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MEP learning pack

Masters in Educational Practice: Numeracy learning pack

5

Numeracy and inclusive practice

5.3

Dyscalculia

Dyscalculia as a specific learning difficulty

Dyscalculia was first recognised by the DfES in 2001. 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. Even if they produce a correct answer or use a correct method they may do so mechanically and without confidence.

The following offers insight into how dyscalculia might impact for an adult: Blackburn, J (n.d.) Damn the three times table. Loughborough University.

As a specific learning difficulty, while it has a similar prevalence rate to dyslexia, dyscalculia is much less researched than dyslexia, and is a less widely recognised learning disability (Chinn, 2012; Butterworth and Yoe, 2004).

It is possible that dyscalculia is:

  • a deficit in the capacity to represent and process numerosities, e.g. a difficulty being able to grasp that 8 is 8 ones but can also be 4 + 4, 6+2, etc.
  • some difficulty with the specialised neural circuits for numerical processing in the parietal lobe of the brain (Piazza and Izard, 2009)
  • for some heritable.

Professor Sharma (2008) says that the following skills are needed to succeed with mathematics/numeracy:

  • following sequential directions
  • spatial orientation/space organization
  • pattern recognition
  • visualization
  • estimation
  • inductive and deductive thinking.

The following documents are examples of assessment/screening tools for dyscalculia/numeracy difficulties.

  1. Chinn, S. (2012) More trouble with maths: A complete guide to identifying and diagnosing mathematical difficulties (David Fulton Publishers).
  2. Butterworth, B. (2003) Dyscalculia Screener. London: nferNelson

Chinn offers 31 characteristics that can lead to maths failure in his ‘Dyscalculia Checklist’ (2012) and Butterworth offers a ‘Dyscalculia Screener’. For example, learners with dyscalculia:

  • struggle to ‘see’ that four objects are 4 without counting
  • struggle to move beyond the management of numbers by counting on in ones
  • for mental arithmetic, they cannot call on addition facts, but must depend every time on using their fingers/blocks/other concrete methods, to count on in ones to reach an answer for a sum such as 6 +3
  • find subtraction is difficult because it requires counting backwards and they can lose track and make counting errors
  • find estimation difficult
  • cannot generalise that 10-4 has the same outcome as 10p-4p
  • have difficulty with mastering place value.

Learners with dyscalculia require specialist teaching, and need to be helped to acquire number skills, i.e. the building blocks for numeracy (Henderson, Came and Brough, 2003; Butterworth and Yoe, 2004; Chinn, 2012).

Further reading

Offering educators input on the additional needs of such learners is also recommended in Beswick (2008/2009) Influencing Teachers' Beliefs about Teaching Mathematics for Numeracy to Students with Mathematics Learning Difficulties (external link).

Activity 5.04

  • Take three of the above difficulties and reflect on how each difficulty might impact on what you are teaching in numeracy to your learners in your class at this time.
  • Research and draw up a lesson plan to address each of these difficulties for a learner with dyscalculia.

In conclusion, dyscalculia affects a learner’s ability to understand, recall or manipulate numerical information, or conceptualise numbers as abstract concepts. Some learners may feel anxious when having to undertake any mathematics-related tasks and so may avoid situations where they have to do this.

Dyscalculia and other specific learning difficulties (SpLDs)/developmental disorders

As an educator it is important to be aware that research indicates that there is considerable overlap/comorbidity across the specific learning difficulties/developmental disorders. Thus if a learner has a diagnosis of dyslexia for example, it is important to be aware that they may also have additional needs related to focus and concentration (dyslexia and ADHD) and language (SLI and dyslexia), and handwriting difficulties (dyslexia and DCD).

  • Attention deficit hyperactivity disorder (ADHD) and autistic spectrum disorder (ASD): 21 per cent of children with severe ADHD met full criteria for Asperger’s syndrome and 36 per cent showed ‘autistic traits’ (Fitzgerald and Corvin, 2001; Lecavalier, 2006; Fombonne et al. 2001).
  • Developmental coordination disorder (DCD) and ADHD: 30-35 per cent of children have ADHD and DCD (Kirby and Salmon, 2008; Gillberg and Rasmussen, 2010).
  • ADHD, DCD, dyslexia and ASD: extensive evidence of overlap between all four disorders (Kaplan et al. 1998).
  • Dyslexia and ADHD: in about 35–40 per cent  of cases (Willcutt, Pennington, Olson et al. (2007) showed a shared genetic basis).
  • Specific language impairment (SLI) and DCD: 60 per cent of children with specific language impairment showed motor difficulties as well (Missiuna and Gaines, 2007).
  • SLI and dyslexia: greater risk of later dyslexia difficulties in adulthood (Pennington and Bishop , 2009).
  • Dyslexia and ASD (Nation et  al., 2006; Griffiths, 2007).

There are also overlaps with dyscalculia.

Sharma (2008) reports that the indicators of dyscalculia include difficulties with the following, two of which could be indicators of dyslexia.

  • Understanding the concept of positive whole numbers as indicators of order and size.
  • Instinctive judgement of length of time, keeping track of time and planning time schedules.
  • Remembering simple arithmetic facts; employing these to generalise using the place value system.
  • Carrying out everyday financial transactions, such as giving change and handling a bank account.
  • • Following sequential directions – sequencing (including reading numbers out of sequence, substitutions, reversals, omissions and doing operations. backwards), organizing detailed information, remembering specific facts and formulas for completing their mathematical calculations.

It is noted that some learners with dyslexia will have difficulties with numeracy because of the ‘language’ of numeracy (Henderson, 1998; Sharma, 2008).

Sharma (2008) also points out that there is also overlap between DCD and dyscalculia, and the following are strong indicators of dyscalculia and/or DCD.

  • Acquiring spatial orientation/space organisation/direction, easily disoriented (including left/right orientation), trouble reading maps, and grappling with mechanical processes.
  • Learning musical concepts, following directions in sports that demand sequencing or rules, and keeping track of scores and players during games such as cards and board games.

References

Beswick, K. (2008/2009) ‘Influencing Teachers' Beliefs about Teaching Mathematics for Numeracy to Students with Mathematics Learning Difficulties’, in Mathematics Teacher Education and Development 2007/2008, 9, pp.3-20.

Butterworth, B. (2003) Dyscalculia Screener. London: Nfer: Nelson.

Butterworth, B. and Yeo, D. (2004) Dyscalculia Guidance. London: Nfer: Nelson.

Chinn, S. (2012) More trouble with maths: A complete guide to identifying and diagnosing mathematical difficulties. Routledge, David Fulton Book.

DfES (2001) Guidance to Support Pupils with Dyslexia and Dyscalculia. Ref. 0512/2001. London, DfES.

Fitzgerald, M. and Corvin, A. (2001) Diagnosis and Differential Diagnosis of Asperger Syndrome, Advances in Psychiatric Treatment, Volume 7, Issue 4, pp.310-318.

Fombonne, E. et al., (2001) Prevalence of Pervasive Developmental Disorders in the British Nationwide Survey of Child Mental Health Journal of the American Academy of Child and Adolescent Psychiatry, Volume 40, Issue 7, pp.820-827.

Gaines, R. and Missiuna, C. (2007) Early identification: are speech/language-impaired toddlers at increased risk for Developmental Coordination Disorder? Child: Care, Health and Development, Volume 33, Issue 3, pp.325-332.

Griffiths, C. (2007) Pragmatic Abilites in Adults With and Without Dyslexia: A Pilot Study, Dyslexia, Volume 13, Issue 4, pp.276-296.

Henderson, A. (1998) Maths for the Dyslexic: A Practical Guide. London, David Fulton Publishers.

Henderson, A., Came, F. and Brough, M. (2003) Working with Dyscalculia. Learning Works.

Kaplan, B. et al. (1998) DCD may not be a discrete disorder Human Movement Science, Volume 17, Issues 4-5, pp.471-490.

Kirby, A. and Salmon, G. (2008) Schools: Central to Providing Comprehensive CAMH Services in the Future? Child and Adolescent Mental Health, Volume 13, Issue 3, pp.107-114.

Lecavalier, L. (2006) Behavioural and Emotional Problems in Young People with Pervasive Developmental Disorders: Relative Prevalence, Effects of Subject Characteristics, and Empirical Classification, Journal of Autism and Developmental Disorders, Volume 36, Issue 8, pp.1101-1114.

Nation, K. et al. (2006) Patterns of Reading Ability in Children with Autism Spectrum Disorder Journal of Autism and Developmental Disorders, Volume 36, Issue 7, pp.911-919.

Pennington, B. and Bishop, D. (2009) Relations Among Speech, Language and Reading Disorders. Annual Review of Psychology, Volume 60, pp.283-306.

Piazza, M. and Izard, V. (2009) How humans count: numerosity and the parietal cortex. Neuroscientist, 15, 271.

Rasmussen, P. and Gillberg, C. (2000) Natural Outcome of ADHD with Developmental Coordination Disorder at Age 22 Years: A Controlled, Longitudunal, Community Based Study. Journal of the American Academy of Child and Adolescent Psychiatry, Volume 39, Issue 11, pp.1424-1431.

Sharma (2008)

Willcutt, E., Pennington, B., Olson, R. and DeFries, J. (2007) Understanding Comorbidity: A Twin Study of Reading Disability and Attention-Deficit/Hyperactivity Disorder. American Journal of Medical Genetics Part B: Neuropsychiatric Genetics, Volume 144B, Issue 6, pp.709-714.

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