Mathematical Development in Learning Diasbled Children

描述（由申请人提供）：拟议的研究将提供一个为期五年的纵向研究的发展算术程序能力和数字估计技能的儿童在数学学习障碍（MD）和正常的同龄人。 在解决简单算术问题的过程中，MD儿童1）依赖发育不成熟的策略，如手指计数; 2）经常犯计数错误; 3）使用不成熟的计数程序（例如，他们计算两个加数，而不是陈述一个加数的基数值，并计算等于另一个加数的次数）; 4）并且难以从长期记忆中检索基本事实。 研究者目前资助的研究重点是确定基本的认知系统，如工作记忆，这些算术缺陷的基础。 例如，他发现工作记忆与MD儿童对手指计数和计数错误的依赖之间存在密切关系，以及他们使用不成熟计数程序与计数概念知识之间的关系。 换句话说，MD儿童的工作记忆容量低于正常同龄人，这种工作记忆的群体差异部分解释了手指计数和计数错误的群体差异。 相反，计数原则知识的组差异与使用手指计数或计数错误无关，但解释了计数过程中使用的程序类型的组差异的一部分。 拟议中的研究将提供第一个纵向评估MD儿童的算术赤字和基本的认知系统之间的关系，并将扩大评估，包括更复杂的算术问题比大多数以前的研究。 拟议的研究也将是第一个评估MD儿童使用空间表征的能力（即，心理数字线）来进行数字估计，并评估表征形式如何随着正规教育而变化。 目标是记录MD儿童算术和数字估计能力的发展进程，并根据背景和意义部分中描述的理论原理识别认知系统（例如，工作记忆），这是MD儿童发展迟缓和这些能力缺陷的基础。

DESCRIPTION (provided by applicant): The proposed research will provide a five-year longitudinal study of the development of arithmetic-procedural competencies and number estimation skills in children with a learning disability in mathematics (MD) and normal peers. It is well established that during the solving of simple arithmetic problems MD children 1) rely on developmentally immature strategies, such as finger counting; 2) frequently commit counting errors; 3) use immature counting procedures (e.g., they count both addends rather than stating the cardinal value of one addend and counting-on a number of times equal to the value of the other addend); 4) and, have difficulties retrieving basic facts from long-term memory. The focus of the investigator's currently funded research is to identify the basic cognitive systems, such as working memory, that underlie these arithmetic deficits. He has found, for instance, a strong relation between working memory and MD children's reliance on finger counting and counting errors, and a relation between their use of immature counting procedures and knowledge of counting concepts. In other words, MD children have a lower working memory capacity than their normal peers, and this group difference in working memory explains part of the group differences in use of finger counting and counting errors. Group differences in knowledge of counting principles, in contrast, is unrelated to use of finger counting or counting errors, but explains part of the group difference in the type of procedure used during counting. The proposed research will provide the first longitudinal assessment of these relations among MD children's arithmetic deficits and underlying cognitive systems, and will expand the assessments to include more complex arithmetic problems than have been used in most previous studies. The proposed research will also be the first to assess MD children's ability to use spatial representations (i.e., a mental number line) to make number estimations, and assess how the form of the representation changes with formal schooling. The goals are to document the developmental progression of arithmetic and number estimation competencies in MD children, and to identify - based on the theoretical rationale described in the Background and Significance Section - the cognitive systems (e.g., working memory) that underlie MD children's developmental delays and deficits in these competencies.