A Study On Basic Numerical Cognitive Deficits In Young Students With Mathematic Disabilities

Mathematic disability,as an important sub-type of Learning disability,has been investigated broadly in recent years,including the standards of differential diagnosis, the special deficits,and the intrinsic cognitive mechanism of mathematic disabilities and so on.The general cognitive capacities of students with mathematic disability,such as working memory,spatial- visual ability and counting or calculating,have been extensively investigated in recent years,in which working memory has been considered as an essential cognition system for mathematical learning and two aspects of working memory deficits have been demonstrated for students with mathematic disability.It finds that those students with mathematic disability has limited capacity of working memory so that they can't maintain relative information as well as they can't restrain some irrelevant information in counting or calculating.The deficits of working memory, however,can't explain the difficulties of number reading and writing for those students. Along with the effect of cognition psychology and neuropsychological research on mathematic disability,the interest of research has been shifting from counting skills and accessing mathematical facts to numeric understanding and numerical processing.In this paper,24 children with mathematics disabilities are compared to 24 normally achieving peers in tasks for capacity of processing numerosity,accessing number magnitude from symbols,and representation of magnitude from symbolic number.An Arabic number Comparison task,which requires relating a symbol to its quantitative meaning,and a collection comparison task involving no symbolic processing are designed to assess the capacity of accessing number magnitude from symbols and the capacity of processing numerosity in this paper.If MD children have difficulty in accessing numerical semantic from symbols,they would be expected to be impaired when comparing Arabic digits not comparing collections.By contrast,if MD results from a failure to process numerosity as proposed by the defective number module hypothesis,MD children would be expected to be able to compare continuous quantities in the time-controlled condition of the collection comparison task but be impaired in tasks requiring them to process numerosities,that is,in the time-uncontrolled condition of the collection comparison and in the Arabic number comparison.Finally,MD might result from a defect in a central Magnitude system dedicated to the processing of discrete and continuous quantities(Walsh,2003).In this case,all comparison tasks should be equally affected in MD children.It finds that children with mathematics disabilities are only impaired when comparing Arabic digits not comparing collections under the control of respective speed of number distinguishing,and the difficulty of children with mathematics disabilities in accessing numerical semantic from symbols is also found in our dissociative experiment.However, a further investigation conducted in this paper finds that children with mathematics disabilities show obvious difficulty in representing magnitude from symbolic number, which may be the essential reason of series difficulties for children with mathematics disabilities in various numerical processes.At last,the semantic code characteristics of numbers and the relation between numerical magnitude comparisons and semantic code are studied.The results show that the comparison of numerical magnitudes made by both students with and without mathematics disabilities is influenced directly by their semantic representation of numbers.