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Dirac notation is a compact and elegant notation taught to students in advanced quantum mechanics courses. However, students struggle to master Dirac notation and have difficulty translating between the Dirac notation and representations of the same quantum mechanical entity in different situations. We discuss an investigation of student difficulties with Dirac notation in the context of a three-dimensional vector space and the development, validation and evaluation of a Quantum Interactive Learning Tutorial (QuILT) that uses analogical reasoning to improve student understanding of this notation. The QuILT uses analogical reasoning and builds on students prior knowledge of three-dimensional vectors in the familiar context of introductory mechanics to help students build a coherent understanding of Dirac notation before transitioning to the quantum mechanical context. We summarize the development and validation of the QuILT and findings from the in-class evaluation.

PERC SM 20

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

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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?

Measurement uncertainty and experimental error are important concepts taught in undergraduate physics laboratories. Although student ideas about error and uncertainty in introductory classical mechanics lab experiments have been studied extensively, there is relatively limited research on student thinking about experimental measurement uncertainty in quantum mechanics. In this work, we used semi-structured interviews to study advanced physics students interpretations of fictitious data distributions from two common undergraduate laboratory experiments in quantum mechanics and one in classical mechanics. To analyze these interpretations, we developed a coding scheme that classifies student responses based on what factors they believe create uncertainty and differentiates between different types of uncertainty (e.g. imprecision, inaccuracy). We found that participants in our study expressed a variety of ideas about measurement uncertainty that varied with the context (classical/quantum) and the type of uncertainty.

Student reasoning about sources of experimental measurement uncertainty in quantum versus classical mechanics

We are continuing a nationwide effort to develop a systemic understanding of the landscape of informal physics using an organizational theory perspective. We have collected surveys and interviews with informal physics program facilitators, but this information is only from the perspective of the faculty or physics student leaders and does not tell us about the social dynamics within each program. Thus, to complement these data, we need to observe informal physics events as they occur. In this paper, we will discuss our strategy for visits to program sites to observe social interactions between program participants as well as programmatic details in action. We report on an initial site visit to a physics open house event, where we took field-notes and conducted interviews with participating personnel members. Here, we compare the types of data we are able to collect from site visits and interviews/surveys with lead program facilitators.

Perspectives on informal programs: How site visits can help us learn more

Interpretation of student behavior in online learning platforms based on log data is complicated by not being able to directly observe the learner. In this paper, we attempt to identify data patterns that signal either guessing on assessment problems or disengaging from the task for students while working through homework modules in an introductory physics class by contrasting data from the general student population with those who completed homework modules in controlled, observed environments. We found that abnormally short problem solving attempts that were previously modeled as a single guessing or answer copying behavior actually consisted of two different types of "guessing" behavior: rapid and strategic guessing. Both types were associated with lower levels of self-confidence, but had different distribution among proctored and unproctored student populations. More importantly, the fraction of rapid guessing increased significantly after campus closure due to COVID-19, but the fraction of strategic guessing remained constant.

A tale of two guessing strategies: interpreting the time students spend solving problems through online log data

Computer simulations for physics labs may be combined with hands-on lab equipment to boost student understanding and make labs more accessible. Hybrid labs of HTML5-based computer simulations and hands-on lab equipment for topics in mechanics were investigated in a large, algebra-based, studio physics course for life science students at a private, research-intensive institution. Computer simulations were combined with hands-on equipment and compared to traditional hands-on labs alone using an A/B testing protocol. Learning outcomes were measured for the specific topic of momentum conservation by comparing student scores on post-lab exercises, related quiz and exam questions, and a subset of questions on the Energy and Momentum Conceptual Survey (EMCS) administered before and after instruction for both groups. We present our findings of this study and discuss the larger implications of the use of simulations in physics education.

Student learning outcomes with hybrid computer simulations and hands-on labs (PERC)

With ongoing calls to engage students in science through physics lab instruction, understanding how students frame lab environments informs instructional approaches that promote students' productive engagement. To deliberately identify students' frames in a new lab environment, two students who were previously in experimentation physics labs were placed together during the first activity of a content-reinforcement lab. The students initially framed the activity as exploring the phenomena and developing investigations, similar to the previous semester. However, their frames rapidly shifted to filling out a worksheet as they watched their peers finishing the lab. These results demonstrate the speed at which students' frames can dramatically shift as they enter a new lab environment. As goals for lab instruction transition, attending to students frames throughout their undergraduate lab experiences will be vital for promoting positive learning experiences.

“Let’s just pretend”: Students' shifts in frames during a content-reinforcement lab

We have developed the Physics Inventory of Quantitative Literacy (PIQL) as a tool to measure students' quantitative literacy in the context of introductory physics topics. We present the results from various quantitative analyses used to establish the validity of both the individual items and the PIQL as a whole. We show how examining the results from classical test theory analyses, factor analysis, and item response curves informed decisions regarding the inclusion, removal, or modification of items. We also discuss how the choice to include multiple-choice/multiple-response items has informed both our choices for analyses and the interpretations of their results. We are confident that the most recent version of the PIQL is a valid and reliable instrument for measuring students' physics quantitative literacy in calculus-based introductory physics courses at our primary research site. More data are needed to establish its validity for use at other institutions and in other courses.

Toward a valid instrument for measuring physics quantitative literacy

Societal stereotypes and biases pertaining to who belongs in physics and who can excel in physics can impact motivational beliefs, e.g., of women and racial and ethnic minority students in physics courses. This study investigates how the learning environment predicts male and female students motivational beliefs including physics self-efficacy, interest, and identity at the end of year long (spanning two-semester) algebra-based introductory physics courses. These were courses at a large university in the US taken primarily by biological science majors many of whom are interested in health professions. Although women are not underrepresented in these physics courses, societal stereotypes and biases internalized by female students over their lifetime can still impact their motivational beliefs about physics. Our findings show gender gap in motivational beliefs favoring men. These findings can be useful to provide support and create an equitable and inclusive learning environment to help all students excel in these courses.

How the learning environment predicts male and female students motivational beliefs in algebra-based introductory physics

It is a given that not everyone who starts their Ph.D. in physics will complete it. That being said, there are people who have the great potential of being competent and able researchers that leave without the Ph.D. Using techniques from the Georgia Tech Center for Deliberate Innovation, based in developmental psychology and behavioral economics, we are working to see more clearly what might be getting in the way of competent, motivated students who fail to complete their Ph.D. This includes a focus on the advisor/advisee relationship.

Using Deliberate Innovation Methodologies to Enable Graduate Student Success

The United States is facing a critical shortage of grade 7-12 teachers in the STEM disciplines, particularly in physics, chemistry, and mathematics. Faculty members play a major role in their students career choices, and faculty members perceptions of the profession may determine whether students choose to pursue teaching. To this end, we developed two surveys to measure student and faculty perceptions of grade 7-12 teaching. We found that both groups hold many incorrect beliefs about teaching careers. Furthermore, we found that faculty members believe they are quite supportive of future teachers, while students perceive that they are less supportive. Our findings highlight the need for both faculty members and students to be informed about the benefits of careers in grade 7-12 teaching. Additionally, our results suggest that faculty members should work to dispel their internal biases surrounding the teaching profession, which may inadvertently drive students away from grade 7-12 teaching.

College Faculty Support for Grade 7-12 Teaching Careers: Survey Results and Comparisons to Student Perceptions

As part of a larger study of exploring students' problem solving in small groups, we investigated how instructor influences students' epistemic framing in an upper-division electromagnetism class. We use the CAMP (Conceptual, Algorithmic, Mathematics, Physics) framework to investigate the dynamics of students' frames surrounding their interaction with the instructor, tracking frame triplets before, during and after instructor's intervention during the tutorial sessions. We present a case study of one such triplet (AP, CP, AP) by qualitatively analyzing students' interaction with instructor. Careful examination indicates that disagreements during the interaction necessitated the instructor to initiate conceptual discussion thereby causing a frame shift from an algorithmic to a conceptual frame.

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

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Student reasoning about sources of experimental measurement uncertainty in quantum versus classical mechanics

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