Collaborative Research: Beyond Procedures: A Research-Based Approach to Teaching Mathematical Methods in Physics

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。它结合了识别和解决学生在物理概念上的困难，以及理解学生在物理环境中使用和推理数学的方式的努力。数学方法课程是物理专业的一门重点课程，它开始向使用高等微积分、线性代数等方法解决物理问题过渡，是通往物理高年级的门户。该项目将加强迄今为止大部分未被研究的部分课程的研究基础，并将触及和建立相关领域的工作，例如对其他高年级物理课程的研究，以及对本科数学教育的广泛研究基础。先前的数学成功是物理成功的一个强有力的指标，数学课程和物理课程之间的知识差距可能是物理专业人员流失的一个重要来源，可以通过这项工作来解决。该项目将探讨学生在学习和理解中高级物理的背景下对数学理解的发展。该团队将对中、高年级物理课程中的主题进行综合研究、课程开发和评估，特别关注二年级或三年级的数学方法课程。该项目的主要目标是：(a)研究高年级物理背景下学生对数学的理解，重点是中级数学方法课程中涵盖的核心数学方法和推理；(b)开发一个模块化课程材料库（例如，以学生为中心的教程和同伴指导任务），强调数学方法和推理，适用于各种高年级物理课程。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。

This interdisciplinary project brings together physics education research (PER) and research in undergraduate math education (RUME). It combines efforts at identifying and addressing student conceptual difficulties in physics with efforts toward understanding the ways students use and reason about mathematics in physics contexts. The work targets the mathematical methods course, a key course for physics majors as it begins the transition to using advanced calculus, linear algebra, etc. in physics problems and serves as a gateway to the upper-division in physics. 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 related areas, such as research on other upper division physics courses, as well as the extensive research base in undergraduate mathematics education. Prior mathematical success is a strong indicator of success in physics, and the gap of knowledge available between what is taught in mathematics courses and physics course may be a significant source of attrition for physics majors that can be addressed through this work. The project will investigate the development of students' mathematical understanding in the context of learning and understanding middle- and upper-division physics. The team will conduct an integrated program of research, curriculum development, and assessment of topics found in middle- and upper-division physics courses, with particular focus on the sophomore- or junior-level mathematical methods course. The primary objectives of the project are: (a) to conduct research on student understanding of mathematics in upper-division physics contexts, with an emphasis on the core mathematical methods and reasoning covered in an intermediate-level mathematical methods course; and (b) to develop a library of modular curricular materials (such as, student-centered tutorials and Peer Instruction tasks) emphasizing mathematical methods and reasoning suitable for use in a wide variety of upper-division physics courses.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.