Scientific Understanding of Consciousness
Mathematical Intelligence Dyscalculia
Science 27 May 2011: Vol. 332 no. 6033 pp. 1049-1053
Dyscalculia: From Brain to Education
Brian Butterworth1, Sashank Varma2, and Diana Laurillard3
1Centre for Educational Neuroscience and Institute of Cognitive Neuroscience, University College London, Psychological Sciences, Melbourne University, Melbourne VIC 3010, Australia.
2Department of Educational Psychology, University of Minnesota, Minneapolis, MN 55455, USA.
3Centre for Educational Neuroscience and London Knowledge Lab, Institute of Education, University of London, London WC1N 3QS, UK.
Developmental dyscalculia is a mathematical disorder, with an estimated prevalence of about 5 to 7%, which is roughly the same prevalence as developmental dyslexia.
Recent research in cognitive and developmental neuroscience is providing a new approach to the understanding of dyscalculia that emphasizes a core deficit in understanding sets and their numerosities, which is fundamental to all aspects of elementary school mathematics. The neural bases of numerosity processing have been investigated in structural and functional neuroimaging studies of adults and children, and neural markers of its impairment in dyscalculia have been identified. New interventions to strengthen numerosity processing, including adaptive software, promise effective evidence-based education for dyscalculic learners.
Numbers do not seem to be meaningful for dyscalculics—at least, not meaningful in the way that they are for typically developing learners. They do not intuitively grasp the size of a number and its value relative to other numbers. This basic understanding underpins all work with numbers and their relationships to one another.
Neural Basis of Arithmetical Abilities
The neural basis of arithmetical abilities in the parietal lobes, which is separate from language and domain-general cognitive capacities, has been broadly understood for nearly 100 years from research on neurological patients. One particularly interesting finding is that arithmetical concepts and laws can be preserved even when facts have been lost, and conversely, facts can be preserved even when an understanding of concepts and laws has been lost.
Neuroimaging experiments confirm this picture and show links from the parietal lobes to the left frontal lobe for more complex tasks. One important new finding is that the neural organization of arithmetic is dynamic, shifting from one subnetwork to another during the process of learning. Thus, learning new arithmetical facts primarily involves the frontal lobes and the intraparietal sulci (IPS), but using previously learned facts involves the left angular gyrus, which is also implicated in retrieving facts from memory. Even prodigious calculators use this network, although supplementing it with additional brain areas that appear to extend the capacity of working memory.
There is now extensive evidence that the IPS supports the representation of the magnitude of symbolic numbers, either as analog magnitudes or as a discrete representation that codes cardinality, as evidenced by IPS activation when processing the numerosity of arrays of objects. Moreover, when IPS functioning is disturbed by magnetic stimulation, the ability to estimate discrete magnitudes is affected. The critical point is that almost all arithmetical and numerical processes implicate the parietal lobes, especially the IPS, suggesting that these are at the core of mathematical capacities.
Patterns of brain activity in 4-year-olds and adults show overlapping areas in the parietal lobes bilaterally when responding to changes in numerosity. Nevertheless, there is a developmental trajectory in the organization of more complex arithmetical abilities. First, the organization of routine numerical activity changes with age, shifting from frontal areas (which are associated with executive function and working memory) and medial temporal areas (which are associated with declarative memory) to parietal areas (which are associated with magnitude processing and arithmetic fact retrieval) and occipito-temporal areas (which are associated with processing symbolic form). These changes allow the brain to process numbers more efficiently and automatically, which enables it to carry out the more complex processing of arithmetical calculations. As A. N. Whitehead observed, an understanding of symbolic notation relieves “the brain of all unnecessary work … and sets it free to concentrate on more advanced problems”.
This suggests the possibility that the neural specialization for arithmetical processing may arise, at least in part, from a developmental interaction between the brain and experience. Thus, one way of thinking about dyscalculia is that the typical school environment does not provide the right kind of experiences to enable the dyscalculic brain to develop normally to learn arithmetic.
Of course, mathematics is more than just simple number processing and retrieval of previously learned facts. In a numerate society, we have to learn more complex mathematical concepts, such as place value, and more complex procedures, such as “long” addition, subtraction, multiplication, and division. Recent research has revealed the neural correlates of learning to solve complex, multidigit arithmetic problems. Again, this research shows that solving new problems requires more activation in the inferior frontal gyrus for reasoning and working memory and the IPS for representing the magnitudes of the numbers involved, as compared with retrieval of previously learned facts.
The striking result in all of these studies is the crucial role of the parietal lobes. That the IPS is implicated in both simple and complex calculations suggests that the basic representations of magnitude are always activated, even in the retrieval of well-learned single-digit addition and multiplication facts. This is consistent with the well-established “problem-size effect,” in which single-digit problems take longer to solve the larger the operands, even when they are well known. It seems that the typically developing individual, even when retrieving math facts from memory, cannot help but activate the meaning of the component numbers at the same time. If that link has not been established, calculation is necessarily impaired.
Without specialized intervention, most dyscalculic learners are still struggling with basic arithmetic in secondary school. Effective early intervention may help to reduce the later impact on poor numeracy skills, as it does in dyslexia. Although very expensive, it promises to repay 12 to 19 times the investment
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