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

这个跨学科项目汇集了物理教育研究（PER）和本科数学教育研究（RUME）。它结合了努力识别和解决学生在物理概念上的困难，努力理解学生在物理环境中使用和推理数学的方式。这项工作的目标是数学方法课程，这是物理专业的一门关键课程，因为它开始过渡到在物理问题中使用高等微积分，线性代数等，并作为通往物理学高年级的门户。该项目将加强研究基础的课程，这一点上，在很大程度上未经审查的一部分，并将触及，并建立在相关领域的工作，如对其他上师物理课程的研究，以及在本科数学教育的广泛研究基础。先前的数学成功是物理学成功的一个强有力的指标，数学课程和物理课程所教授的知识之间的差距可能是物理专业的一个重要的自然减员来源，可以通过这项工作来解决。该项目将调查学生的数学理解的学习和理解的背景下，中学和高中物理的发展。该团队将进行研究，课程开发和评估中发现的主题的综合计划-和高年级物理课程，特别关注大二或大三水平的数学方法课程。该项目的主要目标是：（a）研究学生在高年级物理背景下对数学的理解，重点是中级数学方法课程所涵盖的核心数学方法和推理;及（B）发展一个单元课程教材图书馆（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各样的上层，该奖项反映了NSF的法定使命，并被认为是值得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的支持。

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.