Psychology Department, Harvard University, Cambridge, MA 02138, USA.
Proc Natl Acad Sci U S A. 2013 Aug 27;110(35):14191-5. doi: 10.1073/pnas.1312640110. Epub 2013 Aug 12.
Human adults from diverse cultures share intuitions about the points, lines, and figures of Euclidean geometry. Do children develop these intuitions by drawing on phylogenetically ancient and developmentally precocious geometric representations that guide their navigation and their analysis of object shape? In what way might these early-arising representations support later-developing Euclidean intuitions? To approach these questions, we investigated the relations among young children's use of geometry in tasks assessing: navigation; visual form analysis; and the interpretation of symbolic, purely geometric maps. Children's navigation depended on the distance and directional relations of the surface layout and predicted their use of a symbolic map with targets designated by surface distances. In contrast, children's analysis of visual forms depended on the size-invariant shape relations of objects and predicted their use of the same map but with targets designated by corner angles. Even though the two map tasks used identical instructions and map displays, children's performance on these tasks showed no evidence of integrated representations of distance and angle. Instead, young children flexibly recruited geometric representations of either navigable layouts or objects to interpret the same spatial symbols. These findings reveal a link between the early-arising geometric representations that humans share with diverse animals and the flexible geometric intuitions that give rise to human knowledge at its highest reaches. Although young children do not appear to integrate core geometric representations, children's use of the abstract geometry in spatial symbols such as maps may provide the earliest clues to the later construction of Euclidean geometry.
人类不同文化背景的成年人对欧几里得几何的点、线和图形都有直觉。儿童是否通过借鉴在进化上古老且在发展上早熟的几何表示来发展这些直觉，这些表示指导他们的导航和对物体形状的分析？这些早期出现的表示以何种方式支持后来发展起来的欧几里得直觉？为了探讨这些问题，我们研究了幼儿在以下任务中使用几何的关系：导航；视觉形式分析；以及对符号、纯粹几何地图的解释。儿童的导航取决于表面布局的距离和方向关系，并预测他们会使用带有表面距离标记的符号地图。相比之下，儿童对视觉形式的分析取决于物体的大小不变的形状关系，并预测他们会使用相同的地图，但目标由角标记。尽管两个地图任务使用了相同的指令和地图显示，但儿童在这些任务上的表现并没有显示出距离和角度的综合表示的证据。相反，幼儿灵活地招募了可导航布局或物体的几何表示来解释相同的空间符号。这些发现揭示了人类与各种动物共享的早期出现的几何表示与产生人类最高知识的灵活几何直觉之间的联系。尽管幼儿似乎没有整合核心几何表示，但他们在地图等空间符号中使用抽象几何可能为后来构建欧几里得几何提供最早的线索。
