An official website of the United States government
We examine students’ challenges in determining the number of distinct many-particle stationary states for a system of noninteracting identical particles, focusing on how these insights guided the design, validation, and evaluation of a quantum interactive learning tutorial (QuILT) to aid students’ understanding. Specifically, we focus on systems with a fixed number of available single-particle states and particles, where the total energy is not fixed. The QuILT is designed to provide scaffolding support to help students learn these complex concepts more effectively. This study was conducted in advanced quantum mechanics courses, where written questions were administered to students in class following traditional instruction on the relevant concepts. Additionally, individual interviews were conducted with students to gain deeper insights. Our findings reveal that both upper-level undergraduate and graduate students face similar challenges in understanding these concepts. Additionally, difficulty with basic concepts in combinatorics that are necessary to answer the questions correctly was also found. The QuILT offers scaffolding support to help undergraduate and graduate students systematically reason through these concepts. Published by the American Physical Society2024
more »
« less
Student understanding of Fermi energy, the Fermi–Dirac distribution and total electronic energy of a free electron gas
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.
more »
« less
- Award ID(s):
- 1806691
- PAR ID:
- 10303206
- Publisher / Repository:
- IOP Publishing
- Date Published:
- Journal Name:
- European Journal of Physics
- Volume:
- 41
- Issue:
- 1
- ISSN:
- 0143-0807
- Page Range / eLocation ID:
- Article No. 015704
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
[This paper is part of the Focused Collection in Investigating and Improving Quantum Education through Research.] 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 wave functions 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 wave functions in the position or momentum representation and vice versa. They also struggle when translating the wave function between the position and momentum representations. The research presented here describes the difficulties that students have with these concepts and how the 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 wave functions in position and momentum representation and with translating between these representations. We discuss the effectiveness of the QuILT from in-class implementation and evaluation. Published by the American Physical Society2024more » « less
-
Abstract 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 (SGE) 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 (MQS) 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 SGE after traditional lecture-based instruction versus after engaging with the research-validated MQS administered as clicker questions in which students had the opportunity to discuss their responses with their peers.more » « less
-
Parks, Beth (Ed.)We describe a study focusing on students' and faculty members' reasoning about problems of differing cognitive complexity related to the double-slit experiment (DSE) with single particles. In the first phase of the study, students in advanced quantum mechanics courses were asked these questions in written form. Additionally, individual interviews were conducted with ten students in which they were asked follow-up questions to make their thought processes explicit on the challenging problems. Students did well on the straightforward problem, showing they had some knowledge of the DSE after traditional instruction, but they struggled on the more complex ones. Even if explicitly asked to do so in interviews, students were often uncomfortable performing calculations or making approximations and simplifications, instead preferring to stick with their gut feeling. In the second phase of the study, the problems were broken down into more pointed questions to investigate whether students had knowledge of relevant concepts, whether they would do calculations as part of their solution approach if explicitly asked, and whether they explicitly noted using their gut feeling. While the faculty members' responses suggest that they could seamlessly move between conceptual and quantitative reasoning, most students were unable to combine concepts represented by different equations to solve the problems quantitatively. We conclude with instructional implications.more » « less
-
Abstract Research-validated multiple-choice questions comprise an easy-to-implement instructional tool for scaffolding student learning and providing formative assessment of students’ knowledge. We present findings from the implementation of a research-validated multiple-choice question sequence on the basics of two-state quantum systems, including inner products, outer products, translation between Dirac notation and matrix representation in a particular basis, and change of basis. This study was conducted in an advanced undergraduate quantum mechanics course, in both online and in-person learning environments, across three years. For each cohort, students had their learning assessed after traditional lecture-based instruction in relevant concepts before engaging with the multiple-choice question sequence. Their performance was evaluated again afterward with a similar assessment and compared to their earlier performance. We analyze, compare, and discuss the trends observed in the three implementations.more » « less
