Developing Concept of Variable Among Students With Mathematics Difficulties in Preparation for Algebra 1

代数概念的理解是必要的学生获得STEM途径。然而，最近的教育努力未能改善许多学生的代数成绩，特别是那些有学习障碍和数学持续困难的学生。尽管事先指导和干预，许多8年级的学生数学困难到达代数课程没有成功所需的技能。在代数中取得成功的最基本和最关键的思想之一是代数变量的概念。理解变量对于学习代数和其他数学领域（如函数和几何）至关重要，这两者都是代数课程的基础。这个项目的主要目标是开发一种补充干预，有意识地发展学生的变量概念，因为他们学习（a）解释和评估表达式，（B）使用代数符号表示现实生活中的数学应用问题，（c）解决线性方程。一个重点是澄清有关变量的常见误解将交织在整个程序。该项目产生的产品将为教师提供急需的资源，这些资源旨在帮助苦苦挣扎的学生在代数I中取得成功。干预措施的开发将遵循三个阶段的迭代过程：（1）设计和开发，（2）试点研究，（3）小规模随机对照试验，以评估承诺的证据。干预将集中在关键代数标准的教学，并通过符合这些标准的数学任务支持学生发展变量的概念。该项目是基于数学教育和数学干预文献的研究，并结合了这两个学科的教学实践。项目活动包括编制干预材料、咨询小组的反馈意见、在初步可行性试验期间实施后教师的反馈意见、试点研究和随机对照试验。大约70名学生将参与小规模随机对照试验，并将使用部分嵌套设计的两级模型进行意向治疗分析来评估影响。通过对学生表现的分析以及教师和学生的调查，将评估干预措施的影响和社会有效性。发现研究preK-12计划（DRK-12）旨在通过研究和开发创新资源、模型和工具，显着提高preK-12学生和教师对科学、技术、工程和数学（STEM）的学习和教学。DRK-12项目中的项目建立在STEM教育的基础研究以及为拟议项目提供理论和经验依据的先前研究和开发工作的基础上。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Understanding of algebra concepts is necessary for students to gain access to STEM pathways. However, recent efforts in education have failed to improve algebra outcomes for many students, especially those with learning disabilities and persistent difficulties in mathematics. Despite prior instruction and intervention, many 8th grade students with mathematics difficulties arrive to algebra coursework without the skills needed to be successful. One of the most fundamental—and critical—ideas for success in algebra is the concept of an algebraic variable. Understanding variables is critical for learning algebra and other mathematics domains such as functions and geometry, both of which are foundational to algebra coursework. The primary goal of this project is to develop a supplemental intervention that intentionally develops students' concept of variable as they learn to (a) interpret and evaluate expressions, (b) represent real-life mathematical word problems using algebraic notation, and (c) solve linear equations. A focus on clarifying common misconceptions about variables will be interwoven throughout the program. Products generated from this project will provide teachers with much-needed resources that are designed to prepare struggling students for success in Algebra I.Development of the intervention will follow an iterative process across three phases: (1) design and development, (2) a pilot study, and (3) a small-scale randomized control trial to evaluate evidence of promise. The intervention will focus instruction on key algebra standards and support students in their development of the concept of variable via mathematical tasks that align to these standards. The project is grounded in research from the mathematics education and mathematics intervention literatures and combines instructional practices from both disciplines. Project activities include development of intervention materials, feedback from an advisory panel, teacher feedback following implementation during an initial feasibility test, a pilot study, and a randomized controlled trial. Approximately 70 students will be involved in the small-scale randomized controlled trial and impacts will be assessed using an intent-to-treat analysis with a two-level model for a partially nested design. The impacts and social validity of the intervention will be assessed through analyses of student performance and teacher and student surveys.The Discovery Research preK-12 program (DRK-12) seeks to significantly enhance the learning and teaching of science, technology, engineering and mathematics (STEM) by preK-12 students and teachers, through research and development of innovative resources, models and tools. Projects in the DRK-12 program build on fundamental research in STEM education and prior research and development efforts that provide theoretical and empirical justification for proposed projects. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.