Learning disability definition steps, and math learning disability

A previous post discussed learning disability definition steps.  In order to implement step 3 we have to be familiar with findings about links between poor math functioning and cognitive abilities.

A few research studies looked into these links in the general population.  Some studies used the standardization sample of the WJ3 test.  This test has two parts:  a cognitive part (WJ3COG) which measures CHC abilities and an achievement part (WJ3ACH) which measures reading and math.

Studies which looked into the correlations between children's scores in math tests (in the WJ3ACH) and cognitive abilities, found fluid ability, crystallized knowledge, working memory (a narrow ability within short term ability in WJ3) and processing speed to be related to math achievement.  There are also studies that found that long term storage and retrieval is related to math achievement.

This paper (available for free in the net):

PROCTOR,  B, E., FLOYD R. G. AND SHAVER, R. B. CATTELL-HORN-CARROLL BROAD COGNITIVE ABILITY PROFILES OF LOW MATH ACHIEVERS. Psychology in the Schools, Vol. 42(1), 2005

assessed CHC abilities of children who have poor achievement in math.  Children who had low scores (one or more standard deviation below the mean) on the math tests of the WJ3ACH (but had an average or higher score on the reading tests of the WJ3ACH) participated in the study.  This group was compared to a control group of children that had average or higher scores on the math and reading tests of the WJ3ACH), 

The math tests included two test clusters.  The  math calculation skills cluster (problems in the four math operations, and application of math rules like commutative rule).  The math reasoning cluster included tests of verbal math problems, application of rules and axioms, relations, and math concepts.

Math calculation skills:  there was no difference in CHC abilities between the low math calculation skills group  and the average achieving group!  None of the CHC abilities of the low math calculation skills group was significantly low compared to the population mean.  

Math reasoning:  the low math reasoning group had significantly lower scores in cognitive abilities, in general, compared to the control group.  This might point to   group differences in g.

The fluid ability of the low math reasoning group was significantly lower that the population mean.  The crystallized knowledge of the low math reasoning group was lower than that of the control group but was not lower than the population mean.

Short term memory, processing speed and long term memory were not found in this study to be related to math calculation and to math reasoning skills.

It seems to me, that in order to receive more significant results, maybe it would have been better to choose children whose math performance is lower than the 7-10^th percentile   (not the 16^th percentile).  This is the group which is usually chosen in dyscalculia studies.  In addition, as the authors also write, it would have been better to include children who perform poorly both in math and reading.  Many children with math problems also have difficulties with reading.  Because this study included children with math problems only, it might have not covered the entire range of  poor math achievers.

This study found no pattern of low cognitive abilities among children with low math calculation skills.  It's possible that many children who are referred to us with poor math achievement are not learning disabled in math.  We know that poor math achievement can be a result of exclusionary factors like lack of experience, low motivation, anxiety, bad teaching or inappropriate math books.  I believe that exclusionary factors influence math more than reading.  Addressing exclusionary factors may solve the math problems of some children in this group.