Mathematical Development in Learning Diasbled Children

学习障碍儿童的数学发展

基本信息

批准号：
8319524
负责人：
DAVID C GEARY
金额：
$ 39.44万
依托单位：
UNIVERSITY OF MISSOURI-COLUMBIA
依托单位国家：
美国
项目类别：
财政年份：
2008
资助国家：
美国
起止时间：
2008-08-01 至 2014-07-31
项目状态：
已结题

项目摘要

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.

拟议的研究将对算术过程的发展提供为期 5 年的纵向研究有数学学习障碍的儿童的能力和数字估计技能（MD）和正常同龄人。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，例如数手指； 2）经常提交计数错误； 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值并多次计数等于另一个加数的值]； 4）并且难以从长期记忆中检索基本事实。我们目前资助的重点研究的目的是确定这些算术背后的基本认知系统，例如工作记忆赤字。例如，我们发现工作记忆与 MD 儿童的记忆力之间存在密切关系。对手指计数的依赖和计数错误，以及它们使用不成熟计数之间的关系计数概念的程序和知识。换句话说，MD儿童的工作水平较低记忆能力高于正常同龄人，而这组工作记忆的差异部分解释了手指计数使用和计数错误的群体差异。群体知识差异相反，计数原理与手指计数的使用或计数错误无关，但解释了部分计数过程中使用的程序类型的组差异。拟议的研究将提供对 MD 儿童算术缺陷与底层认知系统，并将扩大评估范围以包括更复杂的算术问题比以前大多数研究中使用的问题都要多。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）来计算数字的能力估计，并评估代表性形式如何随正规学校教育而变化。目标是记录 MD 中算术和数字估计能力的发展进程儿童，并根据背景和意义中描述的理论原理进行识别部分 - MD 儿童发育迟缓的认知系统（例如工作记忆）以及这些能力的缺陷。