Core foundations of abstract geometry
Core foundations of abstract geometry
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DOI：
10.1073/pnas.1312640110
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发表时间：
2013-08-27
影响因子：
11.1
通讯作者：
Spelke, Elizabeth S.
中科院分区：
文献类型：
--
作者：
Dillon, Moira R.;Huang, Yi;Spelke, Elizabeth S.
来自不同文化背景的成年人对欧几里德几何中的点、线和图形有着共同的直觉。孩子们是否通过借鉴遗传学上古老的、发育上早熟的几何表示来发展这些直觉，这些几何表示指导他们的导航和对物体形状的分析？这些早期出现的表征以何种方式支持后来发展的欧几里得直觉？为了解决这些问题，我们调查了幼儿使用几何任务评估之间的关系：导航;视觉形式分析;和符号的解释，纯几何地图。儿童的导航依赖于表面布局的距离和方向关系，并预测他们使用的符号地图与表面距离指定的目标。与此相反，儿童的视觉形式的分析依赖于大小不变的形状关系的对象，并预测他们使用相同的地图，但指定的目标角。即使这两个地图任务使用相同的指令和地图显示，儿童在这些任务上的表现没有证据表明的距离和角度的综合表示。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灵活的几何直觉之间的联系，这些几何直觉使人类知识达到最高水平。虽然幼儿似乎没有整合核心几何表示，儿童使用的抽象几何空间符号，如地图可能提供了最早的线索，后来的欧几里德几何的建设。
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.