Spontaneous perception of numerosity in humans, Nat Commun, (7), 12536.

Humans, including infants, and many other species have a capacity for rapid, nonverbal estimation of numerosity. However, the mechanisms for number perception are still not clear; some maintain that the system calculates numerosity via density estimates-similar to those involved in texture-while others maintain that more direct, dedicated mechanisms are involved. Here we show that provided that items are not packed too densely, human subjects are far more sensitive to numerosity than to either density or area. In a two-dimensional space spanning density, area and numerosity, subjects spontaneously react with far greater sensitivity to changes in numerosity, than either area or density. Even in tasks where they were explicitly instructed to make density or area judgments, they responded spontaneously to number. We conclude, that humans extract number information, directly and spontaneously, via dedicated mechanisms.

A shared numerical representation for action and perception, Elife, (5).

Humans and other species have perceptual mechanisms dedicated to estimating approximate quantity: a sense of number. Here we show a clear interaction between self-produced actions and the perceived numerosity of subsequent visual stimuli. A short period of rapid finger-tapping (without sensory feedback) caused subjects to underestimate the number of visual stimuli presented near the tapping region; and a period of slow tapping caused overestimation. The distortions occurred both for stimuli presented sequentially (series of flashes) and simultaneously (clouds of dots); both for magnitude estimation and forced-choice comparison. The adaptation was spatially selective, primarily in external, real-world coordinates. Our results sit well with studies reporting links between perception and action, showing that vision and action share mechanisms that encode numbers: a generalized number sense, which estimates the number of self-generated as well as external events.

Numerosity but not texture-density discrimination correlates with math ability in children, Dev Psychol, 8 (52), 1206-1216.

Considerable recent work suggests that mathematical abilities in children correlate with the ability to estimate numerosity. Does math correlate only with numerosity estimation, or also with other similar tasks? We measured discrimination thresholds of school-age (6- to 12.5-years-old) children in 3 tasks: numerosity of patterns of relatively sparse, segregatable items (24 dots); numerosity of very dense textured patterns (250 dots); and discrimination of direction of motion. Thresholds in all tasks improved with age, but at different rates, implying the action of different mechanisms: In particular, in young children, thresholds were lower for sparse than textured patterns (the opposite of adults), suggesting earlier maturation of numerosity mechanisms. Importantly, numerosity thresholds for sparse stimuli correlated strongly with math skills, even after controlling for the influence of age, gender and nonverbal IQ. However, neither motion-direction discrimination nor numerosity discrimination of texture patterns showed a significant correlation with math abilities. These results provide further evidence that numerosity and texture-density are perceived by independent neural mechanisms, which develop at different rates; and importantly, only numerosity mechanisms are related to math. As developmental dyscalculia is characterized by a profound deficit in discriminating numerosity, it is fundamental to understand the mechanism behind the discrimination.