Two experiments tested whether 4-year-old children extract and use geometric information in simple maps without task instruction or feedback. Children saw maps depicting an arrangement of three containers and were asked to place an object into a container designated on the map. In Experiment 1, one of the three locations on the map and the array was distinct and therefore served as a landmark; in Experiment 2, only angle, distance and sense information specified the target container. Children in both experiments used information for distance and angle, but not sense, showing signature error patterns found in adults. Children thus show early, spontaneously developing abilities to detect geometric correspondences between three-dimensional layouts and two-dimensional maps, and they use these correspondences to guide navigation. These findings begin to chart the nature and limits of the use of core geometry in a uniquely human, symbolic task.

For many centuries, philosophers and scientists have pondered the origins and nature of human intuitions about the properties of points, lines, and figures on the Euclidean plane, with most hypothesizing that a system of Euclidean concepts either is innate or is assembled by general learning processes. Recent research from cognitive and developmental psychology, cognitive anthropology, animal cognition, and cognitive neuroscience suggests a different view. Knowledge of geometry may be founded on at least two distinct, evolutionarily ancient, core cognitive systems for representing the shapes of large-scale, navigable surface layouts and of small-scale, movable forms and objects. Each of these systems applies to some but not all perceptible arrays and captures some but not all of the three fundamental Euclidean relationships of distance (or length), angle, and direction (or sense). Like natural number (Carey, 2009), Euclidean geometry may be constructed through the productive combination of representations from these core systems, through the use of uniquely human symbolic systems.

Research on navigation has shown that humans and laboratory animals recover their sense of orientation primarily by detecting geometric properties of large-scale surface layouts (e.g. room shape), but the reasons for the primacy of layout geometry have not been clarified. In four experiments, we tested whether 4-year-old children reorient by the geometry of extended wall-like surfaces because such surfaces are large and perceived as stable, because they serve as barriers to vision or to locomotion, or because they form a single, connected geometric figure. Disoriented children successfully reoriented by the shape of an arena formed by surfaces that were short enough to see and step over. In contrast, children failed to reorient by the shape of an arena defined by large and stable columns or by connected lines on the floor. We conclude that preschool children’s reorientation is not guided by the functional relevance of the immediate environmental properties, but rather by a specific sensitivity to the geometric properties of the extended three-dimensional surface layout.

journal homepage: www.elsevier.com/locate/cogpsych

journal homepage: www.elsevier.com/locate/cogpsych

How does the human brain support abstract concepts such as seven or square? Studies of nonhuman animals, of human infants, and of children and adults in diverse cultures suggest these concepts arise from a set of cognitive systems that are phylogenetically ancient, innate, and universal across humans: systems of core knowledge. Two of these systems—for tracking small numbers of objects and for assessing, comparing and combining the approximate cardinal values of sets—capture the primary information in the system of positive integers. Two other systems—for representing the shapes of small-scale forms and the distances and directions of surfaces in the large-scale navigable layout—capture the primary information in the system of Euclidean plane geometry. As children learn language and other symbol systems, they begin to combine their core numerical and geometrical representations productively, in uniquely human ways. These combinations may give rise to the first truly abstract concepts at the foundations of mathematics. For millenia, philosophers and scientists have pondered the existence, nature and origins of abstract numerical and geometrical concepts, because these concepts have striking features. First, the integers, and the figures of the Euclidean plane, are so intuitive to human adults that the systems underlying them are called “natural number ” and, by some, “natural geometry”

and two anonymous reviewers for their helpful comments on the manuscript. Supported by NIH

journal homepage: www.elsevier.com/locate/COGNIT

Navigation as a source of geometric knowledge: Young children’s use of length, angle, distance,