arXiv subjects

Bethany R. Wilcox

Publications and source records attributed to Bethany R. Wilcox.

At least 19 recordsLinked to original sources

arXiv2026

Assessing student learning in quantum computing: Lessons from developing a test item on phase kickback

A major challenge for quantum workforce development is the need to both understand and reliably assess student learning of quantum information science (QIS) fundamentals. Yet student thinking is notoriously difficult to probe, even for seasoned education researchers. This article presents the story of Item 15 on the Quantum Computing Conceptual Survey (QCCS). This assessment item underwent more revision and discussion within the team than the remaining 19 assessment questions combined. This paper provides a behind-the-scenes look at the development of this assessment question: a story that both reveals interesting findings about student reasoning in quantum computing and illustrates why quantum education researchers insist on triangulating diverse quantitative and qualitative data sources when developing and refining assessment items, with implications for any researcher looking to understand and measure student conceptual reasoning in quantum computing, as well as for QIS curriculum and workforce development more broadly.

physics.ed-ph↗

arXiv2026

Measuring student understanding in quantum computing: Development and validation of the Quantum Computing Conceptual Survey

Research-based assessments (RBAs) have proven to be valuable tools in PER, supporting both instructional reform and foundational research. In the rapidly-growing field of Quantum Information Science (QIS), the lack of suitable RBAs limits the field's ability to make evidence-based decisions about curricula and program development. In this paper, we introduce the Quantum Computing Conceptual Survey (QCCS), an instrument developed to help address this gap by measuring student conceptual understanding in the foundations of quantum computing. Using pilot data from over 50 courses and 700 students, we present evidence supporting the validity of the QCCS for use in introductory QIS courses, drawing on analyses from both classical test theory and the Rasch model. We detail the potential uses for the QCCS, intending for it to serve as both a practical tool for instructors and a means of facilitating measurement-driven QIS education research.

physics.ed-ph↗

arXiv2026

Computer-generated QIS tutorial feedback is valued by students, but does not replicate in-class collaboration

PER has consistently demonstrated the effectiveness of small-group tutorials in helping students develop conceptual understanding and fluency, but instructor uptake is limited by resource constraints. To test the effectiveness of out-of-class tutorials using computer-generated feedback as an instructor-friendly alternative, we conducted think-aloud interviews with students in a quantum computing course who were randomly assigned to either a traditional validated small-group, pencil-and-paper tutorial on tensor products, or a solo computerized adaptation thereof. We found that while the computer-generated feedback was broadly considered useful by students, student engagement patterns were markedly different in the solo setting, with students demonstrating reluctance to use the interface's built-in help features and tending to internalize failure in unproductive ways counter to our intention of a formative learning environment. We discuss implications for curriculum design and directions for future research that may help to answer the longstanding question in PER of why tutorials work so well.

physics.ed-ph↗

arXiv2026

Can a CNOT Gate Affect the Control Qubit? Student Resources for Understanding CNOT and Entanglement

The Controlled-Not (CNOT) gate is essential to algorithms in quantum computing for its ability to entangle qubits. As such, it is important to understand how students learning quantum computing reason around the function and use of this critical quantum gate. To investigate this, we conducted think-aloud interviews in which students solved problems involving the CNOT gate to understand students' `CNOT toolbox' -- the strategies and cognitive resources students use when reasoning about the effect of the CNOT gate. We identify three cognitive resources related to the CNOT gate: (1) the procedural resource of applying CNOT to specific states, (2) a qualitative description of CNOT's effect on the target qubit given the control qubit, and (3) the idea that the control qubit is not changed when CNOT is applied to computational basis states. We find that students' use of the first resource is foundational to their understanding of the second and third, that the second and third resources can sometimes lead students to incorrect conclusions, and that students can use each of these resources separately or in tandem. We also explore how students use these resources in conjunction with Dirac notation, superposition states, and entanglement to reason both productively and unproductively about quantum computing problems.

physics.ed-ph↗

arXiv2025

Characterization of Upper-Level Undergraduate Quantum Mechanics Courses in the U.S

Upper-level, undergraduate quantum mechanics (QM) is widely considered a difficult subject with many varied approaches to teaching it and considerable variation in content coverage. For example, two common approaches to undergraduate QM instruction are spins-first, which focuses on the postulates of QM in spin systems before discussing wavefunctions, and wavefunctions-first, which focuses on the Schrödinger equation and its solutions for continuous functions in various potentials before discussing spin. These different approaches, along with the content variability in the textbooks used by instructors, may mean students learn different things in QM classes across the United States (U.S.). In this paper, we offer a characterization of QM courses based on survey responses from instructors at institutions across the U.S. With the responses of 76 instructors teaching QM courses (or sequences), we present results detailing their teaching methodologies, use of pedagogical resources, and coverage of QM topics. We find that the plurality of instructors in our sample are using traditional lecture, but many instructors are using interactive lecture or another non-traditional method. Additionally, instructors are using a wide variety of pedagogical tools (e.g., clicker questions). Many instructors in our sample reported teaching single-semester (or single-quarter) QM courses; these instructors report similar content coverage to instructors teaching first-semester (or quarter) QM courses, though their responses showed greater variability. We additionally report a comparison of content coverage between instructors using wavefunctions-first versus spins-first approaches, finding a large degree of overlap with differences in coverage for a few specific topics. These findings can help inform both future research and instructional efforts in QM education.

physics.ed-ph↗

arXiv2025

Motivating reflection in problem solving: homework corrections in upper-division physics courses

Despite the recognition that reflection is an essential part of problem solving, it is often not emphasized in upper-division physics courses. In this paper, we discuss homework corrections (HWCs) as a pedagogical tool to motivate reflection on homework assignments. We focus on gaining a qualitative understanding of how students may engage with the process of homework corrections, considering potential impacts on content understanding, metacognitive skills, and affect. To do so, we present three comparative case studies to elucidate different aspects of student engagement with HWCs; we also present descriptive statistics of participation in HWCs. We find that HWCs can be a useful pedagogical tool, but more scaffolding may be necessary to support students in identifying and learning from their mistakes, even in upper-division courses.

physics.ed-ph↗

arXiv2024

Perspectives from Physics Graduate Students on Their Experiences in NSF Research Experiences for Undergraduates

National Science Foundation (NSF) funded Research Experiences for Undergraduates (REUs) are explicitly intended to reach minoritized students in STEM and those who have few research opportunities. Many undergraduates are encouraged to seek them out, but their actual efficacy is not well-established, and the out-of-state travel required for many attendees may prove a significant barrier for the very students REUs wish to reach. We interviewed physics graduate students who attended REUs as undergrauates, focusing on how the REUs benefitted them, barriers they faced attending REUs, and their relationship with their REU mentors. Interviewees reported benefits that aligned with the NSF goals: skills, enculturation, and knowledge they had not received in their undergraduate institutions. They also reported financial barriers they faced which they were able to overcome due to their financial privilege. Participants also reported widely varying experiences with their mentors. Some mentors did and some did not meet their mentees where they were at in their career and skill levels. Some students did not know how to approach their mentors with their questions or needs.

physics.ed-ph↗

arXiv2024

Education for expanding the quantum workforce: Student perceptions of the quantum industry in an upper-division physics capstone course

As quantum technologies transition out of the research lab and into commercial applications, it becomes important to better prepare students to enter this new and evolving workforce. To work towards this goal of preparing physics students for a career in the quantum industry, a senior capstone course called "Quantum Forge" was created at the University of Colorado Boulder. This course aims to provide students a hands-on quantum experience and prepare them to enter the quantum workforce directly after their undergraduate studies. Some of the course's goals are to have students understand what comprises the quantum industry and have them feel confident they could enter the industry if desired. To understand to what extent these goals are achieved, we followed the first cohort of Quantum Forge students through their year in the course in order to understand their perceptions of the quantum industry including what it is, whether they feel that they could be successful in it, and whether or not they want to participate in it. The results of this work can assist educators in optimizing the design of future quantum-industry-focused courses and programs to better prepare students to be a part of this burgeoning industry.

physics.ed-ph↗

arXiv2024

Disparities in access to US quantum information education

Driven in large part by the National Quantum Initiative Act of 2018, quantum information science (QIS) coursework and degree programs are rapidly spreading across US institutions. Yet prior work suggests that access to quantum workforce education is unequally distributed, disproportionately benefiting students at private research-focused institutions whose student bodies are unrepresentative of US higher education as a whole. We use regression analysis to analyze the distribution of QIS coursework across 456 institutions of higher learning as of fall 2022, identifying statistically significant disparities across institutions in particular along the axes of institution classification, funding, and geographic distribution suggesting today's QIS education programs are largely failing to reach low-income and rural students. We also conduct a brief analysis of the distribution of emerging dedicated QIS degree programs, discovering much the same trends. We conclude with a discussion of implications for educators, policymakers, and education researchers including specific policy recommendations to direct investments in QIS education to schools serving low-income and rural students, leverage existing grassroots diversity and inclusion initiatives that have arisen within the quantum community, and update and modernize procedures for collecting QIS educational data to better track these trends.

physics.ed-ph↗

arXiv2023

Introductory quantum information science coursework at US institutions: Content coverage

Despite rapid growth of quantum information science and engineering (QIS/QISE) workforce development initiatives, perceived lack of agreement among faculty on core content has made prior research-based curriculum and assessment development initiatives difficult to scale. To identify areas if consensus on content coverage, we report findings from a survey of N=63 instructors teaching introductory QISE courses at US institutions of higher learning. We identify a subset of content items common across a large fraction (>=80%) of introductory QISE courses that are potentially amenable to research-based curriculum development, with an emphasis on foundational skills in mathematics, physics, and engineering. As a further guide for curriculum development, we also examine differences in content coverage by level (undergraduate/graduate) and discipline. Finally, we briefly discuss the implications of our findings for the development of a research-based QISE assessment at the postsecondary level.

physics.ed-ph↗

arXiv2023

How media hype affects our physics teaching: A case study on quantum computing

Popular media is an unspoken yet ever-present element of the physics landscape and a tool we can utilize in our teaching. It is also well-understood that students enter the physics classroom with a host of conceptions learned from the world at large. It stands to reason, then, to suspect that media coverage may be a major contributing factor to students' views on physical phenomena and the nature of science - one whose influence will only grow amid the 21st century digital age. Yet the role of the media in shaping physics teaching and learning has remained largely unexplored in the physics education research (PER) literature so far. Here, we explore the phenomenon of media hype from a theoretical and practical perspective: how media rhetoric of current topics in science and technology evolves, and how it affects students and instructors. We argue that media hype of cutting-edge science can be a double-edged sword for educators, with the same amped-up rhetoric that motivates students to enter the classroom tending to result in inflated preconceptions of what the science and technology can actually do. We draw on examples related to teaching quantum computing as a case study, though the findings we present should generalize to other topics garnering significant media attention - from exoplanets to graphene to batteries for electric vehicles. We conclude with a set of practical recommendations for physics teachers at all levels who wish to be more cognizant of the role exposure to popular media has on students and to tailor our teaching accordingly.

physics.ed-ph↗

arXiv2022

Correlations between student connectivity and academic performance: a pandemic follow-up

Social network analysis (SNA) has been gaining traction as a technique for quantitatively studying student collaboration. We analyze networks, constructed from student self-reports of collaboration on homework assignments, in two courses from the University of Colorado Boulder and one course from the Colorado School of Mines. All three courses occurred during the COVID-19 pandemic, which allows for a comparison between the course at the Colorado School of Mines (in a fully remote format) with results from a previous pre-pandemic study of student collaboration at the Colorado School of Mines (in a hybrid format). We compute nodal centrality measures and calculate the correlation between student centrality and performance. Results varied widely between each of the courses studied. The course at the Colorado School of Mines had strong correlations between many centrality measures and performance which matched the patterns seen in the pre-pandemic study. The courses at the University of Colorado Boulder showed weaker correlations, and one course showed nearly no correlations at all between students' connectivity to their classmates and their performance. Taken together, the results from the trio of courses indicate that the context and environment in which the course is situated play a more important role in fostering a correlation between student collaboration and course performance than the format (remote, hybrid, in-person) of the course. Additionally, we conducted a short study on the effect that missing nodes may have on the correlations calculated from the measured networks. This investigation showed that missing nodes tend to shift correlations towards zero, providing evidence that the statistically significant correlations measured in our networks are not spurious.

physics.ed-ph↗

arXiv2022

Investigating student interpretations of the differences between classical and quantum computers: Are quantum computers just analog classical computers?

Significant attention in the PER community has been paid to student cognition and reasoning processes in undergraduate quantum mechanics. Until recently, however, these same topics have remained largely unexplored in the context of emerging interdisciplinary quantum information science (QIS) courses. We conducted exploratory interviews with 22 students in an upper-division quantum computing course at a large R1 university crosslisted in physics and computer science, as well as 6 graduate students in a similar graduate-level QIS course offered in physics. We classify and analyze students' responses to a pair of questions regarding the fundamental differences between classical and quantum computers. We specifically note two key themes of importance to educators: (1) when reasoning about computational power, students often struggled to distinguish between the relative effects of exponential and linear scaling, resulting in students frequently focusing on distinctions that are arguably better understood as analog-digital than classical-quantum, and (2) introducing the thought experiment of analog classical computers was a powerful tool for helping students develop a more expertlike perspective on the differences between classical and quantum computers.

physics.ed-ph↗

arXiv2022

The interdisciplinary quantum information classroom: Themes from a survey of quantum information science instructors

Interdisciplinary introduction to quantum information science (QIS) courses are proliferating at universities across the US, but the experiences of instructors in these courses have remained largely unexplored in the discipline-based education research (DBER) communities. Here, we address this gap by reporting on the findings of a survey of instructors teaching introduction to QIS courses at institutions across the US, primarily at the undergraduate or hybrid undergraduate/graduate level, as well as follow-up focus interviews with six individual instructors. Key themes from this analysis include challenges and opportunities associated with the diversity of instructor and student backgrounds, student difficulties with the mathematical formalism (especially though not exclusively with linear algebra), and the need for better textbooks and curricular materials. We also find that while course topics are ostensibly similar, each course is crafted by its instructor to tell a different story about QIS and to uniquely balance goals such as accessibility and academic rigor, such that no canonical introduction to QIS course emerges from our dataset. We discuss the implications of this finding with regard to the benefits and risks associated with standardization of curricula as QIS coursework matures.

physics.ed-ph↗

arXiv2021

Investigating Unprompted and Prompted Diagrams Generated by Physics MajorsDuring Problem Solving

Diagrams are ubiquitous in physics, especially in physics education and physics problem solving. Problem solvers may generate diagrams to orient to a scenario, to organize information, to directly extract an answer, or as a tool of communication. In this study, we interviewed 19 undergraduate and graduate physics majors, asking them to solve 18 multiple-choice physics problems -- with no prompting regarding diagrams -- and then six diagramming tasks of situations similar to six of the multiple-choice problems. By comparing spontaneously generated and prompted diagrams, we identify different diagramming elements and features used by physics majors acting towards different ends (\textit{i.e.,} in different epistemic frames). We found that different physical contexts impact how critical it is to draw an accurate diagram, and that the differences in diagramming between cohorts (\textit{e.g.}, between lower-division undergraduate and graduate students) seem to be smaller than the differences within a cohort. We also explore implications for teaching and research.

physics.ed-ph↗

arXiv2021

Investigating graduate student reasoning on a conceptual entropy questionnaire

Student learning in upper division thermal physics has not been studied to the same extent as in other courses like electromagnetism and quantum mechanics. Studies addressing reasoning and learning at the graduate level are even more limited. In this study, we conducted think-aloud interviews with eight graduate students involving questions centered around a set of entropy related conceptual tasks, two of which are similar to tasks presented to undergraduates in other studies. We discuss patterns in student reasoning on each question then discuss themes that appeared across questions. We identify conceptual resources that students frequently used to reason about the interview tasks and compare them to prior work. We observed graduate students commonly thinking about entropy in relationship to a number of states, even in situations where such a connection was not directly relevant. Graduate students also frequently made direct associations between entropy and temperature, despite there being no general, explicit relationship between the two quantities. On the whole, graduate students demonstrated adaptability and metacognitive awareness in their approach to reasoning about entropy.

physics.ed-ph↗

arXiv2020

Online Administration of Research-Based Assessments

The number and use of research-based assessments (RBAs) has grown significantly over the last several decades. Data from RBAs can be compared against national datasets to provide instructors with empirical evidence on the efficacy of their teaching practices. Many physics instructors, however, opt not to use RBAs due to barriers such as having to use class time to administer them. In this article we examine how these barriers can be mitigated through online administrations of RBAs, particularly through the use of free online RBA platforms that automate administering, scoring, and analyzing RBAs (e.g., the Learning About STEM Student Outcomes [LASSO], Colorado Learning Attitudes About Science Survey for Experimental Physics [E-CLASS], Physics Lab Inventory of Critical thinking [PLIC], and PhysPort DataExplorer platforms). We also explore the research into common concerns of administering RBAs online and conclude with a practical how-to guide for instructors.

physics.ed-ph↗

arXiv2020

Retention of conceptual learning after an interactive introductory physics course

The cyclic format of the undergraduate physics curriculum depends on students' ability to recall and utilize material covered in prior courses in order to reliably build on that knowledge in later courses. However, there is evidence to suggest that people often do not retain all, or even most, of what they learned previously. How much information is retained appears to be dependent both on the individuals' approach to learning as well as the style of instruction. In particular, there is evidence to suggest that active engagement techniques in the classroom can improve students' retention of the material over time. Here, we report the findings of a longitudinal investigation of students' retention of conceptual understanding as measured by the Force and Motion Conceptual Evaluation (FMCE) following a first-semester, calculus-based introductory physics course, which features significant active engagement in both lecture and recitation. By administering the FMCE at the end of a first-semester physics course and again at the beginning of the subsequent second-semester physics course, we examine students' knowledge retention over time periods ranging from 1-15 months. We find that the shift in students' FMCE scores between these two courses is positive but corresponds to a small effect size, indicating that students retained effectively all of their conceptual learning (as measured by the FMCE). This finding largely persists even as the length of the gap between the two courses increases. We also find that, when breaking out students' performance on individual questions, the majority of students maintain their score on individual questions. Averaged over all questions, roughly a fifth of the students switched their answers from right to wrong or wrong to right on any given item.

physics.ed-ph↗