Any difficulties in learning or understanding these skills may result in mathematical learning difficulties. It is imperative that we gather information about arithmetic skills in order to perpetuate our understanding of the root cause of dyscalculia. This can be done with the help of the two main neuropsychological models of numerical abilities which are outlined below.
McCloskey, Caramazza, and Basili (1985) have divided arithmetic skills into three main groups: (1) comprehension of number concepts; (2) production of numbers; and (3) calculation. (from Shalev and Gross-Tsur)
These skills call for the ability to process verbal and Arabic representations of numbers. Further it requires an understanding of the processed numbers coupled with the ability to transcode numbers from one representation to another. Calculation refers to arithmetic competency in terms of strategies used to solve problems, a keen grasp of the concepts involved and a decent knowledge of the counting principles.
The "triple-code model" w...
sychological as well as an anatomical basis and its premise is the three basic elements of verbal, visual, and magnitude representation in acquiring arithmetic skills. According to this model verbal processing is done in the left hemisphere of the brain whereas magnitude estimations and visual representations are bilaterally localized.
Any deficit or failure in acquiring these skills is bound to manifest itself as a mathematical disability. Normal children use a particular or judicious mix of strategies in using these skills to solve arithmetic problems but studies have shown that "MD children tend to use immature problem-solving strategies" (Geary 1993, 348)
MATHEMATICAL DISABILITIES FROM A COGNITIVE PERSPECTIVE
MD children presumably have difficulties in the retrieval of basic arithmetic facts from their memories and in the computation or procedures involved in arithmetic processes. According to Geary, "lower order deficits of MD children potentially reside in five component skills: procedural, memory retrieval, conceptual, working memory, and speed of processing." The first two are functional skills and they are important determinants of mathematical performance whereas the latter three skills are underlying components which may influence the output. Studies have shown that MD children are, "characterized by a high frequency of computational and memory-retrieval errors" (Geary 1993, 348) This indicates that these children are not fully cognizant of the tenets of mathematics (poor conception) which is further accentuated by a retrieval deficit memory. Moreover their counting speed is slow and this mars problem- solving ability as the working memory falters and finally decays. MD children are unaware of the errors they make and hence there is repetition of errors.