later on.”
Starr agrees. It’s likely that intuitive number sense plays a role in a person’s math abilities later in life, she adds, but other things—experience, education, motivation, and more—also significantly shape a person’s math achievements. In other words, Starr says, “if you hand me a baby, I can’t look at how long it looks at some dots and predict its SAT scores in high school.”
The study “beautifully” establishes the link between approximate number systems and formal math, say Darko Odic, a fifth year graduate student in the psychological and brain science department at Johns Hopkins University in Baltimore, Maryland, who has authored numerous scientific papers about young children and math and was not involved in the research. Now, he says, researchers need to figure out the basis of that relationship, including what drives it biologically and whether we can use it to help children better learn math.
The team plans to tackle that latter question in future experiments. Now, it is adapting activities such as arithmetic dot-tracking and comparison, shown to improve intuitive number in college-age students, for younger students at the preschool and even infant level. “Designing intervention strategies for infants is trickier,” Starr says, “but hypothetically speaking, in theory some of the ways we work with preschool children could be scaled down to infancy.”