Proceedings of the Annual Meeting of the Cognitive Science Society

In a conventional number-line task, a given number that varies every trial is estimated on a line flanked with 0 and anupper-bound number. An upper-bound number is often arbitrarily selected, although this design variable has been shownto affect non-linearity in estimates. Examining estimates of varying given numbers (design variable 1) with varying upper-bound numbers (design variable 2) can be costly because adding another design variable into the task drastically increasesthe number of trials required to examine the numerical representation. In the present study, a novel Bayesian machinelearning algorithm, dubbed Gaussian Process Active Learning (GPAL), was used to make this costly paradigm feasible bypresenting only the most informative combinations of the design variables every trial. We found that children were morelogarithmic than adults across upper bounds, replicating log-to-linear shifts in development. More importantly, childrenand even educated adults became more logarithmic as the upper bound increased, indicating the persistent use of logrepresentation across age groups.