Mathematical Development in Learning Diasbled Children

这项拟议的研究将提供一项为期5年的算术程序发展的纵向研究 数学和数学学习障碍儿童的能力和数字估计技能 正常的同伴。众所周知，在解决简单算术问题(例如，6+7)时，MD 儿童1)依赖发育不成熟的策略，如数手指；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说明 一个加数的基数值和计数--等于另一个加数的值的次数]；4) 而且，从长期记忆中检索基本事实也有困难。我们目前资助的重点是 研究的目的是确定构成这些运算的基本认知系统，如工作记忆 赤字。例如，我们发现工作记忆和MD儿童之间存在着很强的联系 对手指计数和计数错误的依赖，以及它们对不成熟计数的使用之间的关系 具备计数概念的程序和知识。换句话说，MD儿童的工作率较低 记忆容量超过正常同龄人，这组工作记忆的差异解释了部分 不同组别使用指数和数错数有差异。群体对知识的差异 相比之下，计数原理与手指计数或计数错误的使用无关，但解释了一部分 统计过程中使用的程序类型的组别差异。拟议的研究将提供 对MD儿童算术缺陷和算术缺陷之间关系的首次纵向评估 基础认知系统，并将扩大评估范围，包括更复杂的算术 比以前大多数研究中使用的更多的问题。这项拟议的研究也将是第一个 评估MD儿童使用空间表征(即心理数字线)进行数字运算的能力 估计，并评估代表的形式如何随正规教育的变化而变化。我们的目标是 记录MD在算术和数字估计能力方面的发展进程 并对儿童认同的理论基础进行了阐述--背景和意义 部分--导致MD儿童发育迟缓的认知系统(如工作记忆) 以及这些能力方面的不足。

The proposed research will provide a 5-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 (e.g., 6+7) 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 our currently funded research is to identify the basic cognitive systems, such as working memory, that underlie these arithmetic deficits. We have 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 between 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.