Proceedings of the Annual Meeting of the Cognitive Science Society

There is an ongoing debate over the psychophysical functionsthat best fit human data from numerical estimation tasks. Totest whether one psychophysical function could account fordata across diverse tasks, we examined 40 kindergartners, 38first graders, 40 second graders and 40 adults’ estimates usingtwo fully crossed 2 × 2 designs, crossing symbol (symbolic,non-symbolic) and boundedness (bounded, unbounded) onfree number-line tasks (Experiment 1) and crossing the samefactors on anchored tasks (Experiment 2). Across all 8 tasks,88.84% of participants provided estimates best fit by a mixedlog-linear model, and the weight of the logarithmiccomponent (λ) decreased with age. After controlling for age,the λ significantly predicted arithmetic skills, whereasparameters of other models failed to do so. Results suggestthat the logarithmic-to-linear shift theory provides a unifiedaccount of numerical estimation and provides uniquelyaccurate predictions for mathematical proficiency.