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We discuss an investigation of student difficulties with the representation in which a Hermitian operator corresponding to a physical observable (e.g., the Hamiltonian operator corresponding to energy) is diagonal in the context of degenerate perturbation theory involving the Zeeman effect in the hydrogen atom. 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, knowledge of which can be useful for developing research-validated learning tools.

AAPT SM 21

Student difficulties identifying diagonal operators for degenerate perturbation theory

tutorials

degenerate perturbation theory

quantum mechanics

**Making Physics More Inclusive and Eliminating Exclusionary Practices in Physics**

As a gateway discipline to STEM majors and careers, physics plays a central role in deciding who does, and who doesn't, get to discover and pursue scientific careers. Technical and scientific professionals are rewarded with economic privilege and status which affords them both social and cultural power. Therefore, social justice will be realized only when the opportunity, and the choice, to excel in physics is open to all students. The culture and practices of the physics classroom reflect the culture of physics at large, which raises the question of how our professional physics communities can embrace, rather than inadvertently repel, a diverse group of academics that can help improve physics culture.  To this end, the 2021 Physics Education Research Conference will focus on defining inclusive spaces and practices. Additionally, we will explore strategies for eliminating exclusionary practices in our classrooms, research spaces, and professional organizations. We call on the community to propose sessions that will drive conversations related to these initiatives throughout PERC 2021.

Please download the full program [here. ](https://drive.google.com/file/d/1TRMC_SYJ3PUqXyP7sskA7LRSA8ow0eRE/view?usp=sharing)

PERC SM 21

August 4, 2021 - August 5, 2021 in a Virtual Conference Format

Making Physics More Inclusive and Eliminating Exclusionary Practices in Physics

technical paper

Join AAPT and Physics Educators worldwide in developing and strengthening your professional connections by attending the 2021 AAPT Virtual Summer Meeting. AAPT meetings are a great way to reflect on your teaching, recommit to best practices and re-energize your career with new research, products, and techniques.

Listen to internationally known plenary speakers, attend sessions, workshops, and special activities. Attending the virtual summer meeting is an excellent opportunity to share your expertise and learn from and network with leaders in the field.

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Earning a bachelor's degree is expensive and time-consuming. Many undergraduate students pursue Advanced Placement (AP) courses in high school or transfer coursework from other degree-granting institutions. However, the effect of those transfer courses on the time it takes students to graduate (time-to-degree) is currently not well understood. In this work, we investigated how incoming transfer courses impact students’ time-to-degree. To do so, we explored how well a logistic regression model would predict whether a student graduated before or after 8 semesters, 10 semesters, and 12 semesters. When discerning time-to-degree, there are several other features that were also considered in addition to transfer status: students’ demographic information such as race/ethnicity, gender, first-generation status, and their academic background preparation as measured by their high school GPA and math placement scores. Here, we will discuss the findings of our model as well as the effects of data imputation on our results.

Investigating Impact of Transfer Credits on Time-to-Degree using Regression Models

Transfer students’ and two-year college (TYC) students’ experiences are understudied, but we know they can face unique challenges after transferring and can miss some of the positive aspects of their TYCs at their receiving institutions. We use narrative analysis or narrative inquiry to tell the story of one transfer student from a TYC to a four-year college (FYC) named Nicole. Nicole has social anxiety, but thrived in her relationships with peers and professors while at her TYC. Then she faced difficulties finding study groups and a sense of community belonging at her receiving institution. Pulling from a variety of data sources, including observational field notes, written journal reflections, and semi-structured interviews, we will describe the supporting characters or lack thereof and the aspects of the different settings that contributed to Nicole’s differing experiences at the two institutions.

Narrative Analysis of Two-Year College Transfer Student’s Experiences

Physics majors need context to improve their experiences with physics as a discipline and prepare them for a variety of impactful career paths. Yet, the majority of context-based physics learning comes from internships and research experiences that are not always available to all students. As part of the APS PIPELINE Network and Physics for Tomorrow initiatives, we examined students’ experiences with context-rich physics through internships, co-ops, and undergraduate research. We compared these with students’ perception of physics as it relates to their future career goals and career-relevant skills. Responses from 149 physics majors at 12 institutions were analyzed using descriptive quantitative methods for multiple select questions and emergent thematic qualitative approaches for open-ended questions. We offer considerations for the importance of context-rich physics experiences, as well as how to integrate these into lecture and lab coursework, so that context-based learning can become more accessible to all physics majors.

Preparing students for impactful careers through context-rich physics learning

In this talk, we qualitatively analyze physics majors’ identity development as they transfer from a community college to a four-year university. Students in the study attend a large, public four-year university in which a significant fraction of undergraduate physics majors are transfer students. Research participants had previously enrolled in a required 1-credit introduction to the physics major course designed to cultivate community and identity, as well as foster a broad set of physics-related skills. In one-on-one interviews, students discussed their academic and personal experiences before, during, and after their transition from community college to a four-year university. In this talk, we will discuss how their academic and personal experiences as well as their interactions with physics community members shaped their identity development as physics students. We then consider implications for building institutional supports for physics transfer students.

Research on Identity Development Among Physics Transfer Students

We analyse a session where high school students in a 2-day science camp were asked to explain the workings of a mercury barometer. The session was designed to provide students with opportunities to participate in the knowledge construction process. The pedagogy was inspired by literature on modelling practices and sense making in physics. Given that traditional classrooms in India (and elsewhere) are often dominated by the lecture format, it is important to investigate the tensions that arise when the students from a traditional physics classroom are asked to
engage with modeling and sensemaking. We analysed the video recording of the session to unpack these tensions and characterised them under four broad categories vis a vis: Instructor versus student agency; Answer-making versus sense-making; Qualitative reasoning versus mathematisation; and Substance versus process ontology. Our analysis shows how the flow of conversation was guided by the push and pull of these entangled tensions.

Unpacking tensions in a pedagogical transition from lectures to modelling

We report on an investigation in which we compare the conceptual performance of upper-level undergraduates and graduate students, who worked on two different validated Quantum Interactive Learning Tutorials (QuILTs). One of the QuILTs incorporates mathematical reasoning while focusing on helping students develop a good conceptual understanding of quantum optics using a Mach-Zehnder Interferometer with single photons and polarizers. Performance of students who engaged with this “hybrid” (integrated conceptual and quantitative) QuILT is compared with those who engaged with a conceptual QuILT focusing on the same topics without quantitative tools. Both QuILTs use a guided inquiry-based approach to learning and are based on research on student difficulties in learning these challenging concepts as well as a cognitive task analysis from an expert perspective. We find that the posttest performance on conceptual questions of physics graduate students who engaged with the hybrid QuILT was generally better than those who engaged with the conceptual QuILT. For undergraduate students, the results were mixed.

Impact of mathematical rigor on students’ understanding of quantum optics

The Conceptual Survey of Electricity and Magnetism (CSEM) is a multiple-choice survey that contains a variety of electricity and magnetism concepts at the level of introductory physics used to help inform instructors of student mastery of those concepts. Prior studies suggest that many concepts on the survey are challenging for introductory physics students and the average student scores after traditional instruction are low. The research presented here compares the performance of students in introductory, upper-level, and graduate-level physics courses on five CSEM questions to understand the cross-sectional evolution of student understanding of these concepts from the introductory to upper-level to graduate-level. We discuss five CSEM questions that remain challenging for many upper-level and graduate students.

Evolution in student conceptual understanding of electricity and magnetism

The solving of physics problems is often an important component of introductory physics courses. For many students, approaching a physics problem, organizing their thoughts, and reaching a solution is a novel skill which needs to be taught and mastered. Rubrics can be powerful tools to guide student development of new skills. Here we will discuss the development of problem solving rubric we have implemented in our large enrollment introductory physics course. We will discuss the particular challenges and advantages of using these rubrics in an online course. Finally, we will then discuss the extent to which these rubrics were successful in changing student behavior over the course of two semesters of instruction.

Rubrics to Teach Problem-Solving Strategies in Large Enrollment Online Courses

Selection and application of an appropriate equation is a key step in instructional problem-solving strategies. But what if one cannot exactly recall the relevant equation? We are currently investigating how coherence between physical and mathematical reasoning opens multiple solution pathways for qualitative physics problems. In one-on-one interviews, community college students, 4-year college undergraduates, and graduate students solved qualitative introductory-level E&M questions. Analysis of 18 interviews showed that while many students had initial difficulty in recalling a relevant equation, they demonstrated strategies for making progress. We present two cases from the data corpus. One interviewee was unsure whether the time constant for an RC circuit is RC or 1/(RC) and sought coherence with qualitative reasoning to determine the correct expression. Another student switched to reasoning qualitatively from a physical model after noting that they could not recall a relevant equation. These examples show how mathematical and physical reasoning is opportunistically incorporated in students’ problem solving.

Seeking coherence and switching reasoning after forgetting an equation

The entanglement between physical and mathematical reasoning can be exploited for problem solving, making physical/mathematical coherence seeking a desirable learning goal. We endeavor to enrich the empirical knowledge of students’ coherent physical/mathematical reasoning through a video analysis of problem solving. Drawing from a corpus of 18 interviews with students solving qualitative E&M problems, we discuss a case study of a student who undertakes multiple contradicting lines of reasoning and ultimately reconciles them. We discuss the types of coherent reasoning that they recruit and the central role of physical/mathematical coherence seeking in their problem solving and learning.

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Student difficulties identifying diagonal operators for degenerate perturbation theory

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Investigating Impact of Transfer Credits on Time-to-Degree using Regression Models

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Student difficulties identifying diagonal operators for degenerate perturbation theory