User:Jsettle0330/sandbox

Overview
The approximate number system (ANS) is a cognitive system that encodes the inexact magnitude of a set of objects. The ANS is credited with the non-symbolic representation of all numbers greater than four, with lesser values being carried out by the parallel individuation system, or object tracking system. Beginning in early infancy, the ANS allows an individual to detect differences in magnitude between groups. The precision of the ANS improves throughout childhood development and reaches a final adult level of 15% accuracy, meaning an adult could distinguish 100 items versus 115 items without counting. The ANS plays a crucial role in development of other numerical abilities, such as the concept of exact number. The precision level of a child's ANS has been shown to predict mathematical achievement in school. The ANS has been linked to the intraparietal sulcus of the brain.

Piaget's theory
Jean Piaget was a French psychologist who devoted much of his life to studying how children learn. A book summarizing his theories on number cognition, The Child’s Conception of Number, was published in 1952. Piaget’s work supported the viewpoint that children do not have a stable representation of number until the age of six or seven. His theories indicate that mathematical knowledge is slowly gained and during infancy any concept of sets, objects, or calculation are absent.

Challenging the Piagetian viewpoint
Piaget’s ideas pertaining to the absence of mathematical cognition at birth have been steadily challenged. The work of Rochel Gelman and C. Randy Gallistel in the 1970’s suggested that preschoolers have intuitive understanding of the quantity of a set, expressing surprise when objects disappear without an apparent cause. Research published by Stanislas Dehaene in the 1990’s indicates that when given nonverbal tests toddlers are able to conserve number. Some researchers believe that this suggests Piaget’s methods included verbal skills past those typical of the child’s age. Today, the ANS is generally believed to lay the foundation for higher-level arithmetical concepts. Beginning as infants, people have an innate sense of approximate number that depends on the ratio between sets of objects. Throughout life the ANS becomes more developed, and people are able to distinguish between groups of smaller differences.

Neurological Basis
Brain imaging studies have identified an area within the parietal lobe as being responsible for the ANS. Specifically within this lobe is the intraparietal sulcus which is "active whenever we think about a number, whether spoken or written, as a word or as an Arabic digit, or even when we inspect a set of objects and think about its cardinality". It has been shown that the intraparietal sulcus is activated independently of the type of task being performed with the number. The intensity of activation is dependent on the difficulty of the task, with the intraparietal sulcus showing more activation when the task is harder. Studies in monkeys have shown that individual neurons can fire preferentially to certain numbers over others (nieder & Miller, 2004). For example, a neuron could fire at maximum level every time a group of four objects is seen, but will fire less to a group three or five objects.

Damage to intraparietal sulcus
Damage done to parietal lobe, specifically in the left hemisphere, can produced difficulties in counting and other simple arithmetic. Damage directly to the intraparietal sulcus has been shown to cause acalculia, a severe disorder in mathematical cognition. Symptoms can include the inability to perform simple calculations or to decide that one number is larger than another. Gerstmann syndrome, a disease resulting in lesions in the left parietal and temporal lobes, results in acalculia symptoms and further confirms the importance of the parietal region in the ANS.

Developmental delays
A syndrome known as dyscalculia is seen in children who show little innate understanding of what numbers mean. Dyscalculia can result in children falling significantly behind, despite normal intelligence. This syndrome can manifest in several different ways from the inability to assign a quantity to Arabic numerals to difficulty with times tables. Brain imaging in children exhibiting symptoms of dyscalculia show less gray matter or less activation in the intraparietal regions stimulated normally during mathematical tasks. Morphological studies have revealed abnormal length and depth of the right intraparietal sulcus in individuals suffering from dyscalculia of genetic origin.

Impact of the visual cortex
The intraparietal region relies on several other brain systems to accurately perceive numbers. When utilizing the ANS we must view the sets of objects in order to evaluate their number. The primary visual cortex is responsible for disregarding irrelevant information, such as the size or shape of objects. Visual alterations can sometimes affect how the ANS functions. The effectiveness of the ANS can be altered when items are arranged differently. One arrangement that affects the ANS is visual nesting, or placing the objects within one another. This configuration influences one’s ability to individuate each item and add them together at the same time, resulting in underestimation of the quantity present. Another visual representation that affects the ANS is the spatial numerical association response code, or the SNARC effect. The SNARC effect details the tendency of larger numbers to be responded to faster by the right hand and lower numbers by the left hand, suggesting that the magnitude of a number is linked to a spatial representation.

ANS development and mathematical performance
Although the ANS is present in infancy before any numerical education, research has shown a link between people’s mathematical abilities and the accuracy in which they approximate the magnitude of a set. This correlation is supported by several studies in which children’s ANS abilities are compared to their mathematical achievements. Better ANS acuity corresponds to better mathematical cognition while remaining independent of other subjects, such as reading ability.