Studies on children's understanding of counting examine when and how children acquire the cardinal principle: the idea that the last word in a counted set reflects the cardinal value of the set. Using Wynn's (1990) Give-N Task, researchers classify children who can count to generate large sets as having acquired the cardinal principle…

As adults, we represent and think about number, space, and time in at least two ways: our intuitive--but imprecise--perceptual representations, and the slowly learned--but precise--number words. With development, these representational formats interface, allowing us to use precise number words to estimate imprecise perceptual experiences. We test…

Impaired numerosity perception in developmental dyscalculia (low "number acuity") has been interpreted as evidence of reduced representational precision in the neurocognitive system supporting non-symbolic number sense. However, recent studies suggest that poor numerosity judgments might stem from stronger interference from non-numerical…

Research demonstrating that infants discriminate between small (e.g., 1 vs. 3 dots) and large numerosities (e.g., 8 vs. 16 dots) is central to theories concerning the origins of human numerical abilities. To date, there has been no quantitative meta-analysis of the infant numerical competency data. Here, we quantitatively synthesize the evidential…

The ability to perceive approximate numerosity is present in many animal species, and emerges early in human infants. Later in life, it is moderately heritable and associated with mathematical abilities, but the etiology of the Approximate Number System (ANS) and its degree of independence from other cognitive abilities in infancy is unknown.…

A common measure of number word understanding is the give-N task. Traditionally, to receive credit for understanding a number, N, children must understand that N does not apply to other set sizes (e.g. a child who gives three when asked for 'three' but also when asked for 'four' would not be credited with knowing 'three'). However, it is possible…

Understanding the magnitudes represented by numerals is a core component of early mathematical development and is often assessed by accuracy in situating numerals and fractions on a number line. Performance on these measures is consistently related to performance in other mathematics domains, but the strength of these relations may be…

Ordinality is a fundamental feature of numbers and recent studies have highlighted the role that number ordering abilities play in mathematical development (e.g., Lyons et al. 2014), as well as mature mathematical performance (e.g., Lyons & Beilock, 2011). The current study tested the novel hypothesis that non-numerical ordering ability, as…

Humans represent numbers on a mental number line with smaller numbers on the left and larger numbers on the right side. A left-to-right oriented spatial-numerical association, (SNA), has been demonstrated in animals and infants. However, the possibility that SNA is learnt by early exposure to caregivers' directional biases is still open. We…

Children's knowledge of arithmetic principles is a key aspect of early mathematics knowledge. Knowledge of arithmetic principles predicts how children approach solving arithmetic problems and the likelihood of their success. Prior work has begun to address how children might learn arithmetic principles in a classroom setting. Understanding of…

Children do not understand the meanings of count words like "two" and "three" until the preschool years. But even before knowing the meanings of these individual words, might they recognize that counting is "about" the dimension of number? Here in five experiments, we asked whether infants already associate counting…

Numerical competencies acquired in preschool are foundational and predictive for children's later mathematical development. It remains to be determined whether there are gender differences in these early numerical competencies which could explain the often-reported gender differences in later mathematics and STEM-related abilities. Using a…

The Approximate Number System (ANS) supports basic arithmetic computation in early childhood, but it is unclear whether the ANS also supports the more complex computations introduced later in formal education. "Solving for x" in addend-unknown problems is notoriously difficult for children, who often struggle with these types of problems…

When asked to "find three forks", adult speakers of English use the noun "fork" to identify units for counting. However, when number words (e.g. "three") and quantifiers (e.g. "more", "every") are used with unfamiliar words ("Give me three blickets") noun-specific conceptual criteria are unavailable for picking out units. This poses a problem for…

The present study evaluated 626 5-7-year-old children in the UK, China, Russia, and Kyrgyzstan on a cognitive test battery measuring: (1) general skills; (2) non-symbolic number sense; (3) symbolic number understanding; (4) simple arithmetic--operating with numbers; and (5) familiarity with numbers. Although most inter-population differences were…