Background Graduate teaching assistants (GTAs) often lead laboratory and tutorial sections in science, technology, engineering, and mathematics (STEM), especially at large, research-intensive universities. GTAs’ performance as instructors can impact student learning experience as well as learning outcomes. In this study, we observed 11 chemistry GTAs and 11 physics GTAs in a research-intensive institution in the southeastern USA. We observed the GTAs over two consecutive semesters in one academic year, resulting in a total of 58 chemistry lab observations and 72 physics combined tutorial and lab observations. We used a classroom observation protocol adapted from the Laboratory Observation Protocol for Undergraduate STEM (LOPUS) to document both GTA and student behaviors. We applied cluster analysis separately to the chemistry lab observations and to the physics combined tutorial and lab observations. The goals of this study are to classify and characterize GTAs’ instructional styles in reformed introductory laboratories and tutorials, to explore the relationship between GTA instructional style and student behavior, and to explore the relationship between GTA instructional style and the nature of laboratory activity. Results We identified three instructional styles among chemistry GTAs and three different instructional styles among physics GTAs. The characteristics of GTA instructional styles we identified in our samples are different from those previously identified in a study of a traditional general chemistry laboratory. In contrast to the findings in the same prior study, we found a relationship between GTAs’ instructional styles and student behaviors: when GTAs use more interactive instructional styles, students appear to be more engaged. In addition, our results suggest that the nature of laboratory activities may influence GTAs’ use of instructional styles and student behaviors. Furthermore, we found that new GTAs appear to behave more interactively than experienced GTAs. Conclusion GTAs use a variety of instructional styles when teaching in the reformed laboratories and tutorials. Also, compared to traditional laboratory and tutorial sections, reformed sections appear to allow for more interaction between the nature of lab activities, GTA instructional styles, and student behaviors. This implies that high-quality teaching in reformed laboratories and tutorials may improve student learning experiences substantially, which could then lead to increased learning outcomes. Therefore, effective GTA professional development is particularly critical in reformed instructional environments.
In quantum mechanics, probability amplitudes are complex numbers and the relative phases between the terms in superposition states have measurable effects. This article describes an investigation into sophomore-and junior-level students' reasoning patterns in relating relative phases and real-world quantum phenomena. The investigation involved one observational experiment and three testing experiments, during which we formulated and tested three hypotheses that allow us to gain insights into why students have difficulty recognizing the measurable effects of relative phases. We found that, in both spin-1=2 and infinite square well contexts, many students do not recognize that quantum states differing only by a relative phase are experimentally distinguishable. Moreover, student ability to recognize the measurable effects of relative phase does not improve when given (i) a task that specifically prompts students to compare the probabilities for a particular observable and (ii) a task that does not require taking inner products or changing basis. We also examined the extent to which lacking proficiency with complex numbers may have hindered student understanding of relative phase. The data indicate that most students are proficient with complex numbers. These findings suggest that many students do not, in fact, recognize the purpose of using complex numbers in superposition states. We discuss possible explanations for why students do not seem to recognize this purpose, and we also provide suggestions for future avenues of research.
Quantum states have complex probability amplitudes that are sometimes represented by positive real numbers multiplied by complex exponentials. Although the overall phase of a superposition state does not affect the probabilities, the relative phases between the component basis states can have measurable effects. A thorough grasp of relative phase is needed for students to understand various key ideas in quantum mechanics, including quantum interference and time dependence. We present preliminary results from an investigation into student understanding of the measurable effects of relative phases that was conducted in sophomore-and junior-level quantum mechanics courses at the University of Washington (UW). The findings suggest that many students do not recognize that relative phases have measureable effects and tend to overlook the important role that complex numbers play in quantum mechanics. I.
Time dependence is an important concept in quantum mechanics that has been shown to be difficult for many students. In trying to understand the problems that students encounter, the Physics Education Group at the University of Washington is examining student ability to reason about the period of quantum states. As part of this investigation, we have begun to probe student understanding of period in other contexts (e.g., phasors and circular motion). Results from analogous written tasks administered in introductory and sophomore-level courses reveal related difficulties. The findings have implications for instruction and are guiding the design of curriculum (Tutorials in Physics: Quantum Mechanics) that is intended to improve student understanding of time dependence in quantum mechanics.
The Born rule, which describes the formalism for determining probabilities, is one of the most fundamental postulates in quantum mechanics. This paper presents results from an investigation into how students apply the Born rule to determine probabilities for energy and position measurements. The investigation includes two stages with independent methods: a quantitative analysis of student written work and a qualitative analysis of student individual interviews. The data from written tasks suggest that after instruction many students have not developed a coherent model for determining probabilities that they can apply to observables regardless of whether the eigenvalues are discrete or continuous. Moreover, many students seem to lack a functional understanding of quantum states and inner products that allows them to translate between Dirac notation and wave function representation. These results motivate student interviews, which allow us to probe student reasoning in depth. Prior research suggests that various features of each notation used in quantum mechanics may have an impact on how students perform computations. We postulate that the features of quantum notations may also interact with student sensemaking. Therefore, we analyze student interviews through the lens of the structural features of quantum notations framework. In particular, we discuss how different structural features may facilitate or hinder student sensemaking about concepts relevant to determining probabilities. The results from both quantitative and qualitative data suggest that unsuccessfully differentiating between a wave function and its associated state vector in Dirac notation may be a primary barrier for students to develop a model for determining probabilities for discrete and continuous cases.
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