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

理解代数概念对于学生获得STEM途径是必要的。然而，最近在教育方面的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。尽管有事先的指导和干预，许多有数学困难的八年级学生在上代数课程时却没有获得成功所需的技能。代数中最基本也是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。该项目的主要目标是开发一种辅助干预，在学生学习(a)解释和计算表达式时有意地培养他们对变量的概念，(b)使用代数符号表示现实生活中的数学单词问题，(c)解决线性方程。重点是澄清关于变量的常见误解，这将贯穿整个课程。该项目产生的产品将为教师提供急需的资源，旨在帮助苦苦挣扎的学生为取得代数i的成功做好准备。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，以评估有希望的证据。干预将侧重于关键代数标准的指导，并通过与这些标准相一致的数学任务来支持学生发展变量概念。该项目以数学教育和数学干预文献的研究为基础，并结合了这两个学科的教学实践。项目活动包括开发干预材料、咨询小组的反馈、初步可行性测试实施后的教师反馈、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的意向治疗分析来评估影响。干预的影响和社会效度将通过学生表现分析和师生调查来评估。探索研究preK-12项目（DRK-12）旨在通过研究和开发创新资源、模型和工具，显著提高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计划中的项目建立在STEM教育的基础研究和先前的研究和开发工作的基础上，为拟议的项目提供了理论和实证依据。 该奖项反映了美国国家科学基金会的法定使命，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.