Abstract: A number of investigators have proposed that human adults' number representations and mathematical thinking depend, in part, on a sense of approximate numerical magnitudes. In the domain of number, animals and preverbal infants have been shown to react to the cardinal values of sets presented in a variety of different stimulus formats. Although infants and animals respond to the approximate number of elements in visual, auditory, and tactile arrays, only human infants have been shown to possess abstract numerical representations that apply to entities of all kinds. The present studies performed to test for infants' numerosity discrimination with auditory sequences designed to control for element duration, and sequence duration. The results provide evidences for abstract numerical representations at the start of postnatal experience, and numerosity discrimination increases in precision over development as well as number computation skills.
Number sense in human infants
One obvious difference between the infant and adult numerical cognition system is that the infant is not born with an innate ability to process symbolic numerical codes, such as digits and number names. It was initially thought that all numerical knowledge had to be constructed through sensory-motor interaction with the environment (Piaget, 1952), but due to the many studies on infant numerical cognition in the past quarter of a century, we now know that infants are born with an ability to represent, discriminate, and operate on numerosity, although with only a limited degree of precision.
In terms of the origins of number sense, a number of recent studies provide evidence that a sense of approximate numerical magnitudes develops in infancy. Infants are able to discriminate between large sets of elements on the basis of numerosity and that their numerical discriminations are ratio limit between 2:3 and 1:2. Infants have been found to discriminate between small numbers of actions, syllables and collections, though the absence of any correlation of number with contour length or volume (Xu, Spelke, & Goddard, 2005).
Dehaene (1997) also found that the emergence of basic components of number sense in young children is considered to occur intuitively, for example, young children are able to count, rapidly and accurately percept small numerosities, compare number magnitudes, and comprehend simple arithmetic operation. Based on the aforementioned studies, number sense is thought as a biologically based "perceptual" sense of quantity.
McCrink and Wynn (2004) have shown that 9-month-olds can approximately add and subtract collections of objects. These approximate representations of number in infants are constrained by the ratio of the two numbers, and improve in precision during the first year of life (Lipton & Spelke, 2003). Although as of yet no imaging evidence is available on the source of these representations in infants, due to the practical difficulties of conducting such studies, these characteristics are similar to the approximate representation present in animals (Gallistel & Gelman, 2000; Nieder, 2005).
Numerical Computation Procedure
Human infants also develop (in the appropriate cultural context) the ability to represent numbers using numerical computation procedure. Wynn and McClink (2003) report that when continuous variables such as area and contour length are controlled, 9-month-old infants successfully add and subtract over numbers of items that exceed object-tracking limits. The perception of small numbers of visual things inevitably recruits object-based processes. Therefore, disentangling the contributions of object-tracking and magnitude-representation mechanisms to performance in small-number tasks is a challenging enterprise. He suggests an account that there exist both an object-tracking system that represents small numbers of visually presented objects and a number system that can represent both large and small approximate magnitudes of items presented in any modality. When an observer is faced with a small array of objects, both systems are likely engaged. In modalities where there are not ''objects'' as such, one can examine representations of numerosity without confound of object hood.
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