Imagine a number line in your head. Got it? Now think about this: how did it get there in the first place; is the ability to map a number line in your mind an innate human ability, or is it a concept that must be learned?
For years, scientists who study our basic mathematical intuitions believed the number-line concept to be inborn. Now, researchers have shown that members of a remote tribe in Papua New Guinea do not intuitively map numbers along a line (despite understanding the concept of numbers), suggesting that the idea of a number line is actually a cultural construct.
To conduct the study, cognitive scientist Rafael Núñez and his colleagues at UC San Diego traveled by plane, (and then by foot) to the isolated mountain regions of Papua New Guinea. There, they met with members of the Yupno — a small group of roughly 5,000 indigenous people, native to the valleys of the country's Finesterre Range.
Most Yupno have little or no exposure to formal schooling, but they are still a number-savvy people. If asked to select three, six or seven items from a pile of fruit, for example, the Yupno comply with ease.
But when Núñez and his colleagues asked unschooled Yupno adults to place the numbers one through ten along a line 22 centimeters in length, something interesting happened. New Scientist's Anil Ananthaswamy explains:
Núñez asked 20 Yupno adults (14 of whom were unschooled, while others had attended middle school) and 10 controls in California to place the numbers 1 to 10 along a 22-centimetre-long black line printed on a white card. The numbers were presented randomly, either as pre-recorded words in Yupno dialects, or as a sequence of tones, or as a set of dots printed on white paper.
The team found that both the controls [control responses are plotted here in blue] and the schooled Yupno [yellow] mapped the numbers on to the line, though the schooled Yupno did so less evenly, tending to place the numbers towards one of the two endpoints. But the unschooled Yupno [red] completely ignored the extent of the number line. They lumped numbers 1 and 2 at one end of the line, and all other numbers at the other end.
Núñez and his colleagues claim these findings represent the first evidence that the concept of the number line is not a "universal intuition," but rather a cultural metaphor used for representing numbers — a claim with interesting implications for researchers who study the origins of mathematics. Elements of culture, Núñez notes, often require training and education to master, but they can also be incredibly subjective; does that imply that mathematics should be thought about in more constructivist terms? Núñez seems to think so:
"Mathematics all over the world — from Europe to Asia to the Americas — is largely taught dogmatically, as objective fact, black and white, right/wrong," he explains. "But our work shows that there are meaningful human ideas in math, ingenious solutions and designs that have been mediated by writing and notational devices, like the number line."
"Perhaps we should think about bringing the human saga to the subject — instead of continuing to treat it romantically, as the 'universal language' it's not. Mathematics is neither hardwired, nor 'out there.'"