arXiv subjects

Chandralekha Singh

Publications and source records attributed to Chandralekha Singh.

At least 109 records · Page 6Linked to original sources

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.

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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.

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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.

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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.

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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.

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arXiv2020

Why Are There So Few Women in Physics? Reflections on the Experiences of Two Women

Some of the reasons for the underrepresentation of women in physics are evident in the reflections of two undergraduate women. Leia is a chemistry major who loves college-level physical chemistry and quantum mechanics but does not identify with the discipline of physics, partly because she has a low level of self-efficacy as a physicist and has received very little recognition for her work and learning in physics. Paulette is a physics major who loves physics but feels isolated by the current physics learning environment. She reluctantly dropped honors introductory lab after being snubbed by her male classmates who partnered with one another, leaving her to work alone. Paulette's experiences with condescending male professors activated a stereotype threat about who can succeed in physics that caused her to disengage in class. We also discuss what these women felt has helped them so far and explore their suggestions for what would help women in physics courses as they pursue their quest for a physical science degree.

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arXiv2020

Can students apply the concept of "which-path" information learned in the context of Mach Zehnder Interferometer to the double-slit experiment?

The ability to use concepts learned in one context to solve problems in a different context (i.e., transfer of learning) is a hallmark of expertise in physics. The majority of the studies on transfer of learning in physics have focused on introductory students. However, compared to advanced students, introductory students have significantly less prior relevant knowledge and skills which may be crucial for promoting effective transfer. Here, we examine upper-level undergraduate and graduate students' ability to transfer their learning about the concept of "which-path" information and its relation to whether or not interference is observed from the context of the Mach Zehnder Interferometer (MZI) to a new context of the double-slit experiment (DSE). Students worked through a tutorial on the MZI in which they learned to use the concept of "which-path" information to reason about interference of single photons when polarizers with various orientations are placed in one or both paths of the MZI. After working on the MZI tutorial, students were asked similar questions in the isomorphic context of the DSE before any instruction about the DSE and we examined the extent to which transfer of learning about "which-path" information occurred from the MZI to the DSE context. We find evidence suggesting that positive transfer of learning from the MZI to the DSE occurred despite the lack of an instructional intervention designed to help students recognize the similarity between the two contexts. The effectiveness of the MZI tutorial in promoting positive transfer of learning from one context to another in quantum mechanics sheds light on the expertise of the advanced physics students. Instructors of advanced physics courses can take advantage of the findings presented here which shows the difference between introductory and advanced students' ability to transfer from one context to another.

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arXiv2020

Inequity exemplified by underrepresented minority students receiving lower grades and having higher rates of attrition across STEM disciplines

Underrepresented minority (URM) students are subjected to historically rooted inequities when pursuing an education, especially in STEM disciplines with little diversity. In order to make STEM education equitable and inclusive, evidence for how students from different racial/ethnic demographics are faring is necessary. We use 10 years of institutional data at a large public university to investigate trends in the majors that Asian, URM, and White students declare, drop after declaring, and earn degrees in as well as the GPA of the students who drop or earn a degree. We find that higher percentages of the URM students drop most majors compared to other students and these trends are particularly pronounced in physics and economics. Moreover, we find alarming GPA trends in that the URM students consistently earn lower grades than their Asian and White peers. Furthermore, in some STEM disciplines, the URM students who earn a degree are earning the same grades as the Asian and White students who dropped the major. This troubling trend may signify lack of sufficient support, mentoring, and guidance to ensure excellence of the URM students who are already severely disadvantaged. These quantitative findings call for making learning environments equitable and inclusive so that many URM students who come to college with severe disadvantages are appropriately supported and can excel similar to other students.

physics.ed-ph↗

arXiv2020

Gender inequities throughout STEM: Women with higher grades drop STEM majors while men persist

Efforts to promote equity and inclusion using evidence-based approaches are vital to correct long-standing societal inequities that have disadvantaged women and discouraged them from pursuing studies, e.g., in many STEM disciplines. We use 10 years of institutional data at a large public university to investigate trends in the majors that men and women declare, drop after declaring, and earn degrees in as well as the GPA of the students who drop or earn a degree. We find that the majors with the lowest number of students also have the highest rates of attrition. Moreover, we find alarming GPA trends, e.g., women who drop majors on average earn higher grades than men who drop those majors, and in some STEM majors, women who drop the majors were earning comparable grades to men who persist in those majors. These quantitative findings call for a better understanding of the reasons students drop a major and for making learning environments equitable and inclusive.

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arXiv2020

A mismatch between self-efficacy and performance: Undergraduate women in engineering tend to have lower self-efficacy despite earning higher grades than men

There is a significant underrepresentation of women in many Science, Technology, Engineering, and Mathematics (STEM) majors and careers. Prior research has shown that self-efficacy can be a critical factor in student learning, and that there is a tendency for women to have lower self-efficacy than men in STEM disciplines. This study investigates gender differences in the relationship between engineering students' self-efficacy and course grades in foundational courses. By focusing on engineering students, we examined these gender differences simultaneously in four STEM disciplines (mathematics, engineering, physics, and chemistry) among the same population. Using survey data collected longitudinally at three time points and course grade data from five cohorts of engineering students at a large US-based research university, effect sizes of gender differences are calculated using Cohen's d on two measures: responses to survey items on discipline-specific self-efficacy and course grades in all first-year foundational courses and second-year mathematics courses. In engineering, physics, and mathematics courses, we find sizeable discrepancies between self-efficacy and performance, with men appearing significantly more confident than women despite small or reverse direction differences in grades. In chemistry, women earn higher grades and have higher self-efficacy. The patterns are consistent across courses within each discipline. All self-efficacy gender differences close by the fourth year except physics self-efficacy. The disconnect between self-efficacy and course grades across subjects provides useful clues for targeted interventions to promote equitable learning environments. The most extreme disconnect occurs in physics and may help explain the severe underrepresentation of women in "physics-heavy" engineering disciplines, highlighting the importance of such interventions.

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arXiv2020

Not all disadvantages are equal: Racial/ethnic minority students have largest disadvantage of all demographic groups in both STEM and non-STEM GPA

An analysis of institutional data to understand the outcome of the many obstacles faced by students from historically disadvantaged backgrounds is important in order to work towards promoting equity and inclusion for all students. We use 10 years of institutional data at a large public research university to investigate the grades earned (both overall and in STEM courses only) by students categorized on four demographic characteristics: gender, race/ethnicity, low-income status, and first-generation college student status. We find that on average across all years of study and for all clusters of majors, underrepresented minority students experience a larger penalty to their mean overall and STEM GPA than even the most disadvantaged non-URM students. Moreover, the underrepresented minority students with additional disadvantages due to socioeconomic status or parental education level were even further penalized in their average GPA. Furthermore, we also find that while women in all demographic groups had a higher average overall GPA, these gender differences are almost completely non-existent in STEM GPA except among the most privileged students. These findings suggest that there is need to provide support to bridge the gaps that emanate from historical disadvantages to certain groups.

physics.ed-ph↗

arXiv2020

Hermione and the Secretary: How gendered task division in introductory physics labs can disrupt equitable learning

Physics labs provide a unique opportunity for students to grow their physics identity and science identity in general since they provide students with opportunity to tinker with experiments and analyze data in a low-stakes environment. However, it is important to ensure that all students are benefiting from the labs equally and have a positive growth trajectory. Through interviews and reflexive ethnographic observations, we identify and analyze two common modes of work that may disadvantage female students in introductory physics labs. Students who adopt the Secretary archetype are relegated to recording and analyzing data, and thus miss out on much of the opportunity to grow their physics and science identities by engaging fully in the experimental work. Meanwhile, students in the Hermione mode shoulder a disproportionate amount of managerial work, and also do not get adequate opportunity to engage with different aspects of the experimental work that are essential for helping them develop their physics and science identities. Using a physics identity framework, we analyze interviews and observational data to investigate how students under these modes of work may experience stunted growth in their physics and science identity trajectories in their physics lab course. This stunted growth then perpetuates and reinforces societal stereotypes and biases about who does physics. This categorization not only gives a vocabulary to discussions about equity in the lab, but can also serve as a useful touchstone for those who seek to center equity in efforts to transform physics instruction.

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arXiv2019

In a physics curriculum only introductory physics course grades show gender differences but do not predict future course performance for physics majors

Analysis of institutional data for physics majors showing predictive relationships between required mathematics and physics courses in various years is important for contemplating how the courses build on each other and whether there is need to make changes to the curriculum for the majors to strengthen these relationships. We use 15 years of institutional data at a large research university to investigate how introductory physics and mathematics courses predict male and female physics majors' performance on required advanced physics and mathematics courses. We used Structure Equation Modeling (SEM) to investigate these predictive relationships and find that among introductory and advanced physics and mathematics courses, there are gender differences in performance in favor of male students only in the introductory physics courses after controlling for high school GPA. We found that a measurement invariance fully holds in a multi-group SEM by gender, so it was possible to carry out analysis with gender mediated by introductory physics and high school GPA. Moreover, we find that these introductory physics courses that have gender differences do not predict performance in advanced physics courses. Also, introductory mathematics courses predict performance in advanced mathematics courses which in turn predict performance in advanced physics courses. Furthermore, apart from the introductory physics courses that do not predict performance in future physics courses, there is a strong predictive relationship between the sophomore, junior and senior level physics courses.

physics.ed-ph↗

arXiv2019

What's happening in traditional and inquiry-based introductory labs? An integrative analysis at a large research university

There is a growing recognition of the need to replace "cookbook"-style introductory labs with more-meaningful learning experiences. To identify the strengths and weaknesses of a mix of cookbook-style and inquiry-based labs, an introductory lab course currently being reformed was observed following a reflexive ethnographic protocol and pre and post E-CLASS surveys were administered. We analyzed data to identify shortcomings of the current labs and to determine areas for improvement.

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arXiv2019

All aboard! Challenges and successes in professional development for physics lab TAs

At large research universities in the USA, introductory physics labs are often run by graduate student teaching assistants (TAs). Thus, efforts to reform introductory labs should address the need for effective and relevant TA professional development. We developed and implemented a research-based professional development program that focuses on preparing TAs to effectively support inquiry-based learning in the lab. We identify positive effects by examining three possible ways in which the professional development might have impacted TAs and their work. First, we examine lab TAs' written reflections to understand the effect of the program on TAs' ways of thinking about student learning. Second, we observe and categorize TA-student interactions in the lab in order to investigate whether TA behaviors are changing after the professional development. Third, we examine students' attitudes toward experimental science and present one example case in which students' attitudes improve for those TAs who `buy in' to the professional development. Our results suggest lab TA professional development may have a tangible positive impact on TA performance and student learning.

physics.ed-ph↗

arXiv2019

Comparing introductory physics and astronomy students' attitudes and approaches to problem solving

We examined how introductory physics students' attitudes and approaches to problem solving compare to those of introductory astronomy students, using a previously validated survey, the Attitudes and Approaches to Problem Solving (AAPS) survey. In addition, we compared the performance of the introductory physics and astronomy students on the factors which were identified in a factor analysis in the original validation study. We found that introductory astronomy students' overall average AAPS score was significantly more favorable than that of introductory physics students (p < 0.01), and the effect size was large (Cohen's d = 0.81). We also found that introductory astronomy students' scores were more favorable in all clusters of questions except for one factor involving drawing diagrams and writing scratchwork while solving problems. We also found that introductory physics and astronomy students were equally capable of solving two isomorphic problems posed to them, and that the majority of introductory physics and introductory astronomy students reported that the problem posed in the astronomy context was more interesting to them. Interviews suggest that the context of astronomy in problem solving may be more interesting for students and could be one possible explanation for the more favorable AAPS scores amongst introductory astronomy students compared to introductory physics students. Instructors of introductory physics courses should heed these findings which indicate that it may be beneficial for instructors of introductory physics courses to incorporate problems into their instruction which contain real-world contexts, which may serve to increase student interest-level, and which could help create more favorable attitudes and approaches towards problem solving.

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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.

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