"Approximate number system" training: A perceptual learning approach.

Recent research suggests that humans perceive quantity using a non-symbolic "number sense." This sense is then thought to provide a foundation for understanding symbolic numbers in formal education. Given this link, there has been interest in the extent to which the approximate number system (ANS) can be improved via dedicated training, as this could provide a route to improving performance in symbolic mathematics. However, current evidence regarding the trainability of the ANS comes largely from studies that have used short training durations, leaving open the question of whether improvements occur over a longer time span. To address this limitation, we utilized a perceptual learning approach to investigate the extent to which long-term (8,000+ trials) training modifies the ANS. Consistent with the general methodological approach common in the domain of perceptual learning (where learning specificity is commonly observed), we also examined whether ANS training generalizes to: (a) untrained locations in the visual field; (b) an enumeration task; (c) a higher-level ratio comparison task; and (d) arithmetic ability. In contrast to previous short-term training studies showing that ANS learning quickly asymptotes, our long-term training approach revealed that performance continued to improve even after thousands of trials. We further found that the training generalized to untrained visual locations. At post-test there was non-significant evidence for generalization to a low-level enumeration task, but not to our high-level tasks, including ratio comparison, multi-object tracking, and arithmetic performance. These results demonstrate the potential utility of long-term psychophysical training, but also suggest that ANS training alone (even long-duration training) may be insufficient to modify higher-level math skills.