Calculations, Word Problems, and Algebraic Cognition

描述(申请人提供)：数学学习障碍(MLD)影响到5%-9%的学龄人口，导致终身困难，给社会带来经济负担和公共卫生问题。计算和应用题是数学能力的关键方面，从小就开始，一直延续到成年。然而，早期的计算和应用题技能也可能是发展代数认知的重要先驱，而代数认知是数学能力的一个方面，对以后的学校成功至关重要。计算和应用题之间的主要区别是增加了需要儿童构建问题模型的语言信息。这似乎改变了任务的性质，因果比较和相关研究表明，这些领域潜在的能力可能不同。这增加了这样一种可能性，即这些领域的困难可能是不同的；可能需要不同的筛查措施来预测这些领域的困难；在一个领域进行的干预可能不会转移到另一个领域；这些领域的干预可能对学生学习代数的能力有不同的贡献。 在这个项目中，PI招募了一个大的、有代表性的二年级学生样本，他们收集关于儿童特征(人口统计、注意力、认知维度、数字、阅读)的数据。他们随机将二年级的教室分配给控制课、RTI计算课和RTI应用题教学。RTI教学指的是两个层次的研究性原则教学：课堂教学和必要时的小组辅导。PI跟踪学生到四年级。在二年级结束时，在每个RTI条件下，PI形成、比较，然后遵循三个小组：典型发展的学生、最初有反应的表现不佳的学生和最初没有反应的表现不佳的学生。PIS将调查(1)二年级RTI计算或应用题教学对计算、应用题和基本代数结果的短期和长期有效性，评估跨域迁移；(2)计算MLD(CA-MLD)和应用题MLD(WP-MLD)作为教学条件的函数以及在RTI条件下作为对研究性原则教学反应的函数的普及率和诊断稳定性；(3)与计算、应用题和代数技能的发展以及CA-MLD和WPMLD有关的儿童特征；(4)儿童特征，区分典型的发展中学生，最初对研究原则指导做出反应的低表现者，以及最初对研究原则指导没有反应的低表现者；(5)儿童特征如何与教学条件相互作用，影响短期和长期计算、应用题和代数结果。 PIs将评估MLD的患病率、儿童特征和数学特征，在消除了不充分的教学作为数学成绩低下的解释后。研究结果将对了解、识别、预防和治疗MLD具有重要意义。

DESCRIPTION (provided by applicant): Mathematics learning disabilities (MLD) affect 5-9% of the school-age population, leading to life-long difficulties that create financial burdens and a public health problem for society. Calculations and word problems are critical aspects of math competence beginning early and extending through adulthood. However, early calculations and word-problem skills may also be important precursors to the development of algebraic cognition, an aspect of math competence critical for later school success. The major distinction between calculations and word problems is the addition of linguistic information that requires children to construct a problem model. This seems to alter the nature of the task, and causal-comparative and correlational studies suggest that the abilities underlying these domains may differ. This raises the possibility that difficulty in these domains may be distinct; that different screening measures may be required to forecast difficulty in these domains; that intervention conducted in one domain may not transfer to the other; and that intervention in these domains may contribute differentially to students' ability to learn algebra. In this project, the PIs recruit a large, representative sample of 2nd graders for whom they collect data on child characteristics (demographics, attention, cognitive dimensions, numerosity, reading). They randomly assign 2nd-grade classrooms to control vs. RTI calculations instruction vs. RTI word-problem instruction. RTI instruction refers to 2 tiers of research-principled instruction: classroom instruction and, as needed, small group tutoring. The PIs follow students through grade 4. At the end of grade 2, in each RTI condition, the PIs form, compare, and then follow 3 subgroups: typically-developing students, initially low-performing students who respond, and initially low-performing students who do not respond. The PIs will investigate (1) the short- and long-term efficacy of 2nd-grade RTI calculations or word-problem instruction on calculation, word-problem, and basic algebraic outcomes, assessing transfer across domains; (2) the prevalence and diagnostic stability of calculations MLD (CA-MLD) and word-problem MLD (WP-MLD) as a function of instructional condition and, within RTI condition, as a function of response to research-principled instruction; (3) child characteristics associated with development of calculations, word-problem, and algebraic skill and with CA-MLD and WPMLD; (4) child characteristics that distinguish typically developing students, initially low-performers who respond to research-principled instruction, and initially low-performers who fail to respond to research-principled instruction; and (5) how child characteristics interact with instructional condition to affect short and long-term calculations, word problems, and algebra outcomes. The PIs will assess the prevalence, child characteristics, and math profiles of MLD after eliminating inadequate instruction as the explanation for low math performance. Findings will have important implications for understanding, identifying, preventing, and treating MLD.