The need for a unitary definition of dyscalculia

Those of you who've read my presentation – "Learning disability – the story of a definition", saw the difficulties and confusion caused to children and to research by the lack of agreement among experts about almost each of the basic features of learning disability.

This paper strives to get at a unified definition of Developmental Dyscalculia (DD).

Dyscalculia from a developmental and differential perspective

Front Psychol. 2013; 4: 516.  

Liane Kaufmann,  Michèle M. Mazzocco,  Ann Dowker,  Michael von Aster,  Silke M. Göbel,  Roland H. Grabner,  Avishai Henik,  Nancy C. Jordan,  Annette D. Karmiloff-Smith,  Karin Kucian,  Orly Rubinsten,  Denes Szucs,  Ruth Shalev,  and Hans-Christoph Nuerk 

 http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3748433/

The paper distinguishes between three approaches to dyscalculia, which I'll rephrase in light of my own viewpoint and interpretation:

1.  DD is related to basic deficiencies in number sense.  Here we refer to a group of children who have poor grasp of number magnitude.  These children are slower to determine, for instance, whether the amount of dots in an array is equal to a specific numeral (numerals and quantities below 9). Butterworth argues that this specific difficulty indicates deficiency in what he calls "the number module".

2.  DD subtypes are caused by deficits in various cognitive processes.  Deficiencies in verbal working memory, semantic memory, visuospatial processing or fluid ability affect mathematic functioning.  I prefer to name this group "learning disabled" rather than "DD".  This is because the disabilities this group has in cognitive abilities (visuospatial processing, short term memory, comprehension-knowledge etc.) usually affect  not only math but also reading, writing and reading comprehension.  Each of these children is learning disabled in a different way (according to the specific affected cognitive ability) and so his performance in math (and also reading, writing and reading comprehension) will be – I think- different.

3.   DD subtypes are related to specific deficiencies in math beyond the basic deficiencies in number sense.  Here the authors list specific deficiencies in various math areas – magnitude representation, verbal representation of numbers, knowledge of arithmetic facts, visual representation of numbers, ordinality, the base 10 system, finger representations of numbers.  I believe, that at least some of these specific deficits are deficits in acquired math knowledge (knowledge that is learned in school), or in CHC terminology – "quantitative ability" – Gq.  I think that deficiencies in "quantitative ability" might be caused by poor number sense and/or disabilities in cognitive abilities (meaning, situations that are described under 1 and 2 above).  That's why   deficiencies in Gq are only manifestations of learning disability or dyscalculia and not a separate kind of dyscalculia.

The authors go on to point out the following problems caused by the lack of a unitary definition:

A.  Disagreement among experts about which tasks should 

be used to make a differential diagnosis of DD.  Should   we use basic tasks measuring number sense (like quickly comparing a numeral to an array of dots) or should we use complex tasks that include math reasoning and/or reading 
comprehension (like in math problems)?

I think we should use basic tasks measuring number sense 
(like in the Dyscalculia screener about which I posted in july 9^th) – to identify group no, 1.  We should use more complex math tasks as part of the identification process of group no. 2.

B.  Even if agreement is reached about problem A, what should be the cutoff point under which children will be identified as DD (for research purposes)?  Some studies include children whose scores are lower than the 10^th percentile.  Other studies include children whose scores are lower than the 35^th percentile.  Thus studies include a population which might be too heterogenous.

A score higher than the 16^th percentile can be considered to be an average score,  being within one standard deviation below the mean.  So I believe that children with scores above the 16^th percentile in math tests do not satisfy the basic criterion for dyscalculia or learning disability (namely, significant underachievement in math). 

C.  Should we require a discrepancy between the general cognitive ability and math achievement?  Some studies include children with no such discrepancy – children who struggle with broad cognitive deficits. Other studies choose children with at least average general cognitive ability.

I think, that the main diagnosis of a child who has disabilities in many cognitive abilities (visuospatial processing, auditory processing, fluid ability, short term memory, processing speed, long term storage and retrieval, comprehension knowledge)  is not dyscalculia or learning disability.  That's why it's important, in my opinion, not to include children with broad cognitive deficits in groups of children meant to be with dyscalculia or learning disability.