"Representational Change and the Origins of Mathematical Thinking"
ABSTRACT: Cortical specializations for domain-specific functions, such as face recognition and syntactic processing, are often claimed as products of our evolutionary history. What then gives rise to neural specializations for cognitive skills, like reading and symbolic arithmetic, that arose only recently in our cultural history? In this talk, I consider the case of numerical representations. I argue that specializations for representing symbolic values might arise as children learn to associate numerals (1, 2, 3, …) with innate, analog magnitude representations that store numerosity information (e.g., •, ••, •••) in memory. To test this claim, I derive predictions from the psychophysics of non-symbolic number discrimination, and compare children's performance on both symbolic and non-symbolic tasks against these predictions. Across a wide range of tasks, results reveal a very close fit between the logarithmic number sense implied by non-human animals and those of young children. Further, the model accurately predicts the experiences required for children to adopt a more accurate number sense, the relation between an accurate number sense and mathematical skill, and why some schools produce much better young mathematicians than others.
John Opfer is a Professor of Psychology at OSU.
