The ability to learn complex, symbolic math is a uniquely human trait, but it is intricately connected to a primitive sense of magnitude that is shared by many animals, finds a study recently published by the Proceedings of the National Academy of Sciences (PNAS).
"Our results clearly show that uniquely human branches of mathematics interface with an evolutionarily primitive general magnitude system," says lead author Stella Lourenco, a psychologist at Emory University. "We were able to show how variations in both advanced arithmetic and geometry skills specifically correlated with variations in our intuitive sense of magnitude."
Babies as young as six months can roughly distinguish between less and more, whether it's for a number of objects, the size of objects, or the length of time they see the objects. This intuitive, non-verbal sense of magnitude, which may be innate, has also been demonstrated in non-human animals. When given a choice between a group of five bananas or two bananas, for example, monkeys will tend to take the bigger bunch.
"It's obviously of adaptive value for all animals to be able to discriminate between less and more," Lourenco says. "The ability is widespread across the animal kingdom -- fish, rodents and even insects show sensitivity to magnitude, such as the number of items in a set of objects."
Only humans, however, can learn formal math, including symbolic notations of number, quantitative concepts and computational operations. While the general magnitude system has been linked primarily to the brain's intraparietal sulcus (IPS), higher math requires the use of more widely distributed areas of the brain.
For the PNAS study, the researchers wanted to build on work by others indicating that a lower-order sense of number is not just a separate function, but plays a role in the mental capacity for more complex math.
The researchers recruited 65 undergraduate college students to participate in an experiment. To test their knack for estimating magnitude of numbers, participants were shown images of dots in two different colors, flashed for only 200 milliseconds on a computer screen. They then had to choose which color had the greater number of dots. Most people can quickly distinguish that a group of 10 dots is greater than a group of five, but some people have a finer-grained number sense that allows them to discriminate between 10 and nine dots.
The participants were also shown dots of varying sizes and colors to test their ability to gauge magnitude of area.
They then completed a battery of standardized math tests.
The results showed that the more precise the participants' abilities were at estimating the magnitude of a number, the better they scored in advanced arithmetic. The same correlation was found between precision at gauging magnitude of area and the geometry portion of the standardized math test.
"By better understanding the psychological mechanisms underlying math abilities such as arithmetic and geometry, we hope to eventually inform how we come to learn symbolic math, and why some people are better at it than others," says study co-author Justin Bonny, an Emory graduate student of psychology. "It may then be possible to develop early interventions for those who struggle with specific types of math."
U.S. teens lag in math skills compared to other industrialized countries. China ranked number one in math in 2010, the first year that the country participated in the Program for International Student Assessment, while the United States ranked number 31.
"Falling behind in math is a huge problem," Lourenco says, "given that we live in an increasingly technological society and a globally competitive world."
- S. F. Lourenco, J. W. Bonny, E. P. Fernandez, S. Rao. Nonsymbolic number and cumulative area representations contribute shared and unique variance to symbolic math competence. Proceedings of the National Academy of Sciences, 2012; DOI: 10.1073/pnas.1207212109
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