Why Children’s Number-line Estimates Follow Fechner’s Law

Abstract

Estimates of numerical magnitude in young children and Amazon indigene have been observed to follow Fechner’s Law, with estimates increasing logarithmically with actual value. Two models have been proposed to account for this data. The logarithmic model depicts numeric magnitudes as scaled logarithmically with constant Gaussian variability, whereas the accumulator model depicts them as scaled linearly with increasing variability. This paper tests these models by examining number-line estimation with novel magnitudes and ranges (0-100, 0-1000, 900-1000, 900-1900). Results suggest that although both models provide good fits for estimates on 0-1000 number lines, only the fit of the logarithmic model generalizes to estimates for smaller intervals (900-1000) and larger numbers (900-1900).


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