Although most U. S. children can accurately count sets by 4 years of age, many fail to understand the structural analogy between counting and number -- that adding 1 to a set corresponds to counting up 1 word in the count list. While children are theorized to establish this Structure Mapping coincident with learning how counting is used to…

A long-standing debate in the field of numerical cognition concerns the degree to which symbolic and non-symbolic processing are related over the course of development. Of particular interest is the possibility that this link depends on the range of quantities in question. Behavioral and neuroimaging research with adults suggests that symbolic and…

Children and adults show behavioral evidence of psychological overlap between their early, non-symbolic numerical concepts and their later-developing symbolic numerical concepts. An open question is to what extent the common cognitive signatures observed between different numerical notations are coupled with physical overlap in neural processes.…

Adult neuroimaging studies have demonstrated dissociable neural activation patterns in the visual cortex in response to letters (Latin alphabet) and numbers (Arabic numerals), which suggest a strong experiential influence of reading and mathematics on the human visual system. Here, developmental trajectories in the event-related potential (ERP)…

Spatial processing of numbers has emerged as one of the basic properties of humans' mathematical thinking. However, how and when number-space relations develop is a highly contested issue. One dominant view has been that a link between numbers and left/right spatial directions is constructed based on directional experience associated with reading…

Learning of the mathematical number line has been hypothesized to be dependent on an inherent sense of approximate quantity. Children's number line placements are predicted to conform to the underlying properties of this system; specifically, placements are exaggerated for small numerals and compressed for larger ones. Alternative hypotheses…

When placing numbers along a number line with endpoints 0 and 1000, children generally space numbers logarithmically until around the age of 7, when they shift to a predominantly linear pattern of responding. This developmental shift of responding on the number placement task has been argued to be indicative of a shift in the format of the…

In early childhood, humans learn culturally specific symbols for number that allow them entry into the world of complex numerical thinking. Yet little is known about how the brain supports the development of the uniquely human symbolic number system. Here, we use functional magnetic resonance imaging along with an effective connectivity analysis…

The integrated theory of numerical development posits that a central theme of numerical development from infancy to adulthood is progressive broadening of the types and ranges of numbers whose magnitudes are accurately represented. The process includes four overlapping trends: (1) representing increasingly precisely the magnitudes of non-symbolic…

Behavioral research suggests that two cognitive systems are at the foundations of numerical thinking: one for representing 1-3 objects in parallel and one for representing and comparing large, approximate numerical magnitudes. We tested for dissociable neural signatures of these systems in preverbal infants by recording event-related potentials…

The current study presents a series of computational simulations that demonstrate how the neural coding of numerical magnitude may influence number cognition and development. This includes behavioral phenomena cataloged in cognitive literature such as the development of numerical estimation and operational momentum. Though neural research has…

A current issue in developmental science is that greater continuity in cognition between children and adults may exist than is usually appreciated in Piaget-like (stages or "staircase") models. This phenomenon has been demonstrated at the behavioural level, but never at the brain level. Here we show with functional magnetic resonance imaging…

Previous studies have suggested that typically developing 6-month-old infants are able to discriminate between small and large numerosities. However, discrimination between small numerosities in young infants is only possible when variables continuous with number (e.g. area or circumference) are confounded. In contrast, large number discrimination…

Time perception is important for many aspects of human behavior, and a large literature documents that adults represent intervals and that their ability to discriminate temporal intervals is ratio dependent. Here we replicate a recent study by vanMarle and Wynn (2006 ) that used the visual habituation paradigm and demonstrated that temporal…

This paper investigates the ability of infants to attend to continuous stimulus variables and how this capacity relates to the representation of number. We examined the change in area needed by 6-month-old infants to detect a difference in the size of a single element (Elmo face). Infants successfully discriminated a 1:4, 1:3 and 1:2 change in the…