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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.

PERC SM 21

Student difficulties identifying diagonal operators for degenerate perturbation theory

tutorials

degenerate perturbation theory

quantum mechanics

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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AAPT SM 21

poster

**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)

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

The Paradigms in Physics website provides a wide range of tested active engagement activities for upper division courses. Our team has been redesigning this site to add considerable "mortar" content between activities, to make the content more readily searchable, and to make more clear the connections between content. We have also been working to make it easier to keep the content fresh, and to give users a clearer perspective of how we use our own materials. This poster will introduce the features of the new site, and we will solicit audience feedback on how the site could better serve faculty seeking research-based content.

The new Paradigms in Physics Curriculum Website

To develop effective physics-based engineering curricula for K-6 classrooms, we need to understand the areas of support teachers need most, as well as their assumptions about their elementary students’ abilities to succeed in engineering activities. To understand teacher perceptions of the relationships between the teacher, the students, and the physics-based engineering content we analyzed semi-structured interviews with five 4–6th grade teachers who participated in a curricular module centered around the behavior of light as it passes through various materials. Teachers discussed how engineering modules led to more collaborative learning that was student-driven and created space for increased engagement for students who normally are reluctant to participate. On the other hand, teachers felt that materials required for the activities served as a barrier for implementation of the activities while the level of mathematics incorporated into the activities served as a barrier for younger students. These findings may inform future curriculum development to best support teachers in implementing physics-based engineering curricula in their classrooms.

Relations between Teacher, Student, and Content in Physics-based Engineering Activities

We developed a number of digital tools to support teaching quantum mechanics. The idea behind that is main concepts of quantum mechanics are non-intuitive to an uninitiated student due to the lack of daily experience with quantum mechanics: The basis of intuition is experience. Therefore, teaching quantum mechanics with a support of numerical experiments for all main topics of quantum mechanics appears to be essential for an efficient and quick learning process. The numerical experiments are prepared using PYTHON computer codes and a graphical interface. Students and instructors can use the graphical interface to change parameters of the suggested numerical experiments or they can download, modify and run the codes on their personal computers. Finally, a website, gathering overall numerical experiments, was designed. It can be used by universities and institutions in their different educations.

An experience-based course of quantum mechanics: Numerical experiments ranging from stepwise potentials to wave packet propagation and perturbation th

Modeling is an important skill in experimental physics and thus a learning outcome of many laboratory classes. One promising approach to help students develop modeling skills is to incorporate multi-week student-designed projects within lab courses. In order to assess the potential benefits of these projects towards students' modeling abilities, we analyze student coursework and interviews in three upper-division lab courses at different institutions. We present a descriptive analysis of student engagement with modeling in student-designed course projects. We find that the projects in our dataset vary widely with different degrees of modeling and different ways model construction and revision appear as parts of the projects. We additionally investigate how the student engagement depends on features of the projects and observe correlations between features of the projects and the ways the students construct models and enact revisions.

Student Engagement with Modeling in Multi-Week Student-Designed Lab Projects

In Spring 2020, we integrated four sessions with a mixed-reality simulator into GTA training. During each session, GTAs were provided opportunities to practice using different pedagogical skills while teaching a virtual class. While the first three sessions were held and facilitated in-person, the final session occurred remotely due to the COVID-19 pandemic. We decided to hold the final session remotely to balance health risks while closing the loop for GTAs’ professional development and the research project. Additionally, this remote style mimicked the remote teaching GTAs would do to complete the Spring 2020 semester and have continued through Summer 2021. In our study, we explored how two GTAs new to teaching the target courses used the pedagogical skills during their remote (final) session focused on using all previously presented skills. We found both GTAs used two out of three skills during their session. We also observed instances of group management with the same avatar-student group during both GTAs’ sessions. To contextualize their use of the skills during the remote session, we compared their skill count to the Fall 2019 cohort’s final in-person session average. Thus, we found one GTA’s use of both skills to be similar to that of Fall 2019 and the other GTA’s use of one skill to be similar to that of Fall 2019. From our findings, it is implied that remote sessions with the simulator supported GTAs’ practice of the target skills. However, we suggest further investigation is necessary, and we provide questions to guide future work.

GTAs' Use of Pedagogical Skills during a Remote Mixed-reality Simulator Training Session

The process and role of developing new scientific models experimentally is a cornerstone of physics -- and arguably an important learning objective of laboratory courses -- but research in physics education suggests that most current lab curricula do not effectively meet this objective. Many instructional practices leave students believing that in-class experiments exist to supplement conceptual learning and that the sole purpose of real-world experiments is to test theories. As a result, many students frame lab work as an exercise in knowledge confirmation, and expect that all physics that appears in the labs can be found with a Google search. This paper describes an instructional intervention using virtual reality to integrate the process of authentic scientific discovery into the lab curriculum. We developed labs in which students explore and develop mathematical models for unknown force laws between new kinds of particles that we invented. We find that this intervention produced significant shifts in students' epistemologies about experimental physics toward being more expertlike -- specifically regarding the central role experimentation plays for research physicists in making new discoveries and developing theories, and the role of laboratory experiments in teaching a nuanced and unique scientific way of knowing.

Developing expertlike epistemologies about physics empirical discovery using virtual reality

The need for physicists to work with others outside of the discipline of physics has become more prominent due to the growing necessity of interdisciplinary subjects and careers. While this need exists, there are few opportunities for physics students to gain collaborative experiences and skills. This study seeks to investigate the ways in which the interactions between students from different disciplines within a virtual environment affect the formation of a community of practice. We collected qualitative data in the form of interviews and written responses from a team of four undergraduate students, two of which study physics, and two that study graphic design. These data record the students' experiences as they work together to develop a public engagement project aimed at combining physics with art and design. Using a Communities of Practice framework to analyze these data, we are able to characterize how a community of practice formed and how the students developed shared goals along with group norms and relevant skills.

Interactions between physics and design students: developing a community of practice in a virtual, informal space

In a prior study, we investigated graduate student reasoning on a set of entropy-related conceptual tasks in a think-aloud format. The tasks involved entropy from microscopic and macroscopic perspectives, ideal gases, and a novel context involving a system with a dynamic string. In the current study, we conducted interviews with undergraduates using the same questionnaire. Most students were interviewed during the second half of their upper-division Thermal Physics course at the University of Colorado Boulder while two were upper-division undergraduates from other institutions with strong physics programs. We analyze the responses of the undergraduates to a section of the interview involving a novel system of a dynamic string waving in a bath of water and discuss the similarities and differences between the undergraduate and graduate students' responses. The responses from the two populations share many similarities with a few noteworthy exceptions. The undergraduates generally did not produce multiple macrostate classifications in the novel system, and some expressed a concern with what they perceived to be an infinite number of microstates---and thus infinite entropy---which was not a concern among the graduate students.

Comparing undergraduate and graduate student reasoning on a conceptual entropy questionnaire

Assessments provide opportunities for students to make sense of curriculum by connecting their existing ideas to generate new knowledge. As educators, we would like to be able to engage students in this process of sensemaking to help their learning. Through a case study, we present an approach to identifying assessment task features that facilitate sensemaking. The context involves an introductory student's attempt to a physics problem.  We analyze the student's transcript through the lens of sensemaking epistemic game and note the student's actions (`moves') while solving the problem. By analyzing these moves, we argue that the assessment features that played a role in the student's sensemaking can be identified. We find that the presence of a real-world context, engaging with multiple representations, and requiring a physical interpretation of a numerical answer to be instrumental in student's sensemaking. Identifying task features in this way can be instrumental in designing future assessment tasks that increase the chances students engage in sensemaking while working on them.

A methodology for identifying task features that facilitate sensemaking

Understanding the nature of causality is a key component of conceptual understanding in science. The hypothesis of this study is that certain types of causal inference are more challenging than others. If correct, particularly challenging causal inferences may provide a unified explanation for different conceptual difficulties across physics content areas. This paper investigates two aspects of a simple, qualitative force-and-motion problem that may impact the difficulty of the causal inferences required. The first aspect is the type of causal inference required: cause-to-effect (CE), effect-to-cause (EC), or cause-to-cause (CC). The second aspect is information about an alternative cause, which can be explicitly constant, explicitly unknown, or ambiguous. To test the impact of these two problem aspects on participants inference accuracy we conducted an on-line experiment in which participants were randomly assigned to one of thirty-six conditions that systematically varied these two aspects across conditions. The results show that (i) for explicitly constant alternative causes, CC inferences are more difficult than CE or EC inferences, (ii) inferences given explicitly unknown alternative cause information are more difficult than inferences given explicitly constant alternative causes, and (iii) ambiguous alternative cause information is treated as implying the alternative causes are explicitly constant, which is in line with conversational assumptions rather than a formal, logical perspective. These results hint at the potential fruitfulness of understanding the causal inferences underlying conceptual difficulties in physics.

Student difficulties identifying diagonal operators for degenerate perturbation theory

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The new Paradigms in Physics Curriculum Website

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Student difficulties with diagonal operators for degenerate perturbation theory

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