Calculations, Word Problems, and Algebraic Cognition

计算、应用题和代数认知

• 批准号: 7736801
• 负责人: Lynn S Fuchs
• 金额: $ 57.81万
• 依托单位: VANDERBILT UNIVERSITY
• 依托单位国家: 美国
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-12-01 至 2013-11-30
• 项目状态: 已结题
• 来源: https://reporter.nih.gov/project-details/7736801
• 关键词: Accounting; Achievement; Address; Adult; Affect; Age; Algorithms; Area; Attention; Characteristics; Child; Cognition; Cognitive; Competence; Concept Formation; Data; Development; Diagnostic; Digit structure; Dimensions; Educational Intervention; Employment; Equation; Foundations; General Population; Goals; Incidence; Income; Individual; Instruction; Intelligence; Intervention; Investigation; Jordan; Language; Learning; Learning Disabilities; Life; Linguistics; Literature; Long-Term Effects; Masks; Mathematics; Measures; Methods; Modeling; Nature; Outcome; Performance; Poverty; Prevalence; Problem Solving; Procedures; Process; Productivity; Public Health; Randomized; Reading; Reading Disabilities; Recruitment Activity; Relative (related person); Research; Research Design; Risk; Route; Sampling; Scheme; School-Age Population; Schools; Screening procedure; Short-Term Memory; Societies; Socioeconomic Status; Solid; Solutions; Source; Specificity; Students; Subgroup; Text; Time; Work; Workplace; base; comparative; demographics; design; disability; effective intervention; experience; follow-up; improved; indexing; innovation; insight; neglect; phonology; prevent; processing speed; programs; research study; response; skills; success; teacher

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.

描述（由申请人提供）：数学学习障碍（MLD）影响5-9%的学龄人口，导致终身困难，造成经济负担和社会公共卫生问题。计算和应用题是数学能力的重要方面，从早期开始，一直延伸到成年。然而，早期的计算和文字问题技能也可能是代数认知发展的重要先驱，这是数学能力的一个方面，对以后的学校成功至关重要。计算题和应用题的主要区别在于增加了语言信息，需要孩子构建一个问题模型。这似乎改变了任务的性质，并且cabinet比较和相关性研究表明，这些领域的能力可能不同。这就提出了以下可能性：这些领域的困难可能是不同的;可能需要不同的筛选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的样本，他们收集儿童特征（人口统计学，注意力，认知维度，数字，阅读）的数据。他们随机分配二年级教室控制与RTI计算指令与RTI单词问题指令。RTI教学是指两个层次的研究原则的教学：课堂教学和，根据需要，小组辅导。PI跟随学生通过4年级。在2年级结束时，在每个RTI条件下，PI形成，比较，然后遵循3个亚组：典型发展的学生，最初表现不佳的学生谁回应，最初表现不佳的学生谁不回应。PI将调查（1）二年级RTI计算或文字问题教学对计算、文字问题和基本代数结果的短期和长期有效性，评估跨领域的迁移;（2）计算MLD（CA-MLD）和应用题MLD（WP-MLD）的患病率和诊断稳定性与教学条件的关系;（3）与计算、应用题和代数技能发展以及与CA-MLD和WPMLD相关的儿童特征;（4）区分典型发展中学生的儿童特征，最初表现不佳的学生对以研究为原则的教学作出反应，和最初的低性能谁未能响应研究原则的指令;和（5）如何儿童的特点与教学条件相互作用，影响短期和长期的计算，文字问题，代数的结果。 PI将评估MLD的患病率、儿童特征和数学概况，排除不适当的教学作为数学成绩低的解释。研究结果将对理解，识别，预防和治疗MLD具有重要意义。