Collaborative Research: Research on Learning and Teaching at the Physics-Mathematics Interface

该奖项支持一个项目，旨在调查本科生在学习物理的背景下，特别是在解决具有挑战性的高分物理问题时，对数学理解的发展。该项目团队将进行一项综合计划，包括研究、课程开发和评估主题，涵盖典型的二年级或三年级数学方法课程。主要目标是对学生资源进行研究，研究从数学到物理的转化过程以及这两个学科知识的共同进化，并开发一套适合教学、研究和评估材料的数学/物理任务，将具有挑战性的数学内容与高级物理核心课程涵盖的主题相结合。这个项目有可能影响到物理专业高年级的入门课程。课程材料将通过电子信息交换所和出版的研究共享，预计该项目将为国内和国际的教学--包括数学方法课程和随后使用数学的物理课程--提供信息。加州州立大学富勒顿分校的学生群体包括许多来自传统上在物理学领域代表性较低的群体的学生，因此该项目将为这些学生提供获取基于研究的材料的途径，并确保研究群体的多样性。这个跨学科项目将物理教育研究(PER)和本科数学教育研究(RUME)结合在一起。它将识别和解决学生在物理上的概念困难的努力与理解数学知识转移的努力结合在一起。这项工作的目标是物理专业的一门关键课程，即数学方法课程，这门课程在大多数院系的大二或大三开设。本课程通常旨在成为物理入门和微积分课程与学生在电学和磁学、经典力学和现代物理/量子力学等核心课程中遇到的更具挑战性的数学和物理之间的桥梁。该项目将加强课程的一部分的研究基础，到目前为止，这部分课程在很大程度上没有得到审查，并将涉及并加强几个相关领域的工作，包括其他高级课程的PER以及本科数学教育的广泛研究基础。这项拟议的工作将通过探讨学生理解的性质在多大程度上取决于学科背景，为迁移提供重要的见解。研究小组在PER和RUM方面有多年的经验，并在热物理和物理-数学接口的高级部门合作进行了成功的研究和课程开发项目。

This award supports a project to investigate the development of undergraduate students' mathematical understanding in the context of learning physics, particularly while solving challenging upper-division physics problems. The project team will conduct an integrated program of research, curriculum development, and assessment of topics covering a typical sophomore- or junior-level course in mathematical methods. The broad goals are to conduct research on student resources, study the process of transfer from mathematics to physics and the coevolution of knowledge in the two disciplines, and develop a set of Math / Physics tasks suitable for instruction, research, and assessment materials that will integrate challenging math content with topics covered in upper-division physics core courses. This project has the potential to impact a gateway course to the upper division for physics majors. Curricular materials will be shared through electronic clearinghouses and via published research and it is anticipated that the project will inform instruction - both of math methods courses and subsequent physics courses in which the mathematics is used - nationally and internationally. The student population at California State University Fullerton includes many students from groups traditionally underrepresented in physics, so this project will provide access to research-based materials for these students and also ensure a diverse research population. This interdisciplinary project brings together physics education research (PER) and research in undergraduate math education (RUME). It blends efforts at identifying and addressing student conceptual difficulties in physics with efforts toward understanding knowledge transfer in mathematics. The work targets a key course for physics majors, the mathematical methods course that is offered in most departments at the sophomore- or junior-level. This course is typically intended to be a bridge between introductory physics and calculus courses and the more challenging mathematics and physics encountered by students in the core courses of electricity and magnetism, classical mechanics, and modern physics / quantum mechanics. The project will strengthen the research base in a portion of the curriculum that has, to this point, largely gone unexamined, and will touch upon, and build upon, work in several related areas, including PER in other upper-division courses as well as the extensive research base in undergraduate mathematics education. This proposed work will provide significant insights into transfer by probing the extent to which the nature of student understanding depends upon the disciplinary context. The research team has many years' experience in PER and RUME and have collaborated on successful research and curriculum development projects at the upper division in thermal physics and the physics-mathematics interface.