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Dyscalculia – What is Maths Disability?

In my previous life (while studying at Wits), I was a tutor for Master Maths. This invariably had me meeting students who struggled with maths. However, there is one little boy that I have always remembered. He was a grade 5, A-student in every subject except maths. He didn’t get it. He tried incredibly hard and worked even harder. I remember the one day he arrived for his lesson in tears. He had failed another maths test. He was devastated. And, being the good psychology student that I was at the time, we went out to have a chat on the balcony and to calm down before figuring out what to do about his mathematics skills. He left the centre a couple of months later. His story has always stayed with me and after doing some research I wonder if perhaps he should have been diagnosed with Dyscalculia.

 

      

Dyscalculia is a very fancy name for Maths Disability and is generally described as a condition that prevents a person from gaining mathematical skills. There are two main definitions that are used widely in the literature. The UK Department of Education and Skills states that Developmental Dyscalculia is:

A condition that affects the ability to acquire arithmetical skills. Dyscalculic learners may have difficulty understanding simple number concepts, lack an intuitive grasp of numbers, and have problems learning number facts and procedures.”  (6)

While the Diagnostic and Statistical Manual of Mental Disorders, fourth edition states that a person with dyscalculia will have the following characteristics:

“Mathematical ability, as measured by individually administered standardised tests, is substantially below that expected given the person’s chronological age, measured intelligence, and age-appropriate education, which significantly interferes with academic achievement or activities of daily living that require mathematical ability.” (7).

Essentially, what these two definitions are saying is that a student with Dyscalculia has difficulty in learning maths skills, as well as coping in situations that require some maths to be used (for example, working out how much change you should receive). However, these students have an average IQ and are coping in their other subjects. In other words, it is weird for this particular student not to be coping with, or at least achieving at an average rate, in the maths class.

There are many signs of dyscalculia. These children will often also experience math anxiety both inside the classroom and at home or other situations (3, 7). These children have difficulty with tasks that require number sense such as counting, arranging numbers and number patterns (3). They have difficulty learning maths facts and doing calculations (7). They have fewer methods for doing maths and they often apply the wrong method to a problem (7). Cortiella and Horowitz (2014) state that the following characteristics are common:

 

  • Difficulty with counting, learning number facts and doing math calculations.
  • Difficulty with measurement, telling time, counting money and estimating number quantities.
  • Trouble with mental maths and problem solving strategies.”

Some other issues are given in the pictures below:


Approximately 7% of the school population is thought to experience dyscalculia (2), while 17% of all schoolchildren in the USA have a learning difficulty (8). Approximately 40% of students with a maths disability also have a reading disability, and many believe that maths disability is another sign of a reading disability (7).  Researchers suggest that in these students there are “deficits in the cognitive processes that support reading” along with maths (4). However, Fuchs, Fuchs and Prentice (2004) found in their research that the cognitive profiles of children with reading disability, with or without maths disability differed. Thus, although there is a strong overlap between the two disabilities (1), they are not linked in any way.

The question many have struggled with is how does dyscalculia work? It has been the subject of much research and there are two main camps. The first is the working memory camp. Working memory is the part of short-term memory that is occupied with processing auditory and visual information. According to Passolunghi and Siegel (2004) working memory is very important for calculations and solving arithmetic word problems. They have found that working memory has been found to be one of the main areas lacking in children with dyscalculia. They suggest that the problem in working memory is that children with dyscalculia are unable to inhibit irrelevant information thus “distracting” them from their main task. Furthermore, working memory deficits have an affect on completing basic arithmetic sums, recalling number facts and consolidating or arranging them, solving problems and counting based procedures (3).

The second main theory is that dyscalculia is caused by deficiencies in the Approximate Number System (ANS). The ANS is thought to be another system in the brain that is responsible for a system of approximate number representations. These number systems are used both in real-world everyday maths – for example, deciding which set of items is bigger – to symbolic number tasks, for example using the Arabic numbers to decide which is bigger or smaller. This system is in use whenever someone uses numbers (5). Mazzocco, Feigenson and Halberda (2011) found that children with maths disability had a deficit in their ANS and that it was likely to be specific to a particular domain within the ANS.

Essentially, maths disability stems from a lack of an intuitive grasp of what a number really means (6). These children do not understand the difference in value between 3 and 4 and this flows into all their other mathematics. So, how do we deal with it? Butterworth (2003) suggests that items and sets are used for counting and manipulation (such as beans or marbles) so that the concepts of numerosity can be solidified. He also suggests that teachers start with the very basics of mathematics. Butterworth has also suggested the use of a calculator for students with dyscalculia as it is the basic arithmetic and mental maths that they struggle with and not so much things like algebra and geometry. Passolunghi and Siegel (2004) also suggest that teachers should think about the amount of stress the child is under before considering diagnosing them with Dyscalculia. In the diagram below there are more suggestions for dealing with dyscalculia in the classroom:

All of this will require hard work on the part of the teacher and the student. There will be many extra hours spent learning a new love for maths and new techniques for coping with this disadvantage. But don’t worry, even Cher has dyscalculia and look where she is today. Don’t be discouraged; keep working hard with your student or on your own and you will eventually reap the rewards!

References:

  1. Kovas, Y., Haworth, C.M.A., Harlaar, N., Petrill, S.A., Dale, P.S., and Plomin, R. (2007) Overlap and Specificity of Genetic and Environmental Influences on Mathematics and Reading Disability in 10-year-old Twins. Journal of Child Psychology and Psychiatry, 48 (9), 914 – 922.
  2. Passolunghi, M.C. and Siegel, L.S. (2004) Working Memory and Access to Numerical Information in Children with Disability in Mathematics. Journal of Experimental Child Psychology, 88(4), 348 – 367.
  3. MacKinnon McQuarrie, M.A., Siegel, L.S., Perry, N.E. and Weinberg, J. (2014) Reactivity to Stress and the Cognitive Components of Maths Disability in Grade 1 Children. Journal of Learning Disabilities, 47 (4) 349 – 365
  4. Swanson, H.L., Jerman, D., and Zheng, X. (2009) Maths Disabilities and Reading Disabilities: Can they be Separated? Journal of Psychoeducational Assessment, 27 (3) 175 – 196.
  5. Mazzocco, M.M.M., Feigenson, L. and Halberda, J. (2011) Impaired Acuity of the Approximate Number System Underlies Mathematical Learning Disability (Dyscalculia) Child Development, 82(4), 1224 – 1237.
  6. Butterworth, B. (2005) The Development of Arithmetical Abilities Journal of Child Psychology and Psychiatry, 46 (1), 3 -18.
  7. Butterworth, B. (2003) Dyscalculia Screener, nfer Nelson Publishing Company Limited, London, UK.
  8. http://www.understood.org/en/learning-attention-issues/child-learning-disabilities/dyslexia/dyslexia-by-the-numbers
  9. Cortiella, C. and Horowitz, S.H. (2014) The State of Learning Disabilities, 3rd ed. National Centre for Learning Disabilities. http://www.ncld.org/wp-content/uploads/2014/11/2014-State-of-LD.pdf
  10. Fuchs, L.S., Fuchs, D. and Prentice, K. (2004) Responsiveness to Mathematical Problem-Solving Instruction: Comparing Students at Risk of Mathematical Disability With and Without Reading Disability. Journal of Learning Disabilities, 37 (4) 293 – 306.
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