Math Practice for Physics: Building Math Fluency in an Introductory Undergraduate Physics Context

在NSF改善本科生STEM教育计划：教育和人力资源(IUSE：EHR)的支持下，该项目旨在通过提高物理入门课程中的数学流利性来服务于国家利益。目标是使用基于研究的原则，以及认知心理学和教育研究的方法，来开发、实施和评估一套称为数学实践的实践作业。数学练习基于俄亥俄州立大学现有的在线平台Essential Skills。这个项目的初始范围是提高关于如何解决学生在数学技能方面的困难的知识，这些技能是在物理入门课程中取得成功所必需的。这项初步工作将使目标学校的15,000名学生参加物理入门课程。然而，由于这种干预既低成本，又易于实施，它可能会提高全国每年招收的50万物理班级学生的成绩和留存率。此外，尽管数学练习应用程序旨在帮助所有学生，但它很可能特别有助于准备不足的学生在物理课程中取得成功并继续学习。这一建议的干预措施的设计是基于成熟的研究性学习方法，包括间隔和交错掌握练习，并立即反馈。这种方法有望自动化，从而减少在物理中应用基本数学程序所涉及的认知负担。减少认知负荷很重要，因为物理学往往有复杂的、感知上丰富的符号和背景。实验设计将包括控制条件和“A/B测试”，以探索最佳实践任务和形式，例如比较替代解决方案以及通用和背景丰富的形式实践的组合。评估将包括经过验证的数学工具、课程表现和动机调查量表。这些评估将被用来反复改进材料，调查学生困难的领域，并调查潜在的重要学生水平的表现和动机因素。因此，实践任务和作业设计将具有较强的实证和理论基础。此外，这个项目期望在物理入门的背景下，通过基本的数学技能和这些困难背后的机制来促进对学生困难的了解。此外，它有望促进对几种特定类型的经验性和理论性有前景的数学实践任务的有效性的了解。最后，该项目预计将确定学生的特征和动机与这种干预相互作用的程度。因此，它可能会提供有关困难机制的信息，并为生产性干预提供更多途径。鉴于数学在所有STEM学科中都是必不可少的，从这个项目中学到的信息可能会扩展到所有STEM教育。例如，学生在物理导论中使用符号记法的困难也可能在STEM的其他领域遇到。NSF IUSE：EHR计划支持研究和开发项目，以提高所有学生的STEM教育的有效性。通过参与的学生学习路径，该计划支持有前景的实践和工具的创建、探索和实施。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

With support from the NSF Improving Undergraduate STEM Education Program: Education and Human Resources (IUSE: EHR), this project aims to serve the national interest by improving math fluency in introductory physics courses. The goal is to use research-based principles, together with methods from cognitive psychology and education research, to develop, implement, and assess a set of practice assignments called Math Practice. Math Practice is based on Essential Skills, an existing online platform used at Ohio State University. The initial scope of this project is to advance knowledge about how to address students' difficulties with math skills that are needed for success in introductory physics courses. This initial work will involve the 15,000 students in introductory physics courses at the target schools. However, because this intervention is both low-cost and logistically simple to implement, it could potentially improve performance and retention of the 500,000 students enrolled each year in physics classes nationwide. Furthermore, although the Math Practice application will be designed to help all students, it is likely to especially help underprepared students succeed and continue in physics courses. The design of this proposed intervention is based on well-established research-based learning methods, including spaced and interleaved mastery practice with immediate feedback. This method is expected to automate and thereby reduce the cognitive load involved in applying basic math procedures in physics. Reducing cognitive load is important since physics tends to have complex, perceptually rich notation and contexts. The experimental design will include control conditions and "A/B testing" to explore optimal practice tasks and formats, such as comparison of alternative solutions and combinations of generic and context-rich format practice. The assessments will include validated math instruments, course performance, and motivational survey scales. These assessments will be used for iterative improvement of materials, investigation of areas of student difficulty, and investigation of potentially important student-level factors of performance and motivation. As a result, the practice tasks and assignment design will have a strong empirical and theoretical basis. Further, this project is expected to advance knowledge about student difficulties with essential math skills and the mechanisms underlying these difficulties, in an introductory physics context. In addition, it is expected to advance knowledge of the effectiveness of several specific kinds of empirically and theoretically promising math practice tasks. Finally, the project is expected to determine the extent to which student characteristics and motivations interact with this intervention. Thus, it will potentially provide information about the mechanisms of the difficulties and additional avenues for productive interventions. Given that math is essential in all STEM disciplines, the information learned in this project could potentially extend to all of STEM education. For example, the difficulties students have with symbolic notation in introductory physics are also likely to be encountered in other areas of STEM. The NSF IUSE: EHR Program supports research and development projects to improve the effectiveness of STEM education for all students. Through the Engaged Student Learning track, the program supports the creation, exploration, and implementation of promising practices and tools.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.