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Science in Mind

Fine-tuning understanding of geometric reasoning skills

In a Cambridge lab, 4-year-olds were given a series of geometric problems to solve, using fenced-off variations of triangles, some without complete sides, some without corners.

Courtesy of Moira Dillon, Harvard University

In a Cambridge lab, 4-year-olds were given a series of geometric problems to solve, using fenced-off variations of triangles, some without complete sides, some without corners.

Is our understanding of basic geometric concepts innate? For centuries, psychologists and philosophers have considered the question, in forums ranging from Socratic dialogue to tests of an isolated, unschooled Amazonian tribe whose members are capable of the same basic geometric reasoning as people who learned to use protractors and compasses in school in Boston.

For years, researchers at a child development laboratory at Harvard University have been probing the question by trying to understand how geometric reasoning abilities develop in the first place.

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In a study published last Monday, those researchers tested 4-year-old childrens’ ability to use a map to locate a particular spot in a triangular enclosure and found the children used skills with deep evolutionary roots, shared by other animals. By subtly altering the triangle environment, researchers could test which of two different sets of spatial reasoning skills the children were using.

“Either humans have something altogether new that allows them to have these abstract thoughts about geometric intuitions, or these abstract abilities have an origin that comes from our evolutionary ancestors — we’re building on something that was already there to begin with,” said Moira Dillon, a graduate student at Harvard who led the work, published in the Proceedings of the National Academy of Sciences.

In a laboratory in Cambridge, the 45 children were given a series of geometric problems to solve. Those included tests of how well they oriented themselves in a rectangular fenced-off area after being blindfolded and spun around, and a computer test of their ability to recognize different types of geometric patterns.

Then, the children stood in the center of an area that was fenced off in the shape of a right triangle with white foam walls. In one scenario, the triangle was missing all three corners and had only three opposing walls. In another, the triangle was missing its sides, but had three corners. In both tasks, the researcher showed the children the same map, depicting a dot at a particular spot along the edge of the triangle, where the child was asked to place a stuffed animal.

Other studies had shown that humans and animals use two kinds of geometric information: either situating themselves by examining distances and direction, or by using angles and the relative length of objects in the environment.

What the researchers found was that in the two different navigation tasks, children used the two different systems that animals have, but not simultaneously.

That suggests humans’ earliest geometric abilities are the same as the ones animals use to navigate their environments, and that they are able to adapt which information they use, depending on the situation. The question now is how children go from map reading and flexible use of basic geometric information to understanding Euclidean geometry.

Carolyn Y. Johnson can be reached at cjohnson@globe.com. Follow her on Twitter @carolynyjohnson.
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