Approximate number system

The approximate number system (ANS) is a cognitive system that supports the estimation of the magnitude of a group without relying on language or symbols. 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 approximately 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 and simple arithmetic. The precision level of a child's ANS has been shown to predict subsequent mathematical achievement in school. The ANS has been linked to the intraparietal sulcus of the brain. The approximate number system (ANS) is a cognitive system that supports the estimation of the magnitude of a group without relying on language or symbols. 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 approximately 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 and simple arithmetic. The precision level of a child's ANS has been shown to predict subsequent mathematical achievement in school. The ANS has been linked to the intraparietal sulcus of the brain. Jean Piaget was a Swiss developmental 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 is absent. 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 among others in the 1970s suggested that preschoolers have intuitive understanding of the quantity of a set and its conservation under non cardinality-related changes, expressing surprise when objects disappear without an apparent cause. 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 having smaller differences in magnitude. The ratio of distinction is defined by Weber's law, which relates the different intensities of a sensory stimulus that is being evaluated. In the case of the ANS, as the ratio between the magnitudes increases, the ability to discriminate between the two quantities increases. Today, some theorize that the ANS lays the foundation for higher-level arithmetical concepts. Research has shown that the same areas of the brain are active during non-symbolic number tasks in infants and both non-symbolic and more sophisticated symbolic number tasks in adults. These results could suggest that the ANS contributes over time to the development of higher-level numerical skills that activate the same part of the brain. However, longitudinal studies do not necessarily find that non-symbolic abilities predict later symbolic abilities. Conversely, early symbolic number abilities have been found to predict later non-symbolic abilities, not vice versa as predicted. In adults for example, non-symbolic number abilities do not always explain mathematics achievement. Brain imaging studies have identified the parietal lobe as being a key brain region for numerical cognition. 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'. When comparing groups of objects, activation of the intraparietal sulcus is greater when the difference between groups is numerical rather than an alternative factor, such as differences in shape or size. This indicates that the intraparietal sulcus plays an active role when the ANS is employed to approximate magnitude. Parietal lobe brain activity seen in adults is also observed during infancy during non-verbal numerical tasks, suggesting that the ANS is present very early in life. A neuroimaging technique, functional Near-Infrared Spectroscopy, was performed on infants revealing that the parietal lobe is specialized for number representation before the development of language. This indicates that numerical cognition may be initially reserved to the right hemisphere of the brain and becomes bilateral through experience and the development of complex number representation. 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 intense activation when the task is more difficult. In addition, studies in monkeys have shown that individual neurons can fire preferentially to certain numbers over others. 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.