The Origins of Numerical Concepts from Nonverbal Perception

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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.