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

该项目将设计一个基于学习级数的功能概念评估。学习进度描述了学生如何随着时间的推移发展对一个主题的理解。函数是代数学习和理解的一个重要概念。本项目中评估和学习进阶设计的目标是专门纳入关于代数课程中传统上服务不足和表现不佳的学生的学习结果。该项目将在制定评估任务时考虑初高中学生的社会和文化经验。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），该进度可以捕捉学生的表现范围，并适当地将他们置于不同的表现水平上。这项工作的重要贡献是开发了一个学习进程和相关的评估任务，这些任务说明了经常在数学方面得不到充分服务的学生的经历。探索研究K-12项目（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pre -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。学习进阶的发展将从比较和整合已有的学习进阶与函数学习的研究现状开始。该项目将通过经验恢复（寻找学习理论的理论水平重建）开发基于学习进展的学生功能知识评估。经验恢复是通过收集数据来重建所述学习进展的各个层次、阶段或顺序的过程。任务和任务模型的开发将包括测试计算机交付的、可用于人工和自动评分（取决于任务）的交互式任务和规则。项目反应理论的方法将被用来评估评估任务纳入学习进阶。

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.