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We discuss an investigation of student difficulties with concepts related to the many-particle stationary state wavefunction for a system of non-interacting fermions or bosons in cases in which the many-particle stationary state wavefunction can be written as the product of the spatial and spin parts. 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 these concepts. Many students struggled to write a many-particle stationary state wavefunction consistent with the symmetrization requirements for the system, i.e., a completely antisymmetric wavefunction for a system of fermions or a completely symmetric wavefunction for a system of bosons. We discuss the common difficulties pertaining to these concepts that can be used as a guide to develop research-validated learning tools.

PERC SM 20

Investigating Student Understanding of the Many-Particle Wavefunction for a System of Identical Particles

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Join us in exploring emergent themes in PER as a scholarly endeavor and as a research community!  Since its inception, PER has served as a confluence of discipline, theory, research methodology, practice, and application.  How have these facets and the interplays among them been fruitful for physics education globally, regionally, locally, or otherwise?  And, how have our successes and interactions influenced the very nature of PER itself?
Following the lead of AAPT for the summer meeting, PERC 20/20 was virtual. Enjoy browsing the content.

Since its inception, PER has served as a confluence of discipline, theory, research methodology, practice, and application.  How have these facets and the interplays among them been fruitful for physics education globally, regionally, locally, or otherwise?  And, how have our successes and interactions influenced the very nature of PER itself?

Diagrams are ubiquitous in STEM. These diagrams vary from problem solving tools (like force diagrams) to ways to visualize information and concepts (like a cell diagram or ATP cycle) or understand an equation or data set (like graphs). I will describe the two theories - affordance and visual attention and I will present several cases from the literature and my own research showing how these theories are lenses for understanding student difficulties with diagrams. In addition, I will present data from a set of experiments my group has done that examines prior student knowledge and its effect on diagram use and visual attention within images of fluid flow through pipes. This data illustrates that, while current STEM diagrams have a lot of room for improvement as instructional tools, designing improvements for these diagrams will be complex.

Visual Attention and Affordance Lenses for: Understanding Student Diagram Use and Designing Improved Instruction of Fluid Dynamics in a Physics for Life Science Class

Instructional physics labs are critical junctions for many STEM majors to develop an understanding of experimentation in the sciences. Students can acquire useful experimental skills and grow their identities as scientists. However, many traditionally-instructed labs do not necessarily involve authentic physics experimentation features in their curricula. Recent research calls for a reformation in undergraduate labs that incorporate more student agency and choice in the learning processes. In our institution, we have adopted open-ended lab teaching in the introductory physics courses. By using reformed curricula that provide higher student agency, we analyzed approximately 100 students in the introductory-level lab courses to examine their views towards the open-ended physics labs. Between the start and the end of the semester, we found a statistically significant shift in students' perceptions about the autonomy given in lab activities. We also examined student views across gender and found no significant gender effect on students' agency views.

Sense of agency, gender, and students perception in open-ended physics labs

The Physics and Astronomy Department at a large, diverse, public university has recently implemented a pedagogy training course for graduate teaching assistants (GTAs). Using survey and interview testimonies from GTAs and other lab instructors over the course of three semesters, we identify potential areas of growth that can result from taking the pedagogy course. These areas include: developing a growth mindset and asset-based thinking, identifying the need for inclusive teaching practices, and implementing such practices. To help inform future pedagogy training courses, we have identified four personas that represent key archetypes of instructors that are likely to teach physics and astronomy labs. By cross-examining both sets of data, we have observed multiple areas that each persona is likely to develop as a result of training. We aim to use these results as evidence to further demonstrate the necessity for professional development for early career instructors.

Pedagogy training for the development of GTA mindsets and inclusive teaching practices

Covariational reasoning---reasoning about how changes in one quantity relate to changes in another quantity---has been examined extensively in mathematics education research. Little research has been done, however, on covariational reasoning in introductory physics contexts. We explore one aspect of covariational reasoning: ``goes like'' reasoning. ``Goes like'' reasoning refers to ways physicists relate two quantities through a simplified function. For example, physicists often say that ``the electric field goes like one over r squared.'' While this reasoning mode is used regularly by physicists and physics instructors, how students make sense of and use it remains unclear. We present evidence from reasoning inventory items which indicate that many students are sense making with tools from prior math instruction, that could be developed into expert ``goes like'' thinking with direct instruction. Recommendations for further work in characterizing student sense making as a foundation for future development of instruction are made.

Exploring student facility with "goes like" reasoning in introductory physics

Research shows a correlation between physics identity and retention of students. A physics identity is deeply related to perceived self-association with the field. Indicators of identity development are enthusiasm about, connection with members of, and recognition of personal contribution to the discipline. Traditionally, informal programs have been characterized as spaces where participants engage voluntarily and have a sense of agency and autonomy. Furthermore, there are varying practices, people and places involved. For these reasons it can be difficult to study informal spaces. Therefore an intricate framework is necessary that looks at identity as a social construct, highlighting the dependency on socio-cultural environments. We operationalize Wegners Community of Practice framework to study facilitators identity formation, adapting it to include the dynamics of identity development and facilitators positionality within the community. To demonstrate the use of the framework we present analysis of the identity development of facilitators of three informal physics programs.

A Community of Practice Approach to Identity Formation-

This study examines the relationship between students' online learning behavior and overall performance in an introductory physics course. We constructed four separate linear regression models, incorporating increasing levels of contextual information, and correlating students' pass-fail events in a sequence of online learning modules with their normalized total course score. We found that the best performing model is the one that includes contextual information on instructional condition, internal condition, and learning strategy. The model shows that while most students failed on a challenging learning module, those who continued to study were more likely to obtain higher total course scores, whereas those who resorted to guessing on the following modules tended to receive lower total scores. A possible interpretation of this observation is that both high and low performing students struggle with the same challenging content, but behavior after experiencing a setback is a characteristic difference between the two cohorts. Our results also demonstrate that considering more contextual information related to each online learning event can be an effective method to improve the quality of learning analytics, leading to more accurate and actionable recommendations for instructors. The results and implications of this study are immediately relevant amid the COVID-19 pandemic, as instructors now face the challenge of abruptly switching to online learning while motivating students to continue their learning effort. Results from our analyses have already been submitted as a journal paper and will be expanded as new data from the current semester become available.

A click is more than a click: exploring the relation between students’ online learning behavior and course performance by increasing contextual information in data analysis

Given the rising importance of computation in science, it is imperative that science undergraduates develop relevant computational skills. We discuss the design of a first year Computational Science course at an R1 institution in Ireland. This course is aimed as a first step on the path to developing students computational skills within the context of science, and requires an understanding of the computational needs from across the scientific disciplines. We present preliminary results of survey data collected from academics and researchers in the college of science, with the aim of understanding who engages in computational practices, what the nature of those practices is, and how they vary across the disciplines. The taxonomy of computational thinking of Weintrop et al. (2015) is used to contextualize those skills for each of the scientific disciplines. The results will inform the course design and the articulation of graduate attributes in relation to computational skills.

Computation for Science: Engaging University Science Students in Computational Thinking

Prior research has shown that physics students often think about experimental procedures and data analysis very differently from experts. One key framework for analyzing student thinking has found that student thinking is more point-like, putting emphasis on the results of a single experimental trial, whereas set-like thinking relies on the results of many trials. Recent work, however, has found that students rarely fall into one of these two extremes, which may be a limitation of how student thinking is evaluated. Measurements of student thinking have focused on probing students procedural knowledge by asking them, for example, what steps they might take next in an experiment. Two common refrains are to collect more data, or to improve the experiment and collect better data. In both of these cases, the underlying reasons behind student responses could be based in point-like or set-like thinking. In this study we use individual student interviews to investigate how advanced physics students believe the collection of more and better data will affect the results of a classical and a quantum mechanical experiment. The results inform future frameworks and assessments for characterizing students thinking between the extremes of point and set reasoning in both classical and quantum regimes.

Student evaluation of more or better experimental data in classical and quantum mechanics - Poster

Identity development is critical to student retention in physics degree programs. Historically, research on physics identity has been conducted at Predominately White Institutions and has largely ignoring the unique identity intersections experienced by Black, Indigenous, and women of color (BIWOC) and women who identify as Lesbian, Gay, Bisexual, Transgender, and Queer (LGBTQ+). In this study, we adopt the theory of identity as performance to better understand how multiply-marginalized students negotiate their multiple intersectional identities in their environments. We conducted semi-structured interviews with women who identify as racial minorities and/or as LGBTQ+ at two Hispanic Serving Institutions located in Central Texas. Our analysis focuses on the way students fragment or integrate their identities in the physics setting and how this may affect their view of themselves as physicists.

Understanding physics identity development through the identity performances of Black, Indigenous, and women of color and LGBTQ+ women in physics

We investigated how changing the physical classroom impacted graduate teaching assistant (GTA) and student behaviors in the recitation sections of an introductory algebra-based physics sequence. Using a modified version of the Laboratory Observation Protocol for Undergraduate STEM (LOPUS), we conducted 35 observations over two semesters for seven GTAs who taught in different styles of classrooms (i.e., active learning classrooms and traditional classrooms). We found that both GTAs and students changed behaviors in response to a change from an active learning classroom to a traditional classroom. GTAs were found to be less interactive with student groups and to lecture at the whiteboard more frequently. Correspondingly, student engagement appeared to decrease as students asked fewer questions during one-on-one interactions. We suggest administrators and departments consider the impact of changing to a traditional classroom when implementing student-centered instruction and emphasize how to use classroom space in GTA professional development.

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Investigating Student Understanding of the Many-Particle Wavefunction for a System of Identical Particles

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Visual Attention and Affordance Lenses for: Understanding Student Diagram Use and Designing Improved Instruction of Fluid Dynamics in a Physics for Life Science Class

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