Number development and developmental dyscalculia - Von Aster et. al. - 2007 - Article

Researchers more and more agree on the fact that the underpinnings of developmental dyscalculia (DD) are a genetically determined disorder of number sense. Number sense is the ability to internally and nonverbally represent and manipulate numbers. To develop this skill (usually during elementary school) you also need additional cognitive components such as number symbolization (language), visual imagery and working memory. Therefore it’s possible that children only developed DD because of genetic factors, but comorbidities such as ADHD, dyslexia and language delay are also very common (two-thirds of the children with DD are comorbid). fMRI studies show that the parietal and frontal regions are under activated in children with DD.

The four step developmental model

The four step developmental model shows the different pathways presented in DD. The core-system representation of numerical magnitude, cardinality (step 1) provides the meaning of ‘number’, a precondition to acquiring linguistic (step 2) and Arabic number symbols (step 3, digits), while a growing working memory enables neuroplastic development of an expanding mental number line during school years (step 4).

If there are any problems developing step 1, the names of numbers can be phonologically learned by memory, but may only function as words without meaning. Many children with DD have a neuropsychological profile comparable with Developmental Right Hemisphere Syndrome and Non-Verbal Learning Disability Syndrome, which both show deficits in visual-spatial and psychomotor functioning.

If primary core-system abilities are preserved but language development is perturbed, the association between nonverbal numerical properties (***) and their linguistic symbolization (three) cannot be established in an age-appropriate manner such as developed in step 2. This could result in deficits in counting routines, arithmetic, counting strategies and number fact storage.

Many children experience problems with the Arabic notation system in preschool, because of the transcoding rules and its place value syntax (which number comes first: twenty-five becomes 25, but with fünf-und-zwanzig, first a five and then a 2, this gets very confusing (step 3).

When children start to identify the ordinal positions of numbers, with reference to the neighboring numbers around them, the mental number line (step 4) comes into play. This seems to work differently in every individual and could be a more complex structure than the theoretical straight line.

Developmental dyscalculia

The normal acquisition of numeracy skills is impaired in the specific learning disorder d evelopmental dyscalculia (DD). This disorder is brain-based, but environmental deprivation and poor teaching also play a role in its development. For the development of numerical concepts in preschool children, it is very important to have intact counting skills. Therefore children with specific language impairment may demonstrate impairments requiring mathematical skills.

The SNARC-effect reflects the observation that people are faster to make a judgment about a number if the hand they use to respond is congruous with the size of the number in question: the left hand quicker for smaller numbers and the right hand faster for larger numbers. This shows that a mental number line is spacially oriented from left (small numbers) to right (larger numbers). The SNARC-effect develops around the third grade. Boys and girls develop the SNARC-effect at the same time, but girls seem not as prepared as girls to use their newly acquired skill. The suggested reason for this phenomenon seems to be that female prefer language dependent strategies, while males prefer visual-spatial and functional-motor strategies.

DD also has a differential diagnosis. Even in a total absence of any basic neuropsychological dysfunction or comorbid disorder, DD may occur as a result of early dysfunctional learning experiences.

When needed, psychotherapy, pharmacotherapy and spelling and reading training should be instituted to treat DD and comorbid disorders. There should be an individual design to train the enhance of calculation abilities and number processing. This should take the profile of individual strengths and weaknesses into account.