Algebraic Learning and Cognition in Learning Disabled Students

该提案是为了响应EHR核心研究（ECR）计划公告NSF 15-509而提交的。在STEM教育的基础研究ECR计划提供资金在关键的研究领域是必不可少的，广泛的和持久的。EHR寻求有助于综合，建立和/或扩大以下重点领域研究基础的建议：STEM学习，STEM学习环境，STEM劳动力发展和扩大STEM参与。ECR计划的特点是强调积累强有力的证据，为以下努力提供信息：（a）理解，（B）建立解释理论，（c）建议干预措施（和创新），以解决在STEM兴趣，教育，学习和参与的持续挑战。高中代数是通往科学，技术，工程和数学（STEM）职业生涯的门户，并可能影响许多非STEM职业的就业能力和工资。高中代数学得不好或不及格的学生会影响就业前景，而那些不能培养出数学能力强的公民的国家可能会影响经济增长。人们对造成学生算术学习困难的因素了解很多，正在制定干预措施来解决这些困难。然而，人们对为什么有些学生在代数上很吃力却知之甚少。因此，该项目将从7年级到高中代数跟踪有风险的学生（包括阅读障碍的学生），并评估他们的先决知识（例如分数技能）、认知系统（例如，记忆），对数学的态度和反应（例如数学焦虑）以及他们在数学课堂上的注意力。对这些学生的综合评价将使我们能够确定影响学习代数不同方面的困难的因素，以及更普遍的代数失败风险。研究结果将为认知和动机对学生理解和学习代数的影响提供独特的科学见解，并确定对高危学生进行干预的领域。调查结果还将用于制定一项筛查措施，以便及早识别有风险的学生，并确定需要采取有针对性的干预措施的具体领域。这项措施将免费提供给美国各地感兴趣的学区。 该项目是对动态影响学生代数学习和认知的先决条件（例如分数），认知（例如工作记忆）和非认知（例如数学焦虑）因素的7至9年级纵向评估，重点关注数学学习障碍的学生。这项研究将提供有史以来最全面的评估代数能力的发展，并组织了一个综合模型的认知和非认知的影响，对学生的参与数学课堂和学习的程序和空间相关方面的代数。重点关注高中代数有可能不及格的学生，是因为对这些学生在数字和算术方面有缺陷的研究，这与以前的工作保持了连续性，并为评估他们在学习代数方面最可能遇到的困难提供了一个强有力的先验框架;具体地说，我们开发了新的方法来评估程序代数的不同方面，（例如，存储代数方程的结构）和空间相关代数（例如，识别常见功能如何映射到坐标空间），这将允许研究不同类型的学习缺陷，并确定更基本的认知能力，例如视觉空间工作记忆，可能是这些缺陷的基础。以前的认知研究在很大程度上忽略了非认知因素的贡献，如数学焦虑，对他们的学习或他们的学习困难如何改变态度和反应的数学（例如增加数学焦虑）。拟议的研究将解决这一重要的疏忽，并将这些非认知因素与教师评估的学生参与预代数和代数教室（和语言艺术教室作为对比）以及课堂参与如何影响程序和空间相关代数的学习。这项研究还将提供一个全面的分析认知和非认知的影响代数学习和认知更普遍，从而通知一般的教育实践。总之，拟议的研究将提供一个全面的模型，一般的学习代数学习和认知，并将提供一个全面的评估相关的赤字学习障碍的学生和学生的风险，高中代数失败。这项研究还将提供修订或新开发的程序和空间相关的代数技能的认知措施，应促进未来的认知科学和代数学习的教育研究。

This proposal was submitted in response to EHR Core Research (ECR) program announcement NSF 15-509. The ECR program of fundamental research in STEM education provides funding in critical research areas that are essential, broad and enduring. EHR seeks proposals that will help synthesize, build and/or expand research foundations in the following focal areas: STEM learning, STEM learning environments, STEM workforce development, and broadening participation in STEM. The ECR program is distinguished by its emphasis on the accumulation of robust evidence to inform efforts to (a) understand, (b) build theory to explain, and (c) suggest interventions (and innovations) to address persistent challenges in STEM interest, education, learning, and participation.High school algebra is the gateway to a career in science, technology, engineering, and mathematics (STEM), and can influence employability and wages in many non-STEM occupations. Students who struggle with or fail high school algebra have compromised occupational prospects, and nations that do not produce mathematically competent citizens may compromise their economic growth. Much is known about the factors that contribute to students' difficulties with arithmetic learning and interventions are being developed to address these difficulties. Little is known, however, about why some students struggle with algebra. Accordingly, the project will follow at risk students (including for example, those with dyslexia) from 7th grade through high school algebra and assess their prerequisite knowledge (e.g. fractions skills), cognitive systems (e.g., memory), attitudes and reactions to mathematics (e.g. math anxiety) and their attentiveness in math classrooms. The comprehensive evaluation of these students will allow us to identify the factors that influence difficulties in learning different aspects of algebra and risk of failing algebra more generally. The results will provide unique scientific insights into the cognitive and motivational influences on students' understanding and learning of algebra and identify areas for intervention with at-risk students. The results will also be used to develop a screening measure for the early identification of at-risk students and to identify specific areas for targeted intervention. The measure will be made freely available to interested school districts throughout the United States. The project is a 7th to 9th grade longitudinal assessment of the prerequisite (e.g. fractions), cognitive (e.g. working memory), and non-cognitive (e.g. math anxiety) factors that dynamically influence students' algebraic learning and cognition, with a focus on students with learning disabilities in mathematics. The study will provide the most comprehensive assessment of the development of algebra competence ever conducted and is organized by an integrative model of cognitive and non-cognitive influences on students' engagement in math classrooms and on the learning of procedural and spatial-related aspects of algebra. The focus on students at risk for failing high school algebra is informed by research on the number and arithmetic deficits of these students, providing continuity with previous work, and a strong a priori framework for assessing their most likely difficulties in learning algebra; specifically, we developed novel measures that assess different aspects of procedural algebra (e.g. memory for the structure of algebra equations) and spatial-related algebra (e.g. recognizing how common functions map to coordinate space) that will allow for the study of different types of learning deficits and a determination of how more basic cognitive abilities, such as visuospatial working memory, may underlie these deficits. Prior cognitive studies of at-risk students have largely ignored the contributions of non-cognitive factors, such as math anxiety, on their learning or how their learning difficulties change attitudes about and reactions to mathematics (e.g. increasing math anxiety). The proposed research will address this important oversight and integrate these non-cognitive factors with assessments of teacher-rated student engagement in pre-algebra and algebra classrooms (and language arts classrooms as a contrast) and how engagement in the classroom influences the learning of procedural and spatial-related algebra. The research will also provide a thorough analysis of cognitive and non-cognitive influences on algebraic learning and cognition more generally, and thus inform general educational practices. In all, the proposed research will provide a comprehensive model for the study algebraic learning and cognition generally, and will provide a comprehensive assessment of associated deficits of learning disabled students and students at risk for failing high school algebra. The research will also make available revised or newly developed cognitive measures of procedural and spatial-related algebra skills that should facilitate future cognitive science and educational studies of algebra learning.