Dyscalculia: Characteristics, causes, and treatments

Price, Gavin R., and Daniel Ansari. "Dyscalculia: Characteristics, causes, and treatments." Numeracy 6.1 (2013): 2.‏

http://scholarcommons.usf.edu/cgi/viewcontent.cgi?article=1112&context=numeracy

While preparing the third presentation in the series "mathematics and cognitive abilities" I came upon this paper.  It is written very clearly, and I highly recommend it.  Here are some interesting findings from this paper:

 Dyscalculia characteristics:

·         Poor retrieval of arithmetic facts from long term memory.  By third grade, typically developing children have developed a store of arithmetic facts in memory, from which they can quickly recall the solution to a given problem.  Children with dyscalculia, on the other hand, typically fail to develop such fluent fact-retrieval mechanisms, continuing to employ procedural strategies long after their typically developing peers have progressed to memory-based  strategies.  One of the immature procedural strategies children with dyscalculia use is "count all", in which the child displays two addends on his fingers or by drawing lines, and then counts the fingers or lines from 1.  As an indicator of the severity of the fact-retrieval deficit in children with dyscalculia, typically developing children have been found to recall an average of three times as many arithmetic facts as those with dyscalculia.

·         Poor number sense.  This difficulty is proven by research finding such as:

o   Israely scholars Avishai Henik and Orly Rubinsten  reported a lack of facilitation from numerical information in  children with dyscalculia during a numerical stroop task.  In this task, the child is presented with two digits differing in physical size (e.g. 3 5 or 3 5).  The child determines as fast as he can which digit is physically larger.  When there is congruence between digit physical size and numerical value  (like this:   3 5), reaction time in typically developing children is faster than when digit size and value are incongruent.  Children with dyscalculia don't show this effect.  It's not clear whether the reason for this is that the underlying semantic representation of quantity is impaired in children with dyscalculia, or whether they have a deficit in the link between the semantic representations and their symbolic referents (i.e., Arabic digits).

·         Children with dyscalculia have slower reaction time to determine which of two digits (having the same physical size) has a larger numerical value.

·         Children with dyscalculia also have a qualitatively different “distance effect”.  The distance effect refers to the behavioral phenomenon that, as the distance between two numbers being compared decreases (e.g., 2 – 9 versus 7 – 9), reaction times and errors increase. In other words, numbers that are closer together are harder to compare than numbers that are further apart. The numerical distance effect (NDE) is taken by many researchers to reflect the integrity of the underlying representation of numerical magnitude along a “mental number line” with a larger NDE indicating a less-precise or more noisy representation. In support of this idea, the NDE decreases in size over the course of development, suggesting an ontogenetic increase in the precision of the number sense. Children with DD have been shown to have larger NDEs than typically developing children, in much the same way that typically developing children show a larger NDE relative to adults, suggesting that DD children may have a less-refined, immature representation of numerical magnitude compared to their typically developing peers. Recent evidence suggests that the magnitude of the developmental delay in the precision of this representation may be on the order of five years, with DD children showing numerical-representation precision equivalent to typically developing children five years their junior.

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.