Attaching meaning to the number words: contributions of the object tracking and approximate number systems.

Children's understanding of the quantities represented by number words (i.e., cardinality) is a surprisingly protracted but foundational step in their learning of formal mathematics. The development of cardinal knowledge is related to one or two core, inherent systems - the approximate number system (ANS) and the object tracking system (OTS) - but whether these systems act alone, in concert, or antagonistically is debated. Longitudinal assessments of 198 preschool children on OTS, ANS, and cardinality tasks enabled testing of two single-mechanism (ANS-only and OTS-only) and two dual-mechanism models, controlling for intelligence, executive functions, preliteracy skills, and demographic factors. Measures of both OTS and ANS predicted cardinal knowledge in concert early in the school year, inconsistent with single-mechanism models. The ANS but not the OTS predicted cardinal knowledge later in the school year as well the acquisition of the cardinal principle, a critical shift in cardinal understanding. The results support a Merge model, whereby both systems initially contribute to children's early mapping of number words to cardinal value, but the role of the OTS diminishes over time while that of the ANS continues to support cardinal knowledge as children come to understand the counting principles.

Analog Magnitudes Support Large Number Ordinal Judgments in Infancy.

Few studies have explored the source of infants' ordinal knowledge, and those that have are equivocal regarding the underlying representational system. The present study sought clear evidence that the approximate number system, which underlies children's cardinal knowledge, may also support ordinal knowledge in infancy; 10 - to 12-month-old infants' were tested with large sets (>3) in an ordinal choice task in which they were asked to choose between two hidden sets of food items. The difficulty of the comparison varied as a function of the ratio between the sets. Infants reliably chose the greater quantity when the sets differed by a 2:3 ratio (4v6 and 6v9), but not when they differed by a 3:4 ratio (6v8) or a 7:8 ratio (7v8). This discrimination function is consistent with previous studies testing the precision of number and time representations in infants of roughly this same age, thus providing evidence that the approximate number system can support ordinal judgments in infancy. The findings are discussed in light of recent proposals that different mechanisms underlie infants' reasoning about small and large numbers.

The sound of distance.

Human languages may be more than completely arbitrary symbolic systems. A growing literature supports sound symbolism, or the existence of consistent, intuitive relationships between speech sounds and specific concepts. Prior work establishes that these sound-to-meaning mappings can shape language-related judgments and decisions, but do their effects generalize beyond merely the linguistic and truly color how we navigate our environment? We examine this possibility, relating a predominant sound symbolic distinction (vowel frontness) to a novel associate (spatial proximity) in five studies. We show that changing one vowel in a label can influence estimations of distance, impacting judgment, perception, and action. The results (1) provide the first experimental support for a relationship between vowels and spatial distance and (2) demonstrate that sound-to-meaning mappings have outcomes that extend beyond just language and can - through a single sound - influence how we perceive and behave toward objects in the world.