Development and Empirical Recovery for a Learning Progression-Based Assessment of the Function Concept

该项目将设计一种基于学习进度的函数概念评估。学习进度描述了学生如何随着时间的推移对一个主题进行理解。函数是学习和理解代数的一个重要概念。这个项目的评估和学习进度设计的目标是具体地纳入关于传统上在代数课程中服务不足和表现不佳的学生的学习结果。该项目将包括在制定评估任务时考虑初中生的社会和文化经历。开发的资源应该通过创建一个学习进度来影响数学教学(特别是代数课程)，该学习进度捕捉到学生表现的范围，并适当地将他们置于不同的表现水平。这项工作的重要贡献是开发了一个学习进度和相关的评估任务，这些任务说明了学生在数学方面往往得不到帮助的经历。探索研究K-12计划(DRK-12)旨在通过研究和开发创新资源、模型和工具(RMT)，显著提高K-12学龄前学生和教师在科学、技术、工程和数学(STEM)方面的学习和教学。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，这些研究和开发工作为拟议的项目提供了理论和经验证明。学习进度的发展将从比较和整合现有的学习进展和当前的函数学习研究开始。这个项目将通过经验恢复(寻找学习理论的理论水平的重建)，基于学习进度来开发对学生函数知识的评估。经验恢复是通过收集数据来重建所述学习过程的不同水平、阶段或序列的过程。开发任务和任务模型将包括测试计算机交付的交互式任务和可用于人工评分和自动评分(视任务而定)的规则。项目反应理论方法将被用来评估评估任务与学习进度的结合程度。

The project will design an assessment based on learning progressions for the concept of function. A learning progression describes how students develop understanding of a topic over time. Function is a critical concept for algebra learning and understanding. The goal of the assessment and learning progression design in this project is to specifically incorporate findings about the learning of students traditionally under-served and under-performing in algebra courses. The project will include accounting for the social and cultural experiences of the middle and high school students when creating assessment tasks. The resources developed should impact mathematics instruction (especially for algebra courses) by creating a learning progression which captures the range of student performance and appropriately places them at distinct levels of performance. The important contribution of the work is the development of a learning progression and related assessment tasks that account for the experiences of students often under-served in mathematics. The Discovery Research K-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 (RMTs). 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.The learning progression development will begin by comparing and integrating existing learning progressions and current research on function learning. This project will develop an assessment of student knowledge of function based on learning progressions via empirical recovery (looking for the reconstruction of theoretical levels of the learning theory). Empirical recovery is the process through which data will be collected that reconstruct the various levels, stages, or sequences of said learning progression. The development of tasks and task models will include testing computer-delivered, interactive tasks and rubrics that can be used for human and automated scoring (depending on the task). Item response theory methods will be used to evaluate the assessment tasks' incorporation of the learning progression.