The Origins of Numerical Concepts from Nonverbal Perception

现代人类的数学认知是受进化、发展和环境影响而形成的。研究人员试图了解这些影响如何在认知和神经层面上影响人类儿童的数字概念发展。罗彻斯特大学的这一研究项目测试了儿童早期数字概念起源于原始认知和空间推理神经系统的假设。该研究采用跨学科的方法，将动物认知、认知发展、神经成像和数学教育方法结合起来，对人类儿童数字概念的起源和基本结构进行了综合分析。这种跨学科的方法很强大，因为它允许研究人员以系统的方式，使用一套一致的方法，跨越不同的分析水平，以系统的方式测试单个假设。这些实验测试了：1)使用功能磁共振成像(FMRI)在4至6岁儿童发育中的大脑中数字和空间感知的重叠程度；2)随着儿童接受来自计数教育的文化输入，数字和空间感知变得不同的程度；以及3)人类儿童在数字和空间属性的表征方面表现出与非人类动物相似的知觉整合程度。这些实验讨论了空间知觉是否会在发育中的人脑中引发数学认知，从而揭示了进化和文化对人类数字概念发展轨迹的影响。该研究计划对认知科学、神经科学和数学教育做出了广泛的贡献。来自人类儿童的认知和神经成像数据促进了我们对人脑发育的了解，并为幼儿教育实践和关于个体差异和性别差异的假设提供了关键输入。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导致人类数学概念产生的基本原理，以及幼儿进入学校后对数字概念学习带来的内在知觉偏差。总而言之，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.