Approximate number system

Neurological basis

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 of three or five objects.

Pathology

Damage to intraparietal sulcus

Damage done to the parietal lobe, specifically in the left hemisphere, can produce 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 vary based the location of damage, but 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 individuals who have unexpected difficulty understanding numbers and arithmetic despite adequate education and social environments. This syndrome can manifest in several different ways from the inability to assign a quantity to Arabic numerals to difficulty with times tables. Dyscalculia can result in children falling significantly behind in school, regardless of having normal intelligence levels.

In some instances, such as Turner syndrome, the onset of dyscalculia is genetic. Morphological studies have revealed abnormal lengths and depths of the right intraparietal sulcus in individuals suffering from Turner syndrome. Brain imaging in children exhibiting symptoms of dyscalculia show less gray matter or less activation in the intraparietal regions stimulated normally during mathematical tasks. Additionally, impaired ANS acuity has been shown to differentiate children with dyscalculia from their normally-developing peers with low maths achievement.

Further research and theories

Impact of the visual cortex

The intraparietal region relies on several other brain systems to accurately perceive numbers. When using the ANS we must view the sets of objects in order to evaluate their magnitude. The primary visual cortex is responsible for disregarding irrelevant information, such as the size or shape of the objects. Certain visual cues can sometimes affect how the ANS functions.

Arranging the items differently can alter the effectiveness of the ANS. One arrangement proven to influence the ANS is visual nesting, or placing the objects within one another. This configuration affects the ability to distinguish each item and add them together at the same time. The difficulty results in underestimation of the magnitude present in the set or a longer amount of time needed to perform an estimate.

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. Dehaene and other researchers believe this effect is caused by the presence of a "mental number line" in which small numbers appear on the left and increase as you move right. The SNARC effect indicates that the ANS works more effectively and accurately if the larger set of objects is on the right and the smaller on the left.

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 school-aged children's ANS abilities are compared to their mathematical achievements. At this point the children have received training in other mathematical concepts, such as exact number and arithmetic. More surprisingly, ANS precision before any formal education accurately predicts better math performance. A study involving 3- to 5-year-old children revealed that ANS acuity corresponds to better mathematical cognition while remaining independent of factors that may interfere, such as reading ability and the use of Arabic numerals.

ANS in animals

Many species of animals exhibit the ability to assess and compare magnitude. This skill is believed to be a product of the ANS. Research has revealed this capability in both vertebrate and non-vertebrate animals including birds, mammals, fish, and even insects. In primates, implications of the ANS have been steadily observed through research. One study involving lemurs showed that they were able to distinguish groups of objects based only on numerical differences, suggesting that humans and other primates utilize a similar numerical processing mechanism.

In a study comparing students to guppies, both the fish and students performed the numerical task almost identically. The ability for the test groups to distinguish large numbers was dependent on the ratio between them, suggesting the ANS was involved. Such results seen when testing guppies indicate that the ANS may have been evolutionarily passed down through many species.

Applications in society

Implications for the classroom

Understanding how the ANS affects students' learning could be beneficial for teachers and parents. The following tactics have been suggested by neuroscientists to utilize the ANS in school:

• Counting or abacus games
• Simple board games
• Computer-based number association games
• Teacher sensitivity and different teaching methods for different learners

Such tools are most helpful in training the number system when the child is at an earlier age. Children coming from a disadvantaged background with risk of arithmetic problems are especially impressionable by these tactics.