We investigate upper-division student difficulties with direct integration in multiple contexts involving the calculation of a potential from a continuous distribution (e.g., mass, charge, or current). Integration is a tool that has been historically studied at several different points in the curriculum including introductory and upper-division levels. We build off of these prior studies and contribute additional data around student difficulties with multi-variable integration at two new points in the curriculum: middle-division classical mechanics, and upper-division magnetostatics. To facilitate comparisons across prior studies as well as the current work, we utilize an analytical framework that focuses on how students activate, construct, execute, and reflect on mathematical tools during physics problem solving (i.e., the ACER framework). Using a mixed-methods approach involving coded exam solutions and student problem-solving interviews, we identify and compare students' difficulties in these two different context and relate them to what has been found previously in other levels and contexts. We find that some of the observed student difficulties were persistent accross all three contexts (e.g., identifying integration as the appropriate tool, and expressing the difference vector), while other difficulties seemed to fade as students advanced through the curriculum (e.g., expressing differential line, area, and volume elements). We also identified new difficulties that appear in different contexts (e.g., interpreting and expressing the current density).
Upper-division physics students spend much of their time solving problems. In addition to their basic skills and background, their epistemic framing can form an important part of their ability to learn physics from these problems. Encouraging students to move toward productive framing may help them solve problems. Thus, an instructor should understand the specifics of how student have framed a problem and understand how her interaction with the students will impact that framing. In this study we investigate epistemic framing of students in problem solving situations where math is applied to ph…
Performance of Graduate Students at Identifying Introductory Physics Students' Difficulties Related to Kinematics Graphs
运动学图形理解测试（英语：Test of Understanding Graphs in Kinetics，缩写：TUG-K）是一个由Beichner开发的多项选择测试，用于评估学生对运动学图形的理解。TUG-K上的许多项目都有很强的干扰项选择，这与入门学生在运动学图形方面的常见困难相对应。如果教师不了解这些常见的困难，并在教学设计中考虑到这些困难，教学就不可能有效。我们评估一年级物理研究生的表现，在确定入门学生的共同困难有关的运动学图。特别是，对于TUG-K上的每个项目，研究生被要求识别他们认为最常被物理学入门学生选择的错误答案，如果他们在相关概念的指导后不知道正确答案。我们使用Beichner原始论文中的入门学生数据来评估研究生对入门学生困难的了解。此外，我们选择了四个问题上的TUG-K上的研究生的表现是最差的一个更详细的分析，其中包括有声思维访谈。我们目前的结果，可以部分解释这些问题上的研究生表现不佳，也通知教学专业发展课程。
We discuss an investigation of student difficulties with the corrections to the energy spectrum of the hydrogen atom for the intermediate field Zeeman effect using the degenerate perturbation theory. The investigation was carried out in advanced quantum mechanics courses by administering free-response and multiple-choice questions and conducting individual interviews with students. We find that students share many common difficulties related to relevant physics concepts. In particular, students often struggled with mathematical sense-making in this context of quantum mechanics which requires i…
We discuss an investigation of student difficulties with the corrections to the energy spectrum of the hydrogen atom for the strong and weak field Zeeman effects using degenerate perturbation theory. This investigation was carried out in advanced quantum mechanics courses by administering written free-response and multiple-choice questions and conducting individual interviews with students. We discuss the common student difficulties related to these concepts which can be used as a guide for creating learning tools to help students develop a functional understanding of concepts involving the co…
We investigate student comfort with the material in an upper-division spins-first quantum mechanics course. Pre-lecture surveys probing students' comfort were administered weekly, in which students assigned themselves a "discomfort level" on a scale of 0--10 and provided a written explanation for their choice. The weekly class-wide average discomfort level was effectively constant over the semester, suggesting that the class found no single unit especially jarring nor especially easy. Student written responses were coded according to their reported source of discomfort---math, math-physics con…
Exploring Pedagogical Content Knowledge of Teaching Assistants Using the Test of Understanding Graphs in Kinematics
运动学图形理解测验（英语：Test of Understanding Graphs in Kinetics，缩写：TUG-K）是Beichner在1994年开发的一个多项选择测验，用来评估学生对运动学图形的理解。TUG-K上的许多项目都有很强的干扰项选择，这与学生在运动学图形方面的常见困难相对应。如果教师不了解物理导论学生的共同困难，并在教学设计中明确考虑到这些困难，那么教学就不可能是有效的。我们评估的教学内容的知识，一年级的物理研究生参加了教学助理（TA）培训课程的主题所涵盖的TUG-K。特别是，对于TUG-K上的每个项目，研究生被要求识别他们认为最常被物理学入门学生选择的错误答案，如果他们在相关概念的指导后不知道正确答案。我们使用的研究生数据和数据从Beichner的原始文件介绍物理学的学生，以评估相关的教学内容的知识（PCK）的研究生。我们发现，虽然研究生，平均而言，表现优于随机猜测，在确定介绍学生的困难上的TUG-K，他们没有确定许多常见的困难，介绍学生有图形的运动学，即使在传统的教学。此外，我们发现，研究生的能力，以确定的困难，介绍学生是依赖于上下文。
Students' difficulties in quantum mechanics may be the result of unproductive framing rather than a fundamental inability to solve the problems or misconceptions about physics content. Using the theoretical lens of epistemological framing, we applied previously developed frames to seek an underlying structure to the long lists of published difficulties that span many topics in quantum mechanics. Mapping descriptions of published difficulties into errors in epistemological framing and resource use, we analyzed descriptions of students' problem solving to find their frames, and compared students…
We investigated the difficulties that physics students in upper-level undergraduate quantum mechanics and graduate students after quantum and statistical mechanics core courses have with the Fermi energy, the Fermi-Dirac distribution and total electronic energy of a free electron gas after they had learned relevant concepts in their respective courses. These difficulties were probed by administering written conceptual and quantitative questions to undergraduate students and asking some undergraduate and graduate students to answer those questions while thinking aloud in one-on-one individual i…
Challenges in addressing student difficulties with measurement uncertainty of two-state quantum systems using a multiple-choice question sequence in online and in-person classes
Challenges in addressing student difficulties with time-development of two-state quantum systems using a multiple-choice question sequence in virtual and in-person classes
