Neuropsychological Model Of Number Processing

A. Description of the Model

The abilities, performance patterns, and dissociations described in Section I, together with other findings relating to how human adults represent and process number, led the French cognitive neuroscientist Stanislas Dehaene to develop a cognitive neuropsychological model of number processing that is the dominant model today. In this model, our number knowledge consists of three distinct representational systems. Each of these systems represents numbers in a very different format from the others and so supports different aspects of our numerical knowledge and abilities. Each is localized in a different brain region (see Fig. 2).

A verbal word representational system is located in the classical language-specific areas within the left hemisphere only (such as the left inferior frontal and superior and middle temporal gyri) and is responsible for the recognition and processing of spoken or written number words. This system represents numbers as syntactically organized sequences of words (employing

Triple Code Model
Figure 2 Stanislas Dehaene's triple-code model of number processing (courtesy of Mathematical Cognition).

the syntactic rules governing the number naming system of the language) and operates over phonological representations of the number words. This system also stores well-learned arithmetical facts, such as the memorized facts from addition and multiplication tables (subtraction and division facts are not memorized by rote and so are not hypothesized to be stored within this system). Finally, this system is heavily implicated in precise mental arithmetic such as multi-digit calculations, which involve both retrieval of stored verbal facts and visuospatial representations of numbers.

A visual Arabic numeral representational system, located in the left occipitotemporal region of both hemispheres, underlies the recognition of Arabic digits and numerals. This system represents numbers in their Arabic numeral format as strings of digits.

Finally, an analogical magnitude representational system, located in the inferior parietal cortex regions of both hemispheres, employs representations that inherently embody the magnitude of a given numerical quantity, representations such as those given by the accumulator mechanism, for example. It is only within this third system that information about what we think of as the meaning or sense of a number—its quantity, magnitude, or size—is represented. Thus, comparison and relational information, such as that one number is smaller or larger than another, is only available within this system. This system also supports approximate, as opposed to precise, arithmetic calculations; such calculations depend on a sense of the magnitudes the values being operated on and the outcome value.

Connections exist (a) between the verbal, Arabic numeral, and magnitude systems within the left hemisphere, (b) between the visual and magnitude systems within the right hemisphere (recall that the verbal system exists solely in the left hemisphere), and (c) across the two hemispheric components of the visual system and of the magnitude system. These connections enable access to multiple kinds of information about a number that has been accessed through one of the systems. For example, the connections between the Arabic numeral code and the magnitude code mean that, when we see an Arabic numeral, say seven, we can then access its magnitude and so perform operations over the magnitudes and/or make magnitude judgments, such as which of two numerals represents the larger or smaller number.

There is considerable neuropsychological evidence, from case studies of brain-damaged patients as well as from studies of normal adults, that these systems are both anatomically and functionally distinct.

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