Upper-division Physics Research Articles

Concept image framework for derivatives from contour graphs

Physics experts and students commonly use a variety of representations when working with partial derivatives, including symbols, graphs, and words. One especially powerful representation is the contour graph. In open-ended problem-solving interviews with nine upper-division physics students, we asked students to determine derivatives from contour graphs with electrostatic and thermodynamic contexts. Students undertook three overarching actions: (i) orienting to the given graph, (ii) finding one or more derivatives, and (iii) reflecting on the task. In general, students tended to have more difficulty with the thermodynamic task than the electrostatic one. Students made use of a variety of representational features throughout the interviews, namely by annotating the provided contour graphs in ways that highlighted what is held constant. We use these results to generalize the existing concept image framework for ordinary derivatives to create a framework useful for understanding student ideas about multivariable derivatives. In particular, we add a new layer to the framework—the layer—that calls attention to how students do or do not attend to which variables are changing (or remaining constant) when finding a derivative. We view the change layer as a powerful central idea for both further research and the development of instructional tasks for physics students. Published by the American Physical Society 2024

Implementation of the photovoice methodology in a project-based upper-division physics course

Photovoice is a type of participatory action research in which individuals document their experiences through photography. Through the taking, captioning, and reflecting on photographs that they have taken, participants are able to affect change within their communities. Participants also take part in an interview or focus group about their photos at the end of the photovoice process in which they determine themes that appear in their photos, allowing them to participate in the research being done. We used the photovoice methodology in a small, project-based, upper-division, physics capstone course at the University of Colorado Boulder, in which students worked on an authentic industry project in partnership with a company in the quantum industry. As an example of the types of research results and benefits one could obtain using photovoice, we present a discussion of how we implemented the photovoice process within this course and present some of our results, including students’ experiences with the photovoice process. Photovoice may be particularly useful in understanding new, unique courses, as it allows students to co-create research that highlights ideas about the course that researchers would not know to ask about in more traditional research methodologies such as reflection questions. Published by the American Physical Society 2024

Multivariable calculus textbook representation of non-cartesian coordinates: a misalignment between multivariable calculus textbook content and upper-division physics application

Upper-division undergraduate physics coursework necessitates a firm grasp on and fluid use of mathematical knowledge, including an understanding of non-cartesian (specifically polar, spherical and cylindrical) coordinates and how to use them. A limited body of research into physics students’ thinking about coordinate systems suggests that even for upper-division students, understanding of coordinate system concepts is emergent. To more fully grasp upper-division physics students’ incoming understanding of non-cartesian coordinates, the prevalence of non-cartesian content in seven popular Calculus textbooks was studied. Using content analysis techniques, a coding scheme was developed to gain insight into the presentation of coordinate system content both quantitatively and qualitatively. An initial finding was that non-cartesian basis unit vectors were absent in all but one book. A deeper analysis of three of the calculus textbooks showed that cartesian coordinates comprise an overwhelming proportion of the textbooks’ content and that qualitatively the cartesian coordinate system is presented as the default coordinate system. Quantitative and qualitative results are presented with implications for how these results might impact physics teaching and research at the middle and upper-division.

Exploring student reasoning in statistical mechanics: Identifying challenges in problem-solving groups

Statistical mechanics has received limited attention in physics education research and remains a relatively underrepresented topic even in research on upper-division physics courses. The purpose of this study was to explore potential challenges that physics students encounter when they solve statistical mechanics problems in groups. Adopting a grounded approach, we video recorded and analyzed nine small student groups engaging in collaborative problem solving on the topic. The analysis involved iterative thematic coding, which gave rise to ten emergent categories of challenges. These were later divided into two broad groupings: and . In the first grouping, we list seven identified categories related to the concepts of macrostates and microstates, distinguishable and indistinguishable particles, temperature, entropy, energy, equilibrium, heat bath, the Boltzmann distribution, and the partition function. In the second grouping, we list three categories related to the inappropriate application of common relations, difficulty managing tensions between calculated results and qualitative reasoning, and coming up with definitions of new and inconsistent concepts. Some of our findings are supported by existing research on the topic, and others are previously unreported. Based on our findings, we propose that future research should investigate the relations between the identified challenges on one hand, and students’ epistemological framing, reasoning, and use of multiple representations on the other. Finally, we suggest that teachers should spend time engaging students in a conceptual discussion of the central ideas of statistical mechanics, motivating the choice and pointing out limitations of commonly used toy models, and linking course content to real-world phenomena. Published by the American Physical Society 2024

Physical Reasoning about Climate Modeling: A Bridge to Upper-Division Physics

Physical Reasoning about Climate Modeling: A Bridge to Upper-Division Physics

Implementing a course-based authentic learning experience with upper- and lower-division physics classes

We describe a dual-class authentic learning experience (ALE) in which undergraduate upper-division physics students develop low-cost instruments, which are then used by students in a lower-division course to monitor water quality in rivers. The ALE bridges the experiences of lower- and upper-division physics majors by involving students across different stages of their college careers in a collaborative project. Lower-division physics students characterize, calibrate, and troubleshoot the instrument prototypes developed by their upper-division peers, and their work informs instrument modifications in future upper-division physics classes. This paper describes the first iteration of this project along with student perceptions. We find that lower-division students report an increase in their awareness of possible upper-division projects, an increased sense that their coursework has real-world applications, and a heightened understanding of how physicists can play a role in research on environmental issues.

The discovery of a supermassive black hole at the center of the Milky Way galaxy

Black holes are fascinating astrophysical objects, yet they are rarely encountered in undergraduate-level physics courses. Here, we use concepts accessible to upper division physics majors to explain the discovery of a supermassive black hole at the center of the Milky Way galaxy, which was recognized by the award of the 2020 Nobel Prize in Physics. Infrared observations of the innermost region of the Milky Way galaxy show that many stars orbit around the galactic center at distances comparable to the size of the solar system with decadal-scale periods. We show how, given the sizes and periods of these stellar orbits, Newton's version of Kepler's third law can be used to determine the mass and maximum radius of the concentration of mass at the galactic center. We consider various possible physical interpretations consistent with this mass and maximum radius, rejecting flat disks due to dynamical instabilities, clouds of gas and/or dust due to gravitational instabilities, and clusters of compact objects due to collisional instabilities. This demonstrates that a supermassive black hole is the only possible explanation for the observed orbits of stars close to the galactic center.

Integrating imaging physics into undergraduate STEM education

Physics is a notoriously challenging subject that plays a critical and ubiquitous role in our lives. Undergraduate educators thus need new approaches that will encourage college students to study physics. At Lewis & Clark College, we have addressed this need through the development of a novel undergraduate physics course and supporting textbook that cover the principles, practice, and application of prominent “biophysical” and “biomedical” imaging techniques (i.e., light microscopy and medical imaging) and explore their extensive connections to physics. We chose to focus on imaging because it is a powerful, ubiquitous approach used in biology, medicine, and many other scientific disciplines, and because it has strong foundational ties to physics. Imaging also arises frequently in everyday life in connection with vision, cameras, and the diagnosis and treatment of disease and injury, so students are interested in the topic and appreciate its importance. The physical foundations of imaging often are established using sophisticated theoretical approaches suited for graduate physics and engineering students. However, they also can be established using introductory (largely conceptual) or intermediate (combined conceptual and theoretical) approaches suited for undergraduate students. Our course uses an intermediate approach accessible to most STEM majors and is very enthusiastically received by students at our institution majoring in biology, biochemistry, chemistry, and/or physics, making it our most popular upper-division physics course. This success suggests that other institutions also would profit from offering a course in the spirit of Biomedical Imaging. Here we describe the course content, including highly popular hands-on activities, to help pave the way for other educators who are interested in teaching a similar course.

Validation of a coupled, multiple response assessment for upper-division thermal physics

Validation of a coupled, multiple response assessment for upper-division thermal physics

Inharmonicity in plucked guitar strings

We have considered the vibration of various types of pinned guitar strings and have investigated the deviation of the partials from integer multiples of the string's fundamental vibration frequency. We measured the inharmonicity parameter B and compared it to a direct calculation based on a model equation. We generally found very good agreement between the two determinations of B for monofilament strings, but perhaps not surprisingly, we find rather poor agreement for wound strings. Furthermore, we show that the methodology used to carry out this experiment can easily serve as the basis for an upper division physics laboratory on physical acoustics including a more thorough investigation of the classical wave equation in a real-world application.

Institutionalizing evidence-based STEM reform through faculty professional development and support structures

BackgroundEven though student-centered instruction leads to positive student outcomes, direct instruction methods are still prevalent. Multiple barriers prevent faculty from further adopting evidence-based student-centered practices and holistic approaches to faculty support are necessary to promote faculty change. The Collaborative for Institutionalizing Scientific Learning (CISL) is an HHMI-funded program to reform undergraduate science and mathematics education at a large Hispanic-Serving public research university. The program has established a Faculty Scholar support model to impact the number of science and mathematics faculty using evidence-based practices in their classrooms. Through this program, Scholars are selected to undertake a transformation of a course of their choice and conduct an assessment of the impact of the reform on students—while receiving multiple supports including summer salary, undergraduate Learning Assistants, professional development, course assessment and education research support, and opportunities to develop manuscripts on their course transformations.ResultsCISL has supported over 40 Faculty Scholars in the transformation of both introductory and upper division biology, chemistry, physics and mathematics courses. Faculty are motivated to transform a course due to factors related to their own experiences and beliefs, their students’ needs, the course structure, and/or departmental elements. Quantitative analysis of the impact of the project on student success show that, overall, students in CISL-supported courses have higher passing rates compared to students in traditional classrooms. Survey and interviews of Faculty Scholars identified that the most valuable elements of the program were the personnel support from undergraduate Learning Assistants during reform implementation and guidance from the program’s Assistant Director during design, implementation and evaluation.ConclusionsThe CISL program provides an example of significant effort sustained over several years to systematically improve the quality and culture of undergraduate education in a large research-intensive Hispanic Serving Institution. The program has had an overall positive impact on the professional development of Faculty Scholars and led to an increase in the number of STEM courses implementing evidence-based teaching practices, thus, taking a step towards solidifying a culture of evidence-based instructional strategies in STEM departments.

Simulation led optical design assessments: Emphasizing practical and computational considerations in an upper division physics lecture course

Employing simulation led optical design assessments (SLODAs) in an upper division optics course provides students with a deeper understanding of optical design, interactions, and devices, while reinforcing their understanding of computational methods. The upper division optics course discussed here did not have a required lab component as would be typical at many institutions. Therefore, the practical and expanded experiences students gained via SLODA in lieu of a laboratory experience were particularly crucial in developing advanced student understanding and skills in both optical design and computational applications. SLODA can also supplement a laboratory-based course with computational skill development. After introducing students to various computational methods during the early part of the course via scaffolding in-class preliminary computational activities, students were then assigned more complicated application based SLODA. This paper details each of the preliminary computational activities and SLODA, including their implementation and both the optical and computational considerations these activities and assessments were designed to introduce. An example SLODA is detailed. A reflection on the implementation of SLODA is provided for those interested in adopting the curriculum. A list of online resources is given in the Appendix for faculty wishing to implement SLODA. Finally, a sample of the student work submitted is presented and discussed in the journal's supplementary material. While success was specifically found via the implementation of SLODA in an upper division optics course, the potential exists for adaptation of the simulation led design assessment approach to other practical, design-based courses such as electronics or those within the engineering disciplines.

Color-Coded Algebra

In a typical first physics class, homework consists of problems in which numerical values for physical quantities are given and the desired answer is a number with appropriate units. In contrast, most calculations in upper-division undergraduate physics are entirely symbolic. Despite the need to learn symbolic manipulation, students are often resistant to performing symbolic calculations in their introductory classes. As instructors, we face a choice between encouraging students to use symbolic calculations, including helping them learn the necessary skills to do so, or allowing students to default to numerical calculations, which does not adequately prepare them for their future courses. In this paper, I will describe a color-coded algebra scheme, which helps lower the barriers to symbolic calculations for students.

Transport through quantum dots: An introduction via master equation simulations

In this work, we present a master equation approach to simulating DC transport through single electron transistors and quantum dots suitable for an upper-division undergraduate computational physics project. After introducing the basic theory describing transport through quantum dots, we present a simulation of the simple case of a metallic dot including effects due to the finite temperature of the leads. Building on this example, we simulate published data with orbital and spin states. We envision students building on these simulations to replicate other data in the published literature. Projects of this type would be suitable for an undergraduate independent study or computational project and will give students a strong introduction to the topic of transport through quantum dots without the need for expensive cryogenic and electrical measurement systems or device fabrication necessary for experimental work.

Designing upper-division thermal physics assessment items informed by faculty perspectives of key content coverage

Developing a multiple-choice assessment tool for upper-division thermal physics with ten key topic areas selected to represent the core content taught at most institutions.

Students’ metarepresentational competence with matrix notation and Dirac notation in quantum mechanics

Upper division physics students do not only come to quantum mechanics with difficulties; they also come with strengths, including the ability to critique and understand the general purposes of the various notations used within quantum mechanics.

Students’ understanding of the concept of the electric field through conversions of multiple representations

We conducted a study with introductory and upper-division level physics students in a Mexican and a Spanish university to learn how students recognize the main characteristics of the electric field in three of its more widely used representations, namely, algebraic notation, vector field plot, and electric field lines, and how the students do conversions of them. The students’ abilities to recognize the three representations of the electric field and do conversions gave insight into their understanding of this concept. We used the theory of registers of semiotic representations as a framework to analyze the data. Our results showed that the direction of the conversion is an essential factor in determining the students’ success in performing conversions of electrical field representations. We found close synergy between the vector field plot and the algebraic notation of the electric field. However, we found that the conversions that involve electric field lines do not present synergy. The electric field lines representation is especially difficult for students, both as a source and as a target representation, specifically, the interpretation and representation of the magnitude of the field through the density of field lines. We recommend that teachers and researchers of electricity and magnetism be more conscious of the difficulties that some conversion tasks may present to their students. We specifically invite instructors to be attentive to how they approach the representation of electric field lines and be explicit when performing conversions that involve electric field lines.8 MoreReceived 23 September 2019Accepted 22 April 2020DOI:https://doi.org/10.1103/PhysRevPhysEducRes.16.010135Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasConcepts & principlesScientific reasoning & problem solvingPhysics Education Research

Cosmic Ray Muons on the Slopes of Mauna Kea

In this paper, we describe a study of cosmic ray muon rates and energies at various elevations on Mauna Kea on the island of Hawaii. The study was originally conceived as an extension to the upper-division modern physics laboratory at the University of Hawaii at Hilo and used the TeachSpin Muon Physics apparatus (abbreviated TSMP below) from that lab. The purpose of this paper is to provide a blueprint for similar experiments appropriate to introductory physics laboratory courses and to make students aware of the variety of investigations possible using this type of apparatus. Plans for future work are outlined in the conclusion.

An Inexpensive Semiconducting Device Laboratory: Building a Schottky Barrier Diode

Semiconductor devices, usually made from silicon wafers, are present in the electronic gadgets that we use on a daily basis. In an introductory physics class, the textbook usually devotes a few pages to these devices and moves on. As a result, students may readily forget the material or fail to see how it relates to their lives. A solution is to have the student build a simple semiconductor device such as a diode. Generally, the process for making these devices is expensive, dangerous, and time consuming. While there has been some success in reducing these challenges for certain devices, labs that do this are mostly limited to upper-division engineering or physics classes. The purpose of this paper is to describe a method that can be followed to build a diode from a silicon wafer in less than an hour with limited equipment and with no exposure to dangerous chemicals. This lab can be conducted at the high school level or in an introductory college physics class. It requires an investment of less than $100 for the equipment and consumable materials.

Investigating students’ behavior and performance in online conceptual assessment

Historically, the implementation of research-based assessments (RBAs) has been a driver of educational change within physics and helped motivate adoption of interactive engagement pedagogies. Until recently, RBAs were given to students exclusively on paper and in-class; however, this approach has important drawbacks including decentralized data collection and the need to sacrifice class time. Recently, some RBAs have been moved to online platforms to address these limitations. Yet, online RBAs present new concerns such as student participation rates, test security, and students' use of outside resources. Here, we report on a study addressing these concerns in both upper-division and lower-division undergraduate physics courses. We gave RBAs to courses at five institutions; the RBAs were hosted online and featured embedded JavaScript code which collected information on students' behaviors (e.g., copying text, printing). With these data, we examine the prevalence of these behaviors, and their correlation with students' scores, to determine if online and paper-based RBAs are comparable. We find that browser loss of focus is the most common online behavior while copying and printing events were rarer. We found that correlations between these behaviors and student performance varied significantly between introductory and upper-division student populations, particularly with respect to the impact of students copying text in order to utilize internet resources. However, while the majority of students engaged in one or more of the targeted online behaviors, we found that, for our sample, none of these behaviors resulted in a significant change in the population's average performance that would threaten our ability to interpret this performance or compare it to paper-based implementations of the RBA.