A new study conducted by four Harvard psychologists found that young children without any formal mathematics education are able to understand abstract numbers and perform basic arithmetic tasks.

The findings, which are slated for publication in the Proceedings of the National Academy of Sciences, add evidence to the commonly accepted belief that children are born with intuitive math abilities.

The research is also the “first good evidence” that children, when presented with arrays of dots during the experiment, think in terms of abstract numbers and not visual cues like the size of the dots, said lead author Hilary Barth, who was at Harvard working on the study and is now an assistant professor at Wesleyan University.

“We know that they’re not just saying that this array looks like this much stuff,” Barth said. “They are actually abstracting the number of items present and they are making their computations over numbers rather than over something directly perceptual.”

Researchers conducted four tests on five-year-old preschool children, according to co-author Elizabeth S. Spelke, who is Berkman Professor of Psychology. In one test studying comparison abilities, subjects were shown an array of blue dots on a laptop screen, Spelke wrote in an e-mail. The blue dots were obscured, and then a cluster of red dots appeared. The children were asked if there were more blue or red dots.

To test addition skills, an extra cloud of blue dots flashed on the monitor and were covered up before the red dots were introduced, Spelke wrote.

In two variations of the above tests, the red dots were replaced by a sequence of tones. Children were again asked whether there was a greater number of blue dots or “red beeps,” Spelke wrote.

Throughout the tests, researchers varied the size and other characteristics of the arrays and dots to see if children were relying on visual hints such as size of the dots or area of the clusters instead of representing abstract numbers.

“By manipulating the size of the visual items you’re presenting, you can try to trick the kids into using those kind of cues, such as the area of red stuff,” Barth said. “But we didn’t succeed in tricking them. They by default use the number of things.”

Barth added that researchers did not instruct the children to think in terms of numbers—the subjects did so on their own.

“It tells us more about the power of innate intuition in young children,” she said. “They have no training in symbolic education, yet they could make these very accurate estimations based on abstract numerical information rather than just perceptual information present in the stimulus.”

While University President Lawrence H. Summers caused a furor in January by suggesting the possibility of “intrinsic” differences between men and women’s math and science abilities, the boys and girls in the new study performed equally well.

“When you take the data we published and break it down by sex, you see no difference,” Spelke said in a follow-up telephone interview.

The paper does not explicitly address gender because the sample sizes of each gender were not large enough, she said.

Spelke said she thinks the study’s findings are intriguing in light of the fact that many elementary school students often struggle with learning basic math.

“We know that young children are wizards at learning things, and the number of elementary arithmetic facts is extremely small,” she said. “From what we know about children’s [learning], this should be very easy, but it’s not.”

The finding that children can comprehend abstract numbers suggests that different teaching methods might make math easier for them to learn, Spelke added.

Any new methods “need to be tested systematically,” she said, but “I think it is a promising direction.”

—Staff writer David Zhou can be reached at dzhou@fas.harvard.edu.