The Origins of Numerical Concepts from Nonverbal Perception

现代人类的数学认知受到进化、发展和环境的影响。研究人员试图了解这些影响如何影响人类儿童在认知和神经水平上的数字概念发展。罗彻斯特大学（University of Rochester）的这个研究项目测试了一个假设，即儿童早期的数字概念源于一个用于空间推理的原始认知和神经系统。本研究采用跨学科的方法，将动物认知、认知发展、神经影像学和数学教育措施结合起来，对人类儿童数字概念的起源和基本结构进行综合分析。这种跨学科的方法是强大的，因为它允许研究人员以系统的方式测试一个假设，使用一套一致的方法，跨越不同的分析水平。实验测试：1)利用功能性磁共振成像技术（fMRI）对4 ~ 6岁儿童的数字感知和空间感知重叠程度进行测试；2)当儿童接受计数教育的文化输入时，数字和空间感知变得不同的程度；3)人类儿童在数字和空间属性表征方面表现出与非人类动物相似的感知整合程度。这些实验探讨了空间感知是否会在发展中的人脑中产生数学认知，从而揭示了进化和文化对人类数字概念发展轨迹的影响。该研究项目对认知科学、神经科学和数学教育有广泛的贡献。来自人类儿童的认知和神经成像数据促进了我们对人类大脑发育的了解，并为早期儿童教育实践和关于个体差异和性别差异的假设提供了重要的输入。来自人类儿童和非人类动物的比较数据使研究人员能够确定产生人类数学概念的基本原理，以及幼儿进入学校后对数字概念学习带来的内在感知偏差。总之，这些数据对于理解人类如何成功地发展数学概念至关重要。

Modern human mathematical cognition is shaped by evolutionary, developmental, and environmental influences. Researchers seek to understand how those influence affect the development of numerical concepts in human children at the cognitive and neural levels. This research program at the University of Rochester tests the hypothesis that children's early numerical concepts originate from a primitive cognitive and neural system for spatial reasoning.The proposed research takes an interdisciplinary approach by combining animal cognition, cognitive development, neuroimaging, and mathematics education measures into an integrative analysis of the origins and basic structure of numerical concepts in human children. This interdisciplinary approach is powerful because it allows researchers to test a single hypothesis in a systematic fashion, using a consistent set of methods and across different levels of analysis. The experiments test: 1) the degree to which numerical and spatial perception overlap in the developing brain using functional magnetic resonance imaging (fMRI) with 4- to 6-year-old children; 2) the degree to which numerical and spatial perception become distinct as children receive cultural input from counting education; and 3) the degree to which human children exhibit similar levels of perceptual integration to non-human animals in their representation of numerical and spatial properties. These experiments speak to whether spatial perception gives rise to mathematical cognition in the developing human brain and so reveals the evolutionary and cultural influences on the developmental trajectory of human numerical concepts.The research program contributes widely to cognitive science, neuroscience, and mathematics education. The cognitive and neuroimaging data from human children advance our knowledge of the developing human brain and provide critical input for early childhood education practices and assumptions about individual differences and gender differences. The comparative data from human children and non-human animals allow researchers to identify fundamental principles that give rise to human mathematical concepts and intrinsic perceptual biases that young children bring to numerical concept learning as they enter school. Together, these data are critical for understanding how humans successfully develop mathematical concepts.