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…

Both humans and non-human animals exhibit sensitivity to the approximate number of items in a visual array, as indexed by their performance in numerosity discrimination tasks, and even neonates can detect changes in numerosity. These findings are often interpreted as evidence for an innate 'number sense'. However, recent simulation work has…

Learning the meanings of Arabic numerals involves mapping the number symbols to mental representations of their corresponding, approximate numerical quantities. It is often assumed that performance on numerical tasks, such as number line estimation (NLE), is primarily driven by translating from a presented numeral to a mental representation of its…

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)…

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…

Many students' knowledge of fractions is adversely affected by whole number bias, the tendency to focus on the separate whole number components (numerator and denominator) of a fraction rather than on the fraction's magnitude (ratio of numerator to denominator). Although whole number bias appears early in the fraction learning process and under…

Math relies on mastery and integration of a wide range of simpler numerical processes and concepts. Recent work has identified several numerical competencies that predict variation in math ability. We examined the unique relations between eight basic numerical skills and early arithmetic ability in a large sample (N = 1391) of children across…

A growing body of evidence suggests that non-symbolic representations of number, which humans share with nonhuman animals, are functionally related to uniquely human mathematical thought. Other research suggesting that numerical and non-numerical magnitudes not only share analog format but also form part of a general magnitude system raises…

Does speaking more than one language help a child perform better on certain types of cognitive tasks? One possibility is that bilingualism confers either specific or general cognitive advantages on tasks that require selective attention to one dimension over another (e.g. Bialystok, [Bialystok, E., 2001]; Hilchey & Klein, [Hilchey, M.D.,…

All numerate humans have access to two systems of number representation: an exact system that is argued to be based on language and that supports formal mathematics, and an Approximate Number System (ANS) that is present at birth and appears independent of language. Here we examine the interaction between these two systems by comparing the…

Much research supports the existence of an Approximate Number System (ANS) that is recruited by infants, children, adults, and non-human animals to generate coarse, non-symbolic representations of number. This system supports simple arithmetic operations such as addition, subtraction, and ordering of amounts. The current study tests whether an…

The study assessed the relations among acuity of the inherent approximate number system (ANS), performance on measures of symbolic quantitative knowledge, and mathematics achievement for a sample of 138 (64 boys) preschoolers. The Weber fraction (a measure of ANS acuity) and associated task accuracy were significantly correlated with mathematics…

In the primate brain, sensory information is processed along two partially segregated cortical streams: the ventral stream, mainly coding for objects' shape and identity, and the dorsal stream, mainly coding for objects' quantitative information (including size, number, and spatial position). Neurophysiological measures indicate that such…

Experience engenders learning, but not all learning involves representational change. In this paper, we provide a dramatic case study of the distinction between learning and representational change. Specifically, we examined long- and short-term changes in representations of numeric magnitudes by asking individuals with Williams syndrome (WS) and…

Previous studies have shown that as a group 6-month-old infants successfully discriminate numerical changes when the values differ by at least a 1:2 ratio but fail at a 2:3 ratio (e.g. 8 vs. 16 but not 8 vs. 12). However, no studies have yet examined individual differences in number discrimination in infancy. Using a novel numerical change…