Do we need to learn arithmetic and geometry, or are we born with an intuitive sense of these concepts?
Elizabeth Spelke, a professor of psychology at Harvard University, has tested countless infants, some just a few months old, and concluded that they possess at least a rudimentary grasp of number and shape. And this recognition, Spelke contends, can be found in all humans, even those whose cultures have no formal system of calculation.
“I assume that our mature human concepts, like ‘7’ and ‘triangle,’ are indeed abstract, and possibly uniquely human, but that our sources of these concepts are not,” Spelke said during her presidential lecture, “The Origins of Abstract Knowledge,” at the recent Society for Neuroscience annual meeting in Chicago. “I also assume children use these systems to build the abstract concepts their culture provides.”
For three decades, Spelke has pondered such questions, devising experiments in babies and toddlers that expose the rudiments of human thinking.
“She essentially has found an experimental crowbar for prying open the mind of a growing child,” said her longtime friend and colleague Thomas Carew, professor and chairman of the department of neurobiology and behavior at the University of California, Irvine. As the president of the Society of Neuroscience, Carew invited Spelke to deliver one of four presidential lectures this year because he considers the questions she asks “unique and extremely powerful.”
“She has asked universally relevant questions about the development of the human mind,” Carew said. “She has shown that humans possess a deep, inherited capacity for the acquisition of knowledge.” Some of Spelke’s research also was part of the work of the Dana Foundation’s Arts and Cognition Consortium, which released its report “Learning, Arts, and the Brain” in March 2008, and has received separate Dana Foundation grants for her work.
Inborn number sense
Spelke tests infants by measuring one of their few consistent behaviors—they gaze at objects that interest them and look away when they get bored. In “Spelkeland,” as her lab is known among students, the longer an infant’s gaze, the greater the infant’s interest.
Using this measure of attention, Spelke and her colleagues tease out evidence of a child’s understanding. For example, if presented with a computer screen displaying eight balls, followed by a screen displaying 16 balls, infants tend to look longer at the second screen, suggesting that they recognize that an interesting change has taken place.
This sensitivity to such a difference in number is “robust,” according to Spelke. “At six months, infants will react to a difference between a puppet that jumps 8 times versus 16 times, or to 8 versus 16 drum beats,” she said.
From this type of evidence, Spelke has concluded that our abstract notions of number and geometry, like our capacity for speech, rest on an inborn cognitive system rather than developing completely from accumulated sensory input.
And humans are not the only species with this capacity. Animals, including chicks and pigeons as well as non-human primates, also respond to number in much the same way that infants do, “giving us reason to think that this system of numerical representation did not emerge with our species,” Spelke said. “It’s much older than we are, and emerged in some distant long-ago ancestor common to these vertebrates and us.”
Where in the brain does this awareness reside?
Numerous studies have shown that the parietal cortex at the crown of the brain responds to symbolic number. For instance, when this region is disturbed by injury or by techniques such as transcranial magnetic stimulation, patients show impairments in symbolic numerical processing.
Similar activation appears in the same region of non-human primates. Recordings from individual neurons in monkeys’ brains have revealed individual cells that respond to a specific number and that respond in a graded manner to adjacent numbers. “So a cell that peaks at 5 will respond more to 6 than to 4,” Spelke said.
A knack for navigation
Children also possess a sense of spatial navigation—a form of geometrical knowledge—Spelke said. When children are placed in a rectangular room, for example, where they observe a toy hidden in one corner, and then they are picked up and spun around with their eyes covered to disorient them, they will search for the toy either in the correct corner or in the geometrically opposite one.
“It’s as though before they were disoriented, they represented the shape of the room,” Spelke said. When disoriented, they apparently use that mental map to retrieve the toy.
However, when the same experiment was repeated in a square room with walls of different colors, the children did not use the color differences to help them find the toy. And when placed in a rectangular space drawn on the floor, they could not orient themselves toward the corner with the toy. However, when the boundary of the room was marked by a slightly elevated border less than an inch tall, they could.
Although the math and geometry skills displayed by young children are simple and prone to failure, they provide the foundation for future learning, Spelke said.
“This isn’t a system we kick away,” she said. “It continues to work in us and sharpen in precision.”