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As part of an effort to examine student understanding and use of mathematical representations in quantum mechanics, clinical interviews were conducted and online surveys were administered to students in an upper-division quantum mechanics course. In one interview task, developed to investigate student understanding of representations for probability concepts, students generated expressions in Dirac notation consistent with quantum mechanical formalism, with a number describing their expressions using geometric, vector-like ideas and concepts. Student responses to a survey intended to probe student understanding of Dirac notation inner products are also discussed, as similar vector-like reasoning was found here as well. The beginnings of a symbolic forms analysis of both data sources is discussed, and some preliminary symbol templates used for Dirac notation are proposed.

PERC SM 20

Student Use of Dirac Notation to Express Probability Concepts in Quantum Mechanics

notation

vectors

quantum mechanics

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?

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Students who take lab courses engage in active, collaborative learning that has the potential to teach scientific thinking skills while also stimulating students' interest in science and developing their self-efficacy. We describe different types of collaboration in terms of the mutuality of engagement they represent, and investigate how these different types of collaboration impacted student interest and self-efficacy in introductory physics labs. We surveyed college physics students about their beliefs and experiences regarding working with a lab partner. We find that when asked explicitly about what they valued in a lab partner, a majority of students noted that they wanted a ``fair split'' of the work. However, we find that students experienced improved physics interest and self-efficacy when they participated equally in all aspects of the lab, such as operating the apparatus and recording the data, which is a different form of mutuality of engagement. This form of participation disproportionately benefited women, a traditionally disadvantaged group in physics labs. Our findings suggest that students' physics interest and self-efficacy might be positively impacted in lab courses that are designed to ensure that students participate equally in all aspects of the lab work, as opposed to lab courses in which students split up their work inequitably.

What Makes a Good Physics Lab Partner?

Computational thinking has been emphasized as a main science and engineering practice in the Next Generation Science Standards. However, learning objectives outlined by the standards are written in vague terms that complicate the implementation and assessment of this topic in the classroom. This is especially problematic for high school teachers who have limited experience with computation and are looking to integrate computational modeling in their physics or physical science classrooms. In this study, we explore the variation in computational thinking practices that physics students demonstrate when working through in-class coding activities. Video data of multiple student groups were collected in one high school teachers physics and physical science classrooms. The data were analyzed to create a codebook that describes the different ways students engage in computational thinking practices. Ultimately, this work will help practitioners better understand how to identify these practices in a high school physics setting.

Video Analysis of Variation in Computational Thinking Practices in Physics (PERC)

What happens to aspiring engineers who do not pass their introductory mechanics class? At UIUC, approximately 11 percent of introductory mechanics engineering students earn a D, F, or W. Just 31 percent of these students go on to earn an engineering degree, compared with the 87 percent of students who pass the course on their first attempt. While most students who perform poorly in their introductory physics class choose a non-engineering major or leave the university altogether, there is a unique subset of initially struggling students who choose to persist in an engineering major. We interviewed engineering seniors in this group to learn about their experiences as engineering students who overcame an initial setback. On this poster, we will share big-picture outcomes for students who retake this fundamental course as well as insights into the difficulties some students face and what resources may help them succeed.

When the Gatekeeper Says No: Mechanics Students' Resilience and Success

Undergraduate students are a critical resource for university-community partnerships designed to provide enriching learning opportunities for students who have limited exposure to Science, Technology, Engineering, and Math (STEM). University physics departments who offer outreach programs are often dependent upon undergraduate facilitators to run successfully; however, there is minimal research on this population relative to the youth populations for which outreach programs are designed. Our study investigates the experiences and perspectives of women and non-binary undergraduates who supported The STEMinist Program, an afterschool program designed to engage girls and non-binary youth (ages 9-18) in discussions and explorations with female-identifying scientists and engineers. Analysis of interviews from 13 undergraduate facilitators suggest that educational programs designed for youth may be just as valuable for undergraduate facilitators. These findings can be used to inform physics outreach program development and strengthen the potential benefits of program participation for undergraduates as well as youth participants.

Supporting Undergraduate Facilitators to Strengthen Physics Outreach Programs

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 degree-granting institutions. However, the effect of those transfer courses on the time that it takes students to graduate (time-to-degree) is currently not well understood. We have investigated how incoming transfer courses impact students' time-to-degree by defining three independent groups of transfer students: (1) those entering with college level transfer courses, (2) those with only AP level transfer courses, and (3) those without any transfer credit. The time-to-degree has been shown to be statistically different for each of these groups, with students who enter with college level transfer courses graduating the earliest. We have explored differences in time-to-degree for various demographic information (e.g. gender, race/ethnicity). Cohen's d results suggest disproportionate negative effects on the time-to-degree for women and students of color, in particular. These results provide implications toward how universities advertise graduation in four years, as well as other impacts toward student financial aid such as four-year scholarships.

Analyzing Time-to-Degree for Transfer Students at a Large Midwestern University

Planetariums visits limit the amount of time and agency people have to explore content relevant to their interest and identities as compared to other informal learning environments. We developed the Dome+ model to guide extending engagement beyond planetariums based on the design principles of identity, interest, and choice. We do this through web resources, social media, and hands-on activities centered on a planetarium show. We present research into the development and implementation of the Dome+ model as it applies to the Big Astronomy Project. This is a multi-institutional effort to share the stories of the people and places that make astronomy happen. The work presented focuses on the implementation of the model during production of the planetarium show. We interviewed team members key in the production of the show and find themes that differ based on project role. We also discuss practical challenges in implementing the Dome+ model.

Extending Learning Beyond the Planetarium with the Dome+ Model

Students often struggle to decompose a vector, especially when calculating the vector components of an object on an inclined plane. In this study, we designed a vector survey in the context of physics and implemented it in an undergraduate university. Our preliminary studies indicate the students' learning difficulties in vector decompositions on incline problems. The analysis of the students' responses shows that placing a vector at the position with geometric convenience instead of the center of mass can help them identify angles and calculate vector components more accurately. Based on our current study, we observe an improvement in performance, when students are provided with the formula of vector components along with the definition of the angle in the formula sheet.

Decomposition of forces on inclined planes

We report results from a study designed to identify links between undergraduate students' views about experimental physics and their engagement in multiweek projects in lab courses. Using surveys and interviews, we explored whether students perceived particular classroom activities to be features of experimental physics practice. We focused on 18 activities, including maintaining lab notebooks, fabricating parts, and asking others for help. Interviewees identified activities related to project execution as intrinsic to experimental physics practice based on high prevalence of those activities in interviewees' own projects. Fabrication-oriented activities were identified as conditional features of experimentation based on differences between projects, which interviewees attributed to variations in project resources. Interpersonal activities were also viewed as conditional features of experimentation, dependent upon one's status as novice or expert. Our findings suggest that students' views on experimental physics are shaped by firsthand experiences of their own projects and secondhand experiences of those of others.

Student perceptions of laboratory classroom activities and experimental physics practice

In 2019, Living Physics Portal (livingphysicsportal.org) project leaders (NSF grant 1624185) in collaboration with the American Association of Physics Teachers (AAPT) administered a survey to physics faculty designed to document current pedagogical beliefs and practices in teaching introductory physics for life sciences (IPLS) courses. 383 instructors (out of 762 respondents) reported that they had, in the past two years, taught an IPLS course. We analyzed the beliefs of these instructors about the effectiveness of their IPLS courses in engaging students and examined predictors of differences in their perceived course effectiveness. We found that nearly half viewed their course as moderately effective in engaging students and there was considerable variability in respondents answers. Hierarchical regression analyses identified teaching experience, perceptions of belongingness to a community of practice, and self-reported teaching strategies as independent predictors of perceived course effectiveness. We will discuss our findings and their implications for the IPLS community.

Teaching Experience, Community of Practice Beliefs, and Teaching Strategies Predict IPLS Course Effectiveness

To address the longstanding problem of underrepresentation of women in physics, we developed two classroom interventions that encourage womens future physics intentions. In testing these lessons in a larger study, we found variance in gains between student sub-populations across several teachers. This prompted the current mixed methods analysis to follow up on potential contextual factors leading to these differences, including social and economic setting of the school and student population characteristics, as well as teacher-level effects. We drew upon multiple sources of data collected from both teachers and students including teacher interviews, teacher and student open response surveys, and student artifacts from the lessons. In our preliminary analysis, we found that the broader social and economic environments did not appear to affect how students received the lessons; however, individual teacher implementation of the lessons did.

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What Makes a Good Physics Lab Partner?

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Improving student understanding of Dirac notation by using analogical reasoning in the context of a three-dimensional vector space - Poster