Time required for judgments of numerical inequality: Revisiting symbolic estrangement

Whether the meaning of symbolic numerals is represented by the approximate number system (ANS) is a subject of long-standing interest, with contradictory results reported across educated adults and developing children. To resolve past discrepancies, we investigated the time required to make judgments of numerical inequality across an expansive numerical spectrum (1-999) and range of ratios (1.125-4.5) in 217 children (ages 4-12) and 66 adults. Testing an experience-dependent framework, Study 1 evaluated whether the relative fluency of symbolic and non-symbolic processing changes with age according to the power law of practice. As predicted, the law provided an excellent fit to the data, with cognitive efficiency progressing through three range-dependent phases (prefluent, fluent, and overlearned) that tracked the ecological frequency of numbers. Study 2 evaluated cross-format switch costs, revealing a significant age-by-range interaction. Young children exhibited deeply negative switch costs for triple-digit numbers, with switch costs systematically rising with age. Rather than showing a number-wide overhaul, the data suggest that the time required to process symbolic magnitudes decreases as a non-linear function of experience.