Title: Graduate student understanding of quantum mechanical spin
A framework of cyclic observation and triangulation was applied over a period of 4 years to graduate student difficulties related to quantum spin, in which numerous in-class observations and interviews were used to identify common, persistent difficulties. Written items were iteratively developed over two years to add a quantitative component. Items were administered to graduate students at two collaborating institutions, over three years. We find that students generally obtained scores or correct proportions ranging from 30%-70% on the written items, and answering patterns were similar across all institutions. All items were identified by the course instructors as being relevant to instructional goals of the course. We report on a number of graduate student difficulties with spin, including orthogonality of spin-1/2 states, projections of spin states, spin addition, and exchange symmetry. We briefly discuss possible theoretical frameworks through which to interpret these results. 2022 more »« less
Hurwich, Talia; Nicholas, Diana; Fleming, Fraser F.; Perignat, Elaine; King, Daniel; Katz-Buonincontro, Jennifer; Gondek, Paul
(, International Journal of Designs for Learning)
Founding Editor-in-Chief
Professor Elizabeth Boling, Indiana University
(Ed.)
Two graduate-level courses were designed to advance creative, interdisciplinary teamwork among graduate students. Over three years, the two courses underwent three iterations largely focused on refinements to teamwork, which led to high-quality student products. This design case presents the three course iterations, how course design decisions were made, and the kind of results that were achieved. The paper concludes with reflections for designing higher education courses focused on creativity, interdisciplinarity, and teamwork.
Justice, Paul; Marshman, Emily; Singh, Chandralekha
(, European Journal of Physics)
Abstract 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.
Schaller, Michael D.; Gencheva, Marieta; Gunther, Michael R.; Weed, Scott A.
(, BMC Medical Education)
Abstract Background Traditionally, doctoral student education in the biomedical sciences relies on didactic coursework to build a foundation of scientific knowledge and an apprenticeship model of training in the laboratory of an established investigator. Recent recommendations for revision of graduate training include the utilization of graduate student competencies to assess progress and the introduction of novel curricula focused on development of skills, rather than accumulation of facts. Evidence demonstrates that active learning approaches are effective. Several facets of active learning are components of problem-based learning (PBL), which is a teaching modality where student learning is self-directed toward solving problems in a relevant context. These concepts were combined and incorporated in creating a new introductory graduate course designed to develop scientific skills (student competencies) in matriculating doctoral students using a PBL format. Methods Evaluation of course effectiveness was measured using the principals of the Kirkpatrick Four Level Model of Evaluation. At the end of each course offering, students completed evaluation surveys on the course and instructors to assess their perceptions of training effectiveness. Pre- and post-tests assessing students’ proficiency in experimental design were used to measure student learning. Results The analysis of the outcomes of the course suggests the training is effective in improving experimental design. The course was well received by the students as measured by student evaluations (Kirkpatrick Model Level 1). Improved scores on post-tests indicate that the students learned from the experience (Kirkpatrick Model Level 2). A template is provided for the implementation of similar courses at other institutions. Conclusions This problem-based learning course appears effective in training newly matriculated graduate students in the required skills for designing experiments to test specific hypotheses, enhancing student preparation prior to initiation of their dissertation research.
Dukes, April; Besterfield-Sacre, Mary; Fullerton_Shirey, Susan
(, ASEE Conferences)
Despite calls over the past twenty years to develop graduate STEM education models that prepare students for the new post-graduate workforce, few innovations in graduate STEM education have been disseminated. Given the diversity of graduate candidates’ prior skills, preparation, and individual career aspirations, modernizing STEM graduate programs is needed to support and empower student success in graduate programs and beyond. In this session, participants will learn about new research into the development and implementation of a personalized learning model (PLM) for graduate STEM education employed in a chemical engineering department at an R1 university. Our PLM integrates student-centered approaches in coursework, research, and professional development in multiple programmatic components. The key components of our PLM include guided student creation of independent development plans (IDPs), modularization of graduate courses and professional development streams, scaffolding curricular instruction to prioritize independence and mastery, using IDPs for directed research and career discussions and assessment of student performance and learning, and evaluation of the program from current students, alumni, faculty, and industry partners. Our comprehensive PLM plan is designed to maximize impact through personalized learning touchpoints throughout all aspects of graduate training. This presentation will focus on one element of our PLM, the modularization of the chemical engineering core graduate courses. To ensure the learning in core graduate courses reflects the diverse needs of chemical engineers, we generated a body of knowledge (BOK) for graduate chemical engineering in collaboration with our technical advisory board (TAB), which included chemical engineers and people that work with chemical engineers from industry, national labs, academia, and entrepreneurial representatives. We started by collecting the learning objectives (LO’s) from all core chemical engineering courses: Thermodynamics, Kinetics and Reactor Design, Transport Phenomena, Mathematical Methods, and Issues in Research and Teaching. The LO’s were refined by alignment with course assignments and activities and re-written using the most accurate Bloom’s Taxonomy verbs in collaboration with an instructional designer. We utilized GroupWisdomTM for group concept mapping of the new LO’s and provided an opportunity for the TAB to add new LO’s, identified by the individuals in the TAB to be critical for success in each member’s occupation. LO’s for the chemical engineering core courses were sorted on the level of knowledge (undergraduate, graduate, and specialized) and rated for importance by the TAB. Using GroupWisdom’sTM analytic tool for creating a similarity matrix for sorting the level of LO’s, multidimensional scaling, and hierarchical cluster analysis, all core course LO’s have been grouped into 6 clusters. These clusters, along with the current course list and the LO importance ratings, helped us visualize converting chemical engineering core courses into 1-credit hour modules. This restructured curriculum offers opportunities for ensuring that students have learned the requisite prior knowledge by review of essential undergraduate principles, streamlining essential graduate-level material, and supporting self-directed learning through the selection of specialized modules that align with students’ research and career goals. This proposed approach shifts core graduate chemical engineering education to an asset-based system, addressing knowledge gaps and ensuring rigorous, tailored learning experiences.
Mule’, T; Houston, S.; Piontek, J.; Webb, J.; Harrell-Williams, L.
(, Proceedings of the forty-fourth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)
Lischka, A. E.; Dyer, E. B.; Jones, R. S.; Lovett, J. N.; Strayer, J.; & Drown, S.
(Ed.)
Many higher education institutions in the United States provide mathematics tutoring services for undergraduate students. These informal learning experiences generally result in increased final course grades (Byerly & Rickard, 2018; Rickard & Mills, 2018; Xu et al., 2014) and improved student attitudes toward mathematics (Bressoud et al., 2015). In recent years, research has explored the beliefs and practices of undergraduate and, sometimes graduate, peer tutors, both prior to (Bjorkman, 2018; Johns, 2019; Pilgrim et al., 2020) and during the COVID19 pandemic (Gyampoh et al., 2020; Mullen et al., 2021; Van Maaren et al., 2021). Additionally, Burks and James (2019) proposed a framework for Mathematical Knowledge for Tutoring Undergraduate Mathematics adapted from Ball et al. (2008) Mathematical Knowledge for Teaching, highlighting the distinction between tutor and teacher. The current study builds on this body of work on tutors’ beliefs by focusing on mathematical sciences graduate teaching assistants (GTAs) who tutored in an online setting during the 2020-2021 academic year due to the COVID-19 pandemic. Specifically, this study addresses the following research question: What were the mathematical teaching beliefs and practices of graduate student tutors participating in online tutoring sessions through the mathematics learning center (MLC) during the COVID-19 pandemic?
Heckler, Andrew F., and Porter, Chris D. Graduate student understanding of quantum mechanical spin. Retrieved from https://par.nsf.gov/biblio/10391491. 2022 PERC Proceedings . Web. doi:10.1119/perc.2022.pr.Heckler.
Heckler, Andrew F., & Porter, Chris D. Graduate student understanding of quantum mechanical spin. 2022 PERC Proceedings, (). Retrieved from https://par.nsf.gov/biblio/10391491. https://doi.org/10.1119/perc.2022.pr.Heckler
@article{osti_10391491,
place = {Country unknown/Code not available},
title = {Graduate student understanding of quantum mechanical spin},
url = {https://par.nsf.gov/biblio/10391491},
DOI = {10.1119/perc.2022.pr.Heckler},
abstractNote = {A framework of cyclic observation and triangulation was applied over a period of 4 years to graduate student difficulties related to quantum spin, in which numerous in-class observations and interviews were used to identify common, persistent difficulties. Written items were iteratively developed over two years to add a quantitative component. Items were administered to graduate students at two collaborating institutions, over three years. We find that students generally obtained scores or correct proportions ranging from 30%-70% on the written items, and answering patterns were similar across all institutions. All items were identified by the course instructors as being relevant to instructional goals of the course. We report on a number of graduate student difficulties with spin, including orthogonality of spin-1/2 states, projections of spin states, spin addition, and exchange symmetry. We briefly discuss possible theoretical frameworks through which to interpret these results. 2022},
journal = {2022 PERC Proceedings},
author = {Heckler, Andrew F. and Porter, Chris D.},
editor = {Frank, B. and Jones, D. and Ryan, Q.}
}
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