arXiv subjects

Emily Marshman

Publications and source records attributed to Emily Marshman.

At least 19 recordsLinked to original sources

arXiv2026

Supporting physics instructors to use a variety of evidence-based approaches to improve student learning: An example from quantum mechanics

Physics instructors need support to successfully adopt and adapt evidence-based active engagement (EBAE) approaches because improving teaching and learning is a process and support is needed to ensure that they do not get disheartened if a particular EBAE approach does not produce the desired outcome. The instructors not only need support to refine their implementation of a specific EBAE approach to make them effective, but also to use a variety of EBAE methods to improve student learning. Here we illustrate how, with appropriate support, a quantum mechanics instructor did not give up when an EBAE approach involving implementation of a sequence of clicker questions on addition of angular momentum did not yield expected learning outcomes. The support ensured that the instructor remained optimistic and used another EBAE method that did not require him to spend more time in class on this topic. In particular, the instructor created an opportunity for students to productively struggle with the same problems (they had not performed well on after clicker questions) by giving them grade incentives to correct their mistakes outside of class. Student performance on one of the addition of angular momentum problems posed on the final exam suggests that students who corrected their mistakes benefited from the task and learned about addition of angular momentum better than those who did not correct their mistakes. Encouraging and supporting physics instructors can even be accomplished using an online community of physics educators. This type of support can go a long way in helping students learn physics because it is likely to increase their persistence in using various EBAE approaches as they refine their implementation to suit their students as well as their own instructional style.

physics.ed-ph↗

arXiv2025

A Framework for Understanding the Impact of Integrating Conceptual and Quantitative Reasoning in a Quantum Optics Tutorial on Students' Conceptual Understanding

We investigated the impact of incorporating quantitative reasoning for deeper sense-making in a Quantum Interactive Learning Tutorial (QuILT) on students' conceptual performance using a framework emphasizing integration of conceptual and quantitative aspects of quantum optics. In this investigation, we compared two versions of the QuILT that were developed and validated to help students learn various aspects of quantum optics using a Mach Zehnder Interferometer with single photons and polarizers. One version of the QuILT is entirely conceptual while the other version integrates quantitative and conceptual reasoning (hybrid version). Performance on conceptual questions of upper-level undergraduate and graduate students who engaged with the hybrid QuILT was compared with that of those who utilized the conceptual QuILT emphasizing the same concepts. Both versions of the QuILT focus on the same concepts, use a scaffolded approach to learning, and take advantage of research on students' difficulties in learning. The hybrid and conceptual QuILTs were used in courses for upper-level undergraduates or first-year physics graduate students in several consecutive years at the same university. The same conceptual pre-test and post-test were administered after traditional lecture-based instruction in relevant concepts and after student engaged with the QuILT, respectively. We find that the post-test performance of physics graduate students who utilized the hybrid QuILT on conceptual questions, was better than those who utilized the conceptual QuILT. For undergraduates, the results showed differences for different classes. One possible interpretation of these findings consistent with our framework is that integrating conceptual and quantitative aspects of physics in research-based tools and pedagogies should be commensurate with students' prior knowledge of physics and mathematics involved.

physics.ed-ph↗

arXiv2025

Using multiple representations to improve student understanding of quantum states

One hallmark of expertise in physics is the ability to translate between different representations of knowledge and use the representations that make the problem-solving process easier. In quantum mechanics, students learn about several ways to represent quantum states, e.g., as state vectors in Dirac notation and as wavefunctions in position and momentum representation. Many advanced students in upper-level undergraduate and graduate quantum mechanics courses have difficulty translating state vectors in Dirac notation to wavefunctions in the position or momentum representation and vice versa. They also struggle when translating the wavefunction between the position and momentum representations. The research presented here describes the difficulties that students have with these issues and how research was used as a guide in the development, validation, and evaluation of a Quantum Interactive Learning Tutorial (QuILT) to help students develop a functional understanding of these concepts. The QuILT strives to help students with different representations of quantum states as state vectors in Dirac notation and as wavefunctions in position and momentum representation and with translating between these representations. We discuss the effectiveness of the QuILT from in-class implementation and evaluation.

physics.ed-ph↗

arXiv2021

The challenges of changing teaching assistants' grading practices: Requiring students to show evidence of understanding

Teaching assistants (TAs) are often responsible for grading in introductory physics courses at large research universities. Their grading practices can shape students' approaches to problem solving and learning. Physics education research recommends grading practices that encourage students to provide evidence of understanding via explication of the problem-solving process. However, TAs may not necessarily grade in a manner that encourages students to provide evidence of understanding in their solutions. Within the context of a semester-long TA professional development course, we investigated whether encouraging TAs to use a grading rubric that appropriately weights the problem-solving process and having them reflect upon the benefits of using such a rubric prompts TAs to require evidence of understanding in student solutions. We examined how the TAs graded realistic student solutions to introductory physics problems before they were provided a rubric, whether TAs used the rubric as intended, whether they were consistent in grading similar solutions, and how TAs' grading criteria changed after discussing the benefits of a well-designed rubric. We find that many TAs typically applied the rubric consistently when grading similar student solutions but did not require students to provide evidence of understanding. TAs' written responses, class discussions, and individual interviews suggest that the instructional activities involving the grading rubrics in this study were not sufficient to change their grading practices. Interviews and class discussions suggest that helping TAs value a rubric that appropriately weights the problem-solving process may be challenging partly due to the TAs past educational experiences and the departmental context.

physics.ed-ph↗

arXiv2021

A longitudinal analysis of students' motivational characteristics in introductory physics courses: Gender differences

The lack of diversity and the under-performance of underrepresented students in STEM courses have been the focus of researchers in the last decade. In particular, many hypotheses have been put forth for the reasons for the under-representation and under-performance of women in physics. Here, we present a framework for helping all students learn in science courses that takes into account four factors: 1) characteristics of instruction and learning tools, 2) implementation of instruction and learning tools, 3) student characteristics, and 4) students' environments. While there has been much research on factor 1 (characteristics of instruction and learning tools), there has been less focus on factor 2 (students' characteristics, and in particular, motivational factors). Here, we focus on the baseline motivational characteristics of introductory physics students obtained from survey data to inform factor 2 of the framework. A longitudinal analysis of students' motivational characteristics in two-semester introductory physics courses was performed by administering pre- and post-surveys that evaluated students' self-efficacy, grit, fascination with physics, value associated with physics, intelligence mindset, and physics epistemology. Female students reported lower self-efficacy, fascination and value, and had a more "fixed" view of intelligence in the context of physics compared to male students. Grit was the only factor on which female students reported averages that were equal to or higher than male students throughout introductory physics courses. These gender differences can at least partly be attributed to the societal stereotypes and biases about who belongs in physics and can excel in it. The findings inform the framework and have implications for the development and implementation of effective pedagogies and learning tools to help all students learn.

physics.ed-ph↗

arXiv2020

Holistic framework to help students learn effectively from research-validated self-paced learning tools

With limited time available in the classroom, e-learning tools can supplement in-class learning by providing opportunities for students to study and learn outside of class. Such tools can be especially helpful for students who lack adequate prior preparation. However, one critical issue is ensuring that students, especially those in need of additional help, engage with the tools as intended. Here we first discuss an empirical investigation in which students in a large algebra-based physics course were given opportunities to work through research-validated tutorials outside of class as self-study tools. Students were provided these optional tutorials after traditional instruction in relevant topics and were then given quizzes that included problems that were identical to the tutorial problems with regard to the physics principles involved but had different contexts. We find that students who worked through the tutorials as self-study tools struggled to transfer their learning to solve problems that used the same physics principles. On the other hand, students who worked on the tutorials in supervised, one-on-one situations performed significantly better than them. These empirical findings suggest that many introductory physics students may not engage effectively with self-paced learning tools unless they are provided additional incentives and support, e.g., to aid with self-regulation. Inspired by the empirical findings, we propose a holistic theoretical framework to help create learning environments in which students with diverse backgrounds are provided support to engage effectively with self-study tools.

physics.ed-ph↗

arXiv2020

Student difficulties with finding the corrections to the energy spectrum of the hydrogen atom for the strong and weak field Zeeman effects using degenerate perturbation theory

We discuss an investigation of student difficulties with the corrections to the energy spectrum of the hydrogen atom for the strong and weak field Zeeman effects using degenerate perturbation theory. This investigation was carried out in advanced quantum mechanics courses by administering written free-response and multiple-choice questions and conducting individual interviews with students. We discuss the common student difficulties related to these concepts which can be used as a guide for creating learning tools to help students develop a functional understanding of concepts involving the corrections to the energy spectrum due to the Zeeman effect.

physics.ed-ph↗

arXiv2020

Student difficulties with the corrections to the energy spectrum of the hydrogen atom for the intermediate field Zeeman effect

We discuss an investigation of student difficulties with the corrections to the energy spectrum of the hydrogen atom for the intermediate field Zeeman effect using the degenerate perturbation theory. 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 relevant physics concepts. In particular, students often struggled with mathematical sense-making in this context of quantum mechanics which requires interpretation of the implications of degeneracy in the unperturbed energy spectrum and how the Zeeman perturbation will impact the splitting of the energy levels. We discuss how the common difficulties often arise from the fact that applying linear algebra concepts correctly in this context with degeneracy in the energy spectrum is challenging for students.

physics.ed-ph↗

arXiv2020

Improving student understanding of quantum mechanics underlying the Stern-Gerlach experiment using a research-validated multiple-choice question sequence

Engaging students with well-designed multiple-choice questions during class and asking them to discuss their answers with their peers after each student has contemplated the response individually can be an effective evidence-based active-engagement pedagogy in physics courses. Moreover, validated sequences of multiple-choice questions are more likely to help students build a good knowledge structure of physics than individual multiple-choice questions on various topics. Here we discuss a framework to develop robust sequences of multiple-choice questions and then use the framework for the development, validation and implementation of a sequence of multiple-choice questions focusing on helping students learn quantum mechanics via the Stern-Gerlach experiment that takes advantage of the guided inquiry-based learning sequences in an interactive tutorial on the same topic. The extensive research in developing and validating the multiple-choice question sequence strives to make it effective for students with diverse prior preparation in upper-level undergraduate quantum physics courses. We discuss student performance on assessment task focusing on the Stern-Gerlach experiment after traditional lecture-based instruction vs. after engaging with the research-validated multiple-choice question sequence administered as clicker questions in which students had the opportunity to discuss their responses with their peers.

physics.ed-ph↗

arXiv2020

Student understanding of Fermi energy, the Fermi-Dirac distribution and total electronic energy of a free electron gas

We investigated the difficulties that physics students in upper-level undergraduate quantum mechanics and graduate students after quantum and statistical mechanics core courses have with the Fermi energy, the Fermi-Dirac distribution and total electronic energy of a free electron gas after they had learned relevant concepts in their respective courses. These difficulties were probed by administering written conceptual and quantitative questions to undergraduate students and asking some undergraduate and graduate students to answer those questions while thinking aloud in one-on-one individual interviews. We find that advanced students had many common difficulties with these concepts after traditional lecture-based instruction. Engaging with a sequence of clicker questions improved student performance, but there remains room for improvement in their understanding of these challenging concepts.

physics.ed-ph↗

arXiv2020

Validation and Administration of a Conceptual Survey on the Formalism and Postulates of Quantum Mechanics

We developed and validated a conceptual survey that focuses on the formalism and postulates of quantum mechanics covered in upper-level undergraduate quantum mechanics courses. The concepts included in the Quantum Mechanics Formalism and Postulate Survey (QMFPS) focus on Dirac notation, the Hilbert space, state vectors, physical observables and their corresponding Hermitian operators, compatible and incompatible observables, quantum measurement, time-dependence of quantum states and expectation values, and spin angular momenta. Here we describe the validation and administration of the survey, which has been administered to over 400 upper-level undergraduate and graduate students from six institutions. The QMFPS is valid and reliable for use as a low-stakes test to measure the effectiveness of instruction in an undergraduate quantum mechanics course that covers relevant content. The survey can also be used by instructors to identify student understanding of the formalism and postulates of quantum mechanics at the beginning and end of a graduate quantum mechanics course since graduate students are expected to have taken an undergraduate quantum mechanics course that covers the content included in the survey. We found that undergraduate students who engaged with research-validated learning tools performed better than students who did not on the QMFPS after the first semester of a junior/senior level quantum mechanics course. In addition, the performance of graduate students on QMFPS after instruction in the first semester of a core graduate-level quantum mechanics course was significantly better than the performance of undergraduate students at the end of the first semester of an undergraduate quantum mechanics course. A comparison with the base line data on the validated QMFPS presented here can aid instructors in assessing the effectiveness of their instructional approaches.

physics.ed-ph↗

arXiv2020

Development, validation and in-class evaluation of a sequence of clicker questions on Larmor precession of spin in quantum mechanics

Engaging students with well-designed clicker questions is one of the commonly used research-based instructional strategy in physics courses partly because it has a relatively low barrier to implementation. Moreover, validated robust sequences of clicker questions are likely to provide better scaffolding support and guidance to help students build a good knowledge structure of physics than an individual clicker question on a particular topic. Here we discuss the development, validation and in-class implementation of a clicker question sequence (CQS) for helping advanced undergraduate students learn about Larmor precession of spin, which takes advantage of the learning goals and inquiry-based guided learning sequences in a previously validated Quantum Interactive Learning Tutorial (QuILT). The in-class evaluation of the CQS using peer instruction is discussed by comparing upper-level undergraduate student performance after traditional lecture-based instruction and after engaging with the CQS.

physics.ed-ph↗

arXiv2019

Physics teaching assistants' views of different types of introductory problems: Challenge of perceiving the instructional benefits of context-rich and multiple-choice problems

Given a physics scenario, different problem types presenting that scenario in various ways can emphasize different instructional goals. In this investigation, we examined the views of physics graduate teaching assistants (TAs) about the instructional benefits of different types of introductory problems based upon the same problem scenario. Here we report on TAs' views about two of these problem types that were regarded by TAs as the least instructionally beneficial of all problem types--the context rich and multiple-choice formats. Many TAs listed no pros at all for these problem types, despite being explicitly asked for at least one pro. They viewed multiple-choice questions nearly exclusively as tools for high-stakes summative assessment rather than their possible use as formative assessment tools, e.g., as clicker questions even in large classes. Similarly, TAs viewed context-rich problems as overly challenging, unnecessarily wordy, and too time-consuming to be instructionally beneficial to their students. While TAs' concerns have obvious validity and value, the benefits of well-designed multiple-choice questions as a formative assessment tool was not readily identified by them, nor did the TAs recognize the learning benefits associated with solving context-rich problems. Given the powerful ways multiple-choice and context-rich problems can be used for active engagement and formative assessment in different instructional contexts to meet diverse instructional goals, the lack of enthusiasm for these types of problems has implications for future TA professional development programs.

physics.ed-ph↗

arXiv2017

The impact of peer interaction on the responses to clicker questions in an upper-level quantum mechanics course

In this case study, we investigated the effectiveness of peer interaction on responses to in-class clicker questions in an upper-level quantum mechanics course. We analyzed student performance on clicker questions answered individually and then again after interaction with peers. We also analyzed student performance by topic. In general, the performance on the clicker questions improved after interaction with peers following individual clicker responses. We also find evidence of co-construction of knowledge in that students who did not answer the clicker questions individually were able to answer them correctly after discussion with peers. Finally, we discuss the trends in the percentage of students present in class who responded to the clicker questions in the allotted time as the semester progressed.

physics.ed-ph↗

arXiv2017

Graduate teaching assistants use different criteria when grading introductory physics vs. quantum mechanics problems

Physics graduate teaching assistants (TAs) are often responsible for grading. Physics education research suggests that grading practices that place the burden of proof for explicating the problem solving process on students can help them develop problem solving skills and learn physics. However, TAs may not have developed effective grading practices and may grade student solutions in introductory and advanced courses differently. In the context of a TA professional development course, we asked TAs to grade student solutions to introductory physics and quantum mechanics problems and explain why their grading approaches were different or similar in the two contexts. TAs expected and rewarded reasoning more frequently in the QM context. Our findings suggest that these differences may at least partly be due to the TAs not realizing that grading can serve as a formative assessment tool and also not thinking about the difficulty of an introductory physics problem from an introductory physics student's perspective.

physics.ed-ph↗

arXiv2017

Developing and evaluating an interactive tutorial on degenerate perturbation theory

We discuss an investigation of student difficulties with degenerate perturbation theory (DPT) 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 this topic. We used the difficulties found via research as resources to develop and evaluate a Quantum Interactive Learning Tutorial (QuILT) which strives to help students develop a functional understanding of DPT. We discuss the development of the DPT QuILT and its preliminary evaluation in the undergraduate and graduate courses.

physics.ed-ph↗

arXiv2017

Student difficulties with representations of quantum operators corresponding to observables

Dirac notation is used commonly in quantum mechanics. However, many upper-level undergraduate and graduate students in physics have difficulties with representations of quantum operators corresponding to observables especially when using Dirac notation. To investigate these difficulties, we administered free-response and multiple-choice questions and conducted individual interviews with students in advanced quantum mechanics courses. We discuss the analysis of data on the common difficulties found.

physics.ed-ph↗

arXiv2017

Student difficulties with determining expectation values in quantum mechanics

The expectation value of an observable is an important concept in quantum mechanics. However, upper-level undergraduate and graduate students in physics have both conceptual and procedural difficulties when determining the expectation value of physical observables, especially when using Dirac notation. To investigate these difficulties, we administered free-response and multiple-choice questions and conducted individual interviews with students. Here, we discuss the analysis of data on student difficulties when determining the expectation value.

physics.ed-ph↗