Thesis advisor: Sara Cordes / Thesis advisor: Ellen Winner / Evidence suggests that humans and non-human animals have access to two distinct numerical representation systems: a precise "object-file" system used to visually track small quantities (<4) and an approximate, ratio-dependent analog magnitude system used to represent all natural numbers. Although many studies to date indicate that infants can discriminate exclusively small sets (e.g., 1 vs. 2, 2 vs. 3) or exclusively large sets (4 vs. 8, 8 vs. 16), a robust phenomenon exists whereby they fail to compare sets crossing this small-large boundary (2 vs. 4, 3 vs. 6) despite a seemingly favorable ratio of difference between the two set sizes. Despite these robust failures in infancy (up to 14 months), studies suggest that 3-year old children no longer encounter difficulties comparing small from large sets, yet little work has explored the development of this phenomenon between 14 months and 3 years of age. The present study investigates (1) when in development infants naturally overcome this inability to compare small vs. large sets, as well as (2) what factors may facilitate this ability: namely, perceptual variability and/or numerical language. Results from three cross-sectional studies indicate that infants begin to discriminate between small and large sets as early as 17 months of age. Furthermore, infants seemed to benefit from perceptual variability of the items in the set when making these discriminations. Moreover, although preliminary evidence suggests that a child's ability to verbally count may correlate with success on these discriminations, simply exposure to numerical language (in the form of adult modeling of labeling the cardinality and counting the set) does not affect performance. / Thesis (PhD) — Boston College, 2015. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Psychology.

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