Dyscalculia – is it chronic? Findings from an Israeli long term study

  

Developmental dyscalculia: a prospective six-year follow-up

Ruth S Shalev, Orly Manor and  Varda Gross-Tsur.  

Developmental Medicine & Child Neurology 2005, 47: 121–125

http://onlinelibrary.wiley.com/doi/10.1111/j.1469-8749.2005.tb01100.x/pdf

Prof. Ruth Shalev, Prof. Varda Gross-Tsur  and Dr. Orly Manor followed, for six years, in a wide scope study, a group of children diagnosed with dyscalculia.

How were the children recruited?

In fourth grade, about 3000 children studying in Jerusalem schools took a group arithmetic test.  550 out of the 600 children whose scores were in the low 20% took, in fifth grade, an individually administered arithmetic test.  140 children out of this group scored in or below the 5^th percentile in the arithmetic test and had a WISC-R IQ score above 80.  This group was diagnosed with dyscalculia.  The reading and writing skills of these140 children were assessed,  and they were given other cognitive tests as well (which I'll not go into here for sake of brevity).

After three years, when they were in 8^th grade, 123 children out of this group took a math test and a reading test again.  The math test scores of 95% of the children were in the 25^th percentile or below.  47% of these children were re-diagnosed with dyscalculia, having scored in the 5^th percentile or below.

After three more years, when they were in 11^th grade, 104 of these children took math, reading and writing tests again and were compared to a control group.

What were the findings?

The authors emphasize the performance of the dyscalculia group, but I think it's worthwhile to look also at the control group's performance.

Let's begin with four examples:

·         51% of the 104 11^th grade students identified in 5^th grade with dyscalculia  were not able to solve 8x7, compared to 17% of the control group.

·         71% of the 104 students were not able to solve 24x37, compared to 27% of the control group.

·         49% of the 104 students were not able to solve 45/3 compared to 15% of the control group.

·         63% of the 104 students were not able to solve 5/9+2/9, compared to 17% of the control group.

And in general:

40% of the 104 students scored in or below the 5^th percentile, and were re- diagnosed  with dyscalculia.

The authors point out that the scores of most remaining 60% of children was still "low" – in and under the 25^th percentile.  Since every score which is higher than the 16^th percentile is within one standard deviation below the mean, we can regard such scores as normal performance (even if not high).   The authors don't indicate what percentage of the 104 children had a score higher than the 16^th percentile.

Which 5^th grade measures were related to dyscalculia in 11^th grade?

The 5^th grade general IQ score, calculated without the arithmetic subtest, was in average 6 points lower in the 104 student group than in the control group.  The 104 student group also had more inattention and writing difficulties than the control group.

Which 5^th grade measures were NOT related to dyscalculia in 11^th grade?

Reading, word learning, fluency tests, face recognition and performance in RCFT test were not related to dyscalculia in 11^th grade. 

Educational interventions, socioeconomic status, parental education, gender and family history of learning difficulties were not related to dyscalculia in 11^th grade.

What do we learn from all this?

Apparently, dyscalculia as defined here (a score in or below the 5^th percentile in an arithmetic test and an IQ score within normal limits) is chronic in 40% of the cases.  Had we defined dyscalculia as a score in or below the 16^th percentile in an arithmetic test and an IQ score within normal limits, probably a higher percentage of the 104 student group would have been diagnosed with chronic dyscalculia.

Nevertheless, there were some children in this study who made progress and moved from performance in or below the 5^th percentile in 5^th grade, to performance of above the 16^th percentile in 11^th grade.  It's unclear what caused this improvement.  This is a question worth studying.  We can also hope, that early assessment, much earlier than 5^th grade, maybe even in preschool, and preventive intervention,  will make it possible to prevent the development of dyscalculia in at least some of the children.

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.