Previous research shows a correlation between individual differences in people’s school math abilities and the accuracy with which they rapidly and nonverbally approximate how many items are in a scene. This finding is surprising because the Approximate Number System (ANS) underlying numerical estimation is shared with infants and non-human animals who never acquire formal mathematics. However, it remains unclear whether the link between individual differences in math ability and the ANS depends on formal mathematics instruction. Earlier studies demonstrating this link tested participants only after they had received many years of mathematics education, or assessed participants’ ANS acuity using tasks that required additional symbolic or arithmetic processing similar to that required in standardized math tests. To ask whether the ANS and math ability are linked early in life, we measured the ANS acuity of 200 3- to 5-year-old children using a task that did not also require symbol use or arithmetic calculation. We also measured children’s math ability and vocabulary size prior to the onset of formal math instruction. We found that children’s ANS acuity correlated with their math ability, even when age and verbal skills were controlled for. These findings provide evidence for a relationship between the primitive sense of number and math ability starting early in life.

Human infants in the first year of life possess an intuitive sense of number. This preverbal number sense may serve as a developmental building block for the uniquely human capacity for mathematics. In support of this idea, several studies have demonstrated that nonverbal number sense is correlated with mathematical abilities in children and adults. However, there has been no direct evidence that infant numerical abilities are related to mathematical abilities later in childhood. Here, we provide evidence that preverbal number sense in infancy predicts mathematical abilities in preschool-aged children. Numerical preference scores at 6 months of age correlated with both standardized math test scores and nonsymbolic number comparison scores at 3.5 years of age, suggesting that preverbal number sense facilitates the acquisition of numerical symbols and mathematical abilities. This relationship held even after controlling for general intelligence, indicating that preverbal number sense imparts a unique contribution to mathematical ability. These results validate the many prior studies purporting to show number sense in infancy and support the hypothesis that mathematics is built upon an intuitive sense of number that predates language.analog magnitudes | approximate number system | cognitive development | mathematical cognition W here does the uniquely human capacity for abstract mathematical concepts come from? What are the ontological building blocks that scaffold our ability for representing number symbolically and performing exact arithmetic? One hypothesis is that the preverbal, nonsymbolic numerical capacities exhibited by human infants in the first year of life serve as a conceptual basis for learning to count and acquiring symbolic mathematical knowledge (1, 2). Although many cognitive abilities contribute to math achievement, including working memory, inhibition, and other executive functions (3, 4), symbolic mathematics is commonly thought to build on a domain-specific nonverbal numerical representation (5). This system, the approximate number system (ANS), is an evolutionarily and ontogenetically ancient system that allows approximate representation of number without the need to count or rely on numerical symbols (2, 6).Support for this hypothesis comes from a handful of studies that have shown a correlation between math ability and individual differences in ANS acuity. For example, ANS acuity in adolescence retroactively predicts math ability in elementary school (7) and ANS acuity in preschool-aged children correlates with their current and future math performance (8-12). In addition, children with dyscalculia, a severe deficit specific to math, have poorer ANS acuity than their typically developing peers (9, 11). These findings demonstrate that ANS acuity covaries with math ability, but the direction of this relationship remains unclear. One possibility is that ANS acuity guides the acquisition of the verbal counting system and symbolic math knowledge, such that children with greater ANS acuity learn t...

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 detection paradigm, we present more direct evidence that infants' numerical perception is ratio-dependent even within the range of discriminable ratios and thus adheres to Weber's Law. Furthermore, we show that infants' numerical discrimination at six months reliably predicts their numerical discrimination abilities but not visual short-term memory at nine months. Thus, individual differences in numerical discrimination acuity may be stable within the first year of life and provide important avenues for future longitudinal research exploring the relationship between infant numerical discrimination and later developing math achievement.

Background: A dominant view in numerical cognition is that numerical comparisons operate on a notation independent representation (Dehaene, 1992). Although previous human neurophysiological studies using scalp-recorded event-related potentials (ERPs) on the numerical distance effect have been interpreted as supporting this idea, differences in the electrophysiological correlates of the numerical distance effect in symbolic notations (e.g. Arabic numerals) and nonsymbolic notations (e.g. a set of visually presented dots of a certain number) are not entirely consistent with this view.

Previous research shows that children’s ability to estimate numbers of items using their Approximate Number System (ANS) predicts later math ability. To more closely examine the predictive role of early ANS acuity on later abilities, we assessed the ANS acuity, math ability, and expressive vocabulary of preschoolers twice, six months apart. We also administered attention and memory span tasks to ask whether the previously reported association between ANS acuity and math ability is ANS-specific or attributable to domain-general cognitive skills. We found that early ANS acuity predicted math ability six months later, even when controlling for individual differences in age, expressive vocabulary, and math ability at the initial testing. In addition, ANS acuity was a unique concurrent predictor of math ability above and beyond expressive vocabulary, attention, and memory span. These findings of a predictive relationship between early ANS acuity and later math ability add to the growing evidence for the importance of early numerical estimation skills.

Humans share with other animals a system for thinking about numbers in an imprecise and intuitive way. The Approximate Number System (ANS) that underlies this thinking is present throughout the lifespan, is entirely nonverbal, and supports basic numerical computations like comparing, adding, and subtracting quantities. Humans, unlike other animals, also have a system for representing exact numbers. This linguistically mediated system is slowly mastered over the course of many years and provides the basis for most of our formal mathematical thought. A growing body of evidence suggests that the nonverbal ANS and the culturally invented system of exact numbers are fundamentally linked. In this article, we review evidence for this relationship, describing how group and individual differences in the ANS correlate with and even predict formal math ability. In this way, we illustrate how a system of ancient core knowledge may serve as a foundation for more complex mathematical thought.

As literate adults, we appreciate numerical values as abstract entities that can be represented by a numeral, a word, a number of lines on a scorecard, or a sequence of chimes from a clock. This abstract, notation-independent appreciation of numbers develops gradually over the first several years of life. Here, using functional magnetic resonance imaging, we examine the brain mechanisms that 6-and 7-year-old children and adults recruit to solve numerical comparisons across different notation systems. The data reveal that when young children compare numerical values in symbolic and nonsymbolic notations, they invoke the same network of brain regions as adults including occipitotemporal and parietal cortex. However, children also recruit inferior frontal cortex during these numerical tasks to a much greater degree than adults. Our data lend additional support to an emerging consensus from adult neuroimaging, nonhuman primate neurophysiology, and computational modeling studies that a core neural system integrates notation-independent numerical representations throughout development but, early in development, higher-order brain mechanisms mediate this process.

Apart from motor and behavioral dysfunctions, deficits in cognitive skills are among the well-documented sequelae of preterm birth. However, early identification of infants at risk for poor cognition is still a challenge, as no clear association between pathological findings based on neuroimaging scans and cognitive functions have been detected as yet. The Prechtl General Movement Assessment (GMA) has shown its merits for the evaluation of the integrity of the young nervous system. It is a reliable tool for identifying infants at risk for neuromotor deficits. Recent studies on preterm infants demonstrate that abnormal general movements (GMs) also reflect impairments of brain areas involved in cognitive development. The aim of this systematic review was to discuss studies that included (i) the Prechtl GMA applied in preterm infants, and (ii) cognitive outcome measures in six data bases. Seven studies met the inclusion criteria and yielded the following results: (a) children born preterm with consistently abnormal GMs up to 8 weeks after term had lower intelligence quotients at school age than children with an early normalization of GMs; (b) from 3 to 5 months after term, several qualitative, and quantitative aspects of the concurrent motor repertoire, including postural patterns, were predictive of intelligence at 7–10 years of age. These findings in 428 individuals born preterm suggest that normal GMs along with a normal motor repertoire during the first months after term are markers for normal cognitive development until at least age 10.