Abstract: Developmental dyscalculia (DD) is a special category of learning disability, with almost 3%-6% school-age children affected in the world. DD children have two basic features: (1) the development of number processing and calculating lags heavily behind normal achievement (NA) children; (2) other cognitive abilities, such as intelligence, verbal ability and working memory, develop well. DD has negative effects on children not only in learning but also in daily life. Children who suffer DD are frustrated a lot when learning mathematics, leading to their negative attitude to mathematics. The relationship between children and their teachers or parents also can be hurt awfully. In addition, DD will influence children’s career in the long run. The cognitive mechanism of DD has sparked some controversy among researchers. The defective number module hypothesis proposed that humans were born with a “number module” and used an internal “numerosity code” that represented and manipulated numerosities exactly. The children with DD might suffer from a “defective number module” which led to a range of difficulties in learning arithmetic. However, some different voices could also be heard. For example, Roussell found that the Arabic number processing was badly impaired among DD children. At the same time, the non-symbolic number processing kept intact for DD children. Thus, Roussell proposed the access deficit hypothesis, and he insisted that DD children had difficulty in accessing number magnitude from symbols rather than in processing numerosity per se. In the current study, we used a number comparison paradigm to explore the cognitive mechanism of DD. Nineteen second graders with DD and twenty six NA second graders completed the experiments. In the experiment 1, participants were asked to compare numerical magnitude under three different number formats conditions (non-symbolic, symbolic , mixture of non-symbolic and symbolic). The results showed that symbolic rather than non-symbolic numerical processing was impaired in DD children. Furthermore, the transformation of symbolic and non-symbolic number magnitude was also terribly impaired. In the experiment 2, Chinese characters were used instead of dots materials. We designed this to verify whether 1) Chinese characters processing was damaged among DD children; and 2) the impaired transformation existed in two different symbolic number magnitude. However, results indicated that a deficit was found in Chinese characters processing and there were no evidences supporting the transformation impairment between Chinese characters and Arabic numbers in DD Children. Therefore, the impaired transformation existed only in symbolic and non-symbolic numbers. Our results have important implication in both theory and practice for studying on DD. Theoretically, the results favor the impaired access deficit hypothesis, based on impaired symbolic number processing ability and intact non-symbolic processing. Meanwhile, for the first time the current study finds that the transformation ability between symbolic and non-symbolic number magnitude of DD children is weakened. Practically, our findings would be beneficial for interventions of DD children. The transformation ability is so important that the curriculum designed for DD children should focus not only on symbolic number processing, but also on how to establish strong connection between non-symbolic and symbolic magnitude.

Key words: Developmental dyscalculia, numerical magnitude processing, the impaired access deficit, the transformation of symbol and non-symbol number magnitude

摘要： 本研究拟考察发展性计算障碍儿童的认知缺陷成因。实验1要求被试在三种形式(点/点，数/数，点/数)下进行数量比较，实验2仅将点集替换为汉字数字词。结果表明障碍组和正常组在数/数、点/数和汉字/汉字比较任务上的成绩存在显著差异，而在点/点和汉字/汉字比较上没有差异。据此推论，计算障碍儿童符号加工能力受到损伤，符号与非符号数量转换能力存在缺陷，但非符号加工能力和不同符号间数量转换没有缺陷，支持语义提取缺陷假设。

关键词: 发展性计算障碍, 数量比较, 语义提取缺陷, 符号与非符号数量转换