Dyscalculia

Dyscalculia (difficulty in learning or comprehending mathematics) was originally identified in case studies of patients who suffered specific arithmetic disabilities as a result of damage to specific regions of the brain. Recent research suggests that dyscalculia can also occur developmentally, as a genetically-linked learning disability which affects a person's ability to understand, remember, and/or manipulate numbers and/or number facts (e.g. the multiplication tables). The term is often used to refer specifically to the inability to perform arithmetic operations, but is defined by some educational professionals and cognitive psychologists as a more fundamental inability to conceptualize numbers as abstract concepts of comparative quantities (a deficit in "number sense"^[1]). Those who argue for this more constrained definition of dyscalculia sometimes prefer to use the technical term Arithmetic Difficulties (AD) to refer to calculation and number memory deficits.

Dyscalculia is a lesser known disability, similar and potentially related to dyslexia and Developmental Dyspraxia. Dyscalculia occurs in people across the whole IQ range, and sufferers often, but not always, also have difficulties with time, measurement, and spatial reasoning. Current estimates suggest it may affect about 5% of the population. Although some researchers believe that dyscalculia necessarily implies mathematical reasoning difficulties as well as difficulties with arithmetic operations, there is evidence (especially from brain damaged patients) that arithmetic (e.g. calculation and number fact memory) and mathematical (abstract reasoning with numbers) abilities can be dissociated. That is (some researchers argue), an individual might suffer arithmetic difficulties (or dyscalculia), with no impairment of, or even giftedness in, abstract mathematical reasoning abilities.

The word dyscalculia comes from Greek and Latin which means: "counting badly". The prefix "dys" comes from Greek and means "badly". "Calculia" comes from the Latin "calculare", which means "to count". That word "calculare" again comes from "calculus", which means "pebble" or one of the counters on an abacus.

Dyscalculia can be detected at a young age and measures can be taken to ease the problems faced by younger students. The main problem is understanding the way mathematics is taught to children. In the way that dyslexia can be dealt with by using a slightly different approach to teaching, so can dyscalculia. However, dyscalculia is the lesser known of these learning disorders and so is often not recognized.

Another common manifestation of the condition emerges when the individual is faced with equation type of problems which contain both integers and letters (3A + 4C). It can be difficult for the person to differentiate between the integers and the letters. Confusion such as reading a '5' for an 'S' or not being able to distinguish between a zero '0' for the letter 'O' can keep algebra from being mastered. This particular form of dyscalculia is often not diagnosed until middle or high school is entered.

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Potential symptoms

• Frequent difficulties with arithmetic, confusing the signs: +, −, ÷ and ×.
• Inability to tell which of two numbers is the larger.
• Reliance on 'counting-on' strategies, e.g., using fingers, rather than any more efficient mental arithmetic strategies.
• Difficulty with everyday tasks like checking change and reading analog clocks.
• Inability to comprehend financial planning or budgeting, sometimes even at a basic level; for example, estimating the cost of the items in a shopping basket or balancing a checkbook.
• In some severe cases, the sufferer may have very bad co-ordination, causing them to fall or trip often
• Difficulty with times-tables, mental arithmetic, etc.
• May do fairly well in subjects such as science and geometry, which require logic rather than formulas, until a higher level requiring calculations is obtained.
• Difficulty with conceptualizing time and judging the passing of time.
• Problems differentiating between left and right.
• Having a poor sense of direction (i.e., north, south, east, and west), potentially even with a compass.
• Difficulty navigating or mentally "turning" the map to face the current direction rather than the common North=Top usage.
• Having difficulty mentally estimating the measurement of an object or distance (e.g., whether something is 10 or 20 feet away).
• Inability to grasp and remember mathematical concepts, rules, formulae, and sequences.
• An inability to read a sequence of numbers, or rotating them when repeated such turning 56 into 65.
• Difficulty keeping score during games.
• Difficulty with games such as poker with more flexible rules for scoring.
• Difficulty in activities requiring sequential processing, from the physical (such as dance steps) to the abstract (reading, writing and signaling things in the right order). May have trouble even with a calculator due to difficulties in the process of feeding in variables.
• The condition may lead in extreme cases to a phobia of mathematics and mathematical devices.

Potential causes

Scientists have yet to understand the causes of dyscalculia. They have been investigating in several domains.

• Neurological: Dyscalculia has been associated with lesions to the supramarginal and angular gyri at the junction between the temporal and parietal lobes of the cerebral cortex.^[2][3]
• Deficits in working memory: Adams and Hitch^[4] argue that working memory is a major factor in mental addition. From this base, Geary^[5] conducted a study that suggested there was a working memory deficit for those who suffered from dyscalculia. However, working memory problems are confounded with general learning difficulties, thus Geary's findings may not be specific to dyscalculia but rather may reflect a greater learning deficit.

Studies of mathematically gifted students have shown increased EEG activity in the right hemisphere during algorithmic computational processing. There is some evidence of right hemisphere deficits in dyscalculia.

Other causes may be:

• Short term memory being disturbed or reduced, making it difficult to remember calculations.
• Congenital or hereditary disorders. Studies show indications of this, but the evidence is not yet concrete.^{[citation needed]}
• A combination of these factors.

See also

• Acalculia
• Gerstmann syndrome: dyscalculia is one of a constellation of symptoms acquired after damage to the angular gyrus.
• The DSM-IV diagnosis mathematics disorder can be applied to people whose mathematical abilities are well below the expected level for their age.
• Dyslexia
• Dysgraphia
• Numerical cognition

Further reading

• Henderson Anne, Came Fil, Brough Mel. "Working with Dyscalculia." [1] Learning Works International Ltd, 2003, ISBN 0-9531055-2-0)
• Butterworth, Brian. "Dyscalculia Guidance: Helping Pupils With Specific Learning Difficulties in Maths." (David Fulton Pub, 2004, ISBN 0-7087-1152-9)
• Chinn, Steve. "The Trouble with Maths: A Practical Guide to Helping Learners with Numeracy Difficulties." (RoutledgeFalmer, 2004, ISBN 0-415-32498-X)
• Attwood, Tony. "Dyscalculia in Schools: What It Is and What You Can Do." (First and Best in Education Ltd, 2002, ISBN 1-86083-614-3)
• Abeel, Samantha. "My Thirteenth Winter." (Orchard Books, 2003, ISBN 0-439-33904-9)
• Kosc, Ladislav. (1974). "Developmental dyscalculia." Journal of Learning Disabilities, 7, 159-162. [First systematic study]
• Sharma, Mahesh. "Dyscalculia." http://www.bbc.co.uk/skillswise/tutors/expertcolumn/dyscalculia/
• Sharma, Mahesh and Loveless, Eugene. "Dyscalculia." Focus on Learning Problems in Mathematics, CT/LM, 1988.
• Sharma, Mahesh. Dyslexia, Dyscalculia and other Mathematics Problems. The Math Notebook, CT/LM, 1989.
• Sharma, Mahesh. Berkshire mathematics: www.berkshiremathematics.com

References

1. ^ Dehaene, S. 1997 The Number Sense: How the Mind Creates Mathematics New York, Oxford University Press.
2. ^ Levy LM, Reis IL, Grafman J. Metabolic abnormalities detected by 1H-MRS in dyscalculia and dysgraphia. Neurology. 1999;53(3):639—41. PMID 10449137
3. ^ Mayer E, Martory MD, Pegna AJ, Landis T, Delavelle J, Annoni JM. Free Full Text A pure case of Gerstmann syndrome with a subangular lesion. Brain. 1999;122(6):1107—20. PMID 10356063
4. ^ Adams JW, Hitch GJ. Working memory and children's mental addition. J Exp Child Psychol. 1997;67(1),21—38. PMID 9344485
5. ^ Geary DC. Mathematical disabilities: cognition, neuropsychological and genetic components. Psychol Bull. 1993;114(2) 345—62. PMID 8416036