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Chandralekha Singh

Publications and source records attributed to Chandralekha Singh.

At least 217 records · Page 12Linked to original sources

Performance of Graduate Students at Identifying Introductory Physics Students' Difficulties Related to Kinematics Graphs

The Test of Understanding Graphs in Kinematics (TUG-K) is a multiple choice test developed by Beichner to assess students' understanding of kinematics graphs. Many of the items on the TUG-K have strong distractor choices which correspond to introductory students' common difficulties with kinematics graphs. Instruction is unlikely to be effective if instructors do not know these common difficulties and take them into account in their instructional design. We evaluate the performance of first year physics graduate students at identifying introductory students' common difficulties related to kinematics graphs. In particular, for each item on the TUG-K, the graduate students were asked to identify which incorrect answer choice they thought would be most commonly selected by introductory physics students if they did not know the correct answer after instruction in relevant concepts. We used the introductory student data from Beichner's original paper to assess graduate students' knowledge of introductory students' difficulties. Furthermore, we selected the four questions on the TUG-K on which the graduate student performance was the poorest for a more detailed analysis which included think-aloud interviews. We present results which can partly account for the poor graduate student performance on these questions and also inform instruction in professional development courses.

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Instructional Goals and Grading Practices of Graduate Students after One Semester of Teaching Experience

Teaching assistants (TAs) are often responsible for grading student solutions. Since grading communicates instructors' expectations, TAs' grading decisions play a crucial role in forming students' approaches to problem solving (PS) in physics. We investigated the change in grading practices and considerations of 18 first-year graduate students participating in a TA professional development (PD) course. The TAs were asked to state their beliefs about the purpose of grading, to grade a set of specially designed student solutions, and to explain their grading decisions. We found that after one semester of teaching experience and participation in PD, TAs did not significantly change their goals for grading (i.e., a learning opportunity for both the student and the instructor) or their grading practice. In addition, TAs' grading practice frequently did not align with their goals. However, some TAs' perceptions of the level of explication required in a student solution did change. Our findings suggest that in order for PD to help TAs better coordinate their goals with appropriate grading practices, PD should focus on TAs' perception of sufficient reasoning in student solutions.

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Grading Practices and Considerations of Graduate Students at the Beginning of their Teaching Assignment

Research shows that expert-like approaches to problem-solving can be promoted by encouraging students to explicate their thought processes and follow a prescribed problem-solving strategy. Since grading communicates instructors' expectations, teaching assistants' grading decisions play a crucial role in forming students' approaches to problem-solving in physics. We investigated the grading practices and considerations of 43 graduate teaching assistants (TAs). The TAs were asked to grade a set of specially designed student solutions and explain their grading decisions. We found that in a quiz context, a majority of TAs noticed but did not grade on solution features which promote expert-like approaches to problem-solving. In addition, TAs graded differently in quiz and homework contexts, partly because of how they considered time limitations in a quiz. Our findings can inform professional development programs for TAs.

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A Review of Student Difficulties in Upper-Level Quantum Mechanics

Learning advanced physics, in general, is challenging not only due to the increased mathematical sophistication but also because one must continue to build on all of the prior knowledge acquired at the introductory and intermediate levels. In addition, learning quantum mechanics can be especially challenging because the paradigms of classical mechanics and quantum mechanics are very different. Here, we review research on student reasoning difficulties in learning upper-level quantum mechanics and research on students' problem-solving and metacognitive skills in these courses. Some of these studies were multi-university investigations. The investigations suggest that there is large diversity in student performance in upper-level quantum mechanics regardless of the university, textbook, or instructor and many students in these courses have not acquired a functional understanding of the fundamental concepts. The nature of reasoning difficulties in learning quantum mechanics is analogous to reasoning difficulties found via research in introductory physics courses. The reasoning difficulties were often due to over-generalizations of concepts learned in one context to another context where they are not directly applicable. Reasoning difficulties in distinguishing between closely related concepts and in making sense of the formalism of quantum mechanics were common. We conclude with a brief summary of the research-based approached that take advantage of research on student difficulties in order to improve teaching and learning of quantum mechanics.

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Development and Evaluation of a Tutorial to Improve Students' Understanding of a Lock-in amplifier

A lock-in amplifier is a versatile instrument frequently used in physics research. However, many students struggle with the basic operating principles of a lock-in amplifier which can lead to a variety of difficulties. To improve students' understanding, we have been developing and evaluating a research-based tutorial which makes use of a computer simulation of a lock-in amplifier. The tutorial is based on a field-tested approach in which students realize their difficulties after predicting the outcome of simulated experiments involving a lock-in amplifier and check their predictions using the simulated lock-in amplifier. Then, the tutorial provides guidance and strives to help students develop a coherent understanding of the basics of a lock-in amplifier. The tutorial development involved interviews with physics faculty members and graduate students and iteration of many versions of the tutorial with professors and graduate students. The student difficulties with lock-in amplifiers and the development and assessment of the research-based tutorial to help students develop a functional understanding of this device are discussed.

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Improving Students' Understanding of Lock-In Amplifiers

The lock-in amplifier is a versatile instrument frequently used in physics research. However, many students struggle with the basic operating principles of a lock-in amplifier which can lead to a variety of difficulties. To improve students' understanding, we have been developing and evaluating a research-based tutorial which makes use of a computer simulation of a lock-in amplifier. The tutorial allows students to realize their conceptual difficulties by comparing their predictions about how a lock-in amplifier will behave with the outcome of simulated experiments. After being confronted with discrepancies between their predictions and the lock-in amplifier results, the tutorial targets the common difficulties that students have and leads them to develop a deeper understanding of the principles of lock-in amplification.

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Improving Students' Understanding of Lock-in Amplifiers

A lock-in amplifier is a versatile instrument frequently used in physics research. However, many students struggle with the basic operating principles of a lock-in amplifier which can lead to a variety of difficulties. To improve students' understanding, we have been developing and evaluating a research-based tutorial which makes use of a computer simulation of a lock-in amplifier. The tutorial is based on a field-tested approach in which students realize their difficulties after predicting the outcome of simulated experiments involving a lock-in amplifier and check their predictions using the simulated lock-in amplifier. Then, the tutorial guides and helps students develop a coherent understanding of the basics of a lock-in amplifier. The tutorial development involved interviews with physics faculty members and graduate students and iteration of many versions of the tutorial with professors and graduate students. The student difficulties and the development and assessment of the research-based tutorial are discussed.

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Development of an interactive tutorial on quantum key distribution

We describe the development of a Quantum Interactive Learning Tutorial (QuILT) on quantum key distribution, a context which involves a practical application of quantum mechanics. The QuILT helps upper-level undergraduate students learn quantum mechanics using a simple two state system and was developed based upon the findings of cognitive research and physics education research. One protocol used in the QuILT involves generating a random shared key over a public channel for encrypting and decrypting information using single photons with non-orthogonal polarization states, and another protocol makes use of two entangled spin-1/2 particles. The QuILT uses a guided approach and focuses on helping students build links between the formalism and conceptual aspects of quantum physics without compromising the technical content. We also discuss findings from a preliminary in-class evaluation.

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Analogous Patterns of Student Reasoning Difficulties in Introductory Physics and Upper-Level Quantum Mechanics

Very little is known about how the nature of expertise in introductory and advanced courses compares in knowledge-rich domains such as physics. We develop a framework to compare the similarities and differences between learning and patterns of student difficulties in introductory physics and quantum mechanics. Based upon our framework, we argue that the qualitative patterns of student reasoning difficulties in introductory physics bear a striking resemblance to those found for upper-level quantum mechanics. The framework can guide the design of teaching and learning tools.

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Investigating Student Difficulties with Time dependence of Expectation Values in Quantum Mechanics

Quantum mechanics is challenging even for advanced undergraduate and graduate students. In the Schrödinger representation, the wave function evolves in time according to the time dependent Schrödinger equation. The time dependence of the wave function gives rise to time dependence of the expectation value of observables. We have been exploring the difficulties that advanced undergraduate and graduate students have with time dependence of expectation values in quantum mechanics. We have developed and administered conceptual free response and multiple-choice questions to students to investigate these difficulties. We also interviewed 23 students individually using a think-aloud protocol to obtain a better understanding of the rationale behind students' written responses. We find that many students struggle with time dependence of expectation values of observables. We discuss some findings.

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Investigating Student Difficulties with Dirac Notation

Quantum mechanics is challenging even for advanced undergraduate and graduate students. Dirac notation is a convenient notation used extensively in quantum mechanics. We have been investigating the difficulties that the advanced undergraduate and graduate students have with Dirac notation. We administered written free response and multiple-choice questions to students and also conducted semi-structured individual interviews with 23 students using a think-aloud protocol to obtain a better understanding of the rationale behind their responses. We find that many students struggle with Dirac notation and they are not consistent in using this notation across various questions in a given test. In particular, whether they answer questions involving Dirac notation correctly or not is context dependent.

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Developing an Interactive Tutorial on a Quantum Eraser

We are developing a quantum interactive learning tutorial (QuILT) on a quantum eraser for students in upperlevel quantum mechanics. The QuILT exposes students to contemporary topics in quantum mechanics and uses a guided approach to learning. It adapts existing visualization tools to help students build physical intuition about quantum phenomena and strives to help them develop the ability to apply quantum principles in physical situations. The quantum eraser apparatus in the gedanken (thought) experiments and simulations that students learn from in the QuILT uses a MachZehnder Interferometer with single photons. We also discuss findings from a preliminary in-class evaluation.

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Developing an Interactive Tutorial on a Mach-Zehnder Interferometer with Single Photons

We are developing a Quantum Interactive Learning Tutorial (QuILT) on a Mach-Zehnder Interferometer with single photons to expose upper-level students in quantum mechanics courses to contemporary applications. The QuILT strives to help students develop the ability to apply fundamental quantum principles to physical situations and explore differences between classical and quantum ideas. The QuILT adapts visualization tools to help students build physical intuition about quantum phenomena and focuses on helping them integrate qualitative and quantitative understanding. We also discuss findings from a preliminary in-class evaluation.

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The effect of giving explicit incentives to correct mistakes on subsequent problem solving in quantum mechanics

One attribute of experts is that they are likely to learn from their own mistakes. Experts are unlikely to make the same mistakes when asked to solve a problem a second time, especially if they had access to a correct solution. Here, we discuss a study spanning several years in which advanced undergraduate physics students in a quantum mechanics course were given incentives to correct their mistakes in the midterm exam and they could get back up to 50% of the points lost on each midterm exam problem. The solutions to the midterm exam problems were provided to all students in both groups but those who corrected their mistakes were provided the solution after they submitted their corrections to the instructor. The performance on the final exam on the same problems suggests that students who were given incentives to correct their mistakes significantly outperformed those who were not given an incentive. The incentive to correct mistakes had the greatest impact on the final exam performance of students who performed poorly on the midterm exam.

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Developing and evaluating a tutorial on the double-slit experiment

Learning quantum mechanics is challenging, even for upper-level undergraduate and graduate students. Interactive tutorials which build on students' prior knowledge can be useful tools to enhance student learning. We have been investigating student difficulties with the quantum mechanics pertaining to the double-slit experiment in various situations. Here we discuss the development and evaluation of a Quantum Interactive Learning Tutorial (QuILT) which makes use of an interactive simulation to improve student understanding. We summarize common difficulties and discuss the extent to which the QuILT is effective in addressing them in two types of courses.

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Student difficulties with the probability distribution for measuring energy and position in quantum mechanics

We have been investigating the difficulties that students in upper-level undergraduate courses have in determining the probability distribution for measuring energy and position as a function of time when the initial wave function is explicitly given. We administered written free-response and multiple-choice questions to investigate these difficulties. We find that students have common difficulties with these concepts. We discuss some of the findings.

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Student difficulties with quantum states while translating state vectors in Dirac notation to wave functions in position and momentum representations

We administered written free-response and multiple-choice questions and conducted individual interviews to investigate the difficulties that upper-level undergraduate and graduate students have with quantum states while translating state vectors in Dirac notation to wave functions in position and momentum representations. We find that students share common difficulties with translating a state vector written in Dirac notation to the wave function in position or momentum representation.

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A Framework for Understanding the Patterns of Student Reasoning Difficulties in Quantum Mechanics

Compared with introductory physics, relatively little is known about the development of expertise in advanced physics courses, especially in the case of quantum mechanics. Here, we describe a framework for understanding the patterns of student reasoning difficulties and how students develop expertise in quantum mechanics. The framework posits that the challenges many students face in developing expertise in quantum mechanics are analogous to the challenges introductory students face in developing expertise in introductory classical mechanics. This framework incorporates both the diversity in upper-level students' prior preparation, goals, and motivation in general (i.e., the facts that even in upper-level courses, students may be inadequately prepared, have unclear goals, and have insufficient motivation to excel) as well as the "paradigm shift" from classical mechanics to quantum mechanics. The framework is based on empirical investigations demonstrating that the patterns of reasoning, problem-solving, and self-monitoring difficulties in quantum mechanics bear a striking resemblance to those found in introductory classical mechanics. Examples from research in quantum mechanics and introductory classical mechanics are discussed to illustrate how the patterns of difficulties are analogous as students learn to unpack the respective principles and grasp the formalism in each knowledge domain during the development of expertise. Embracing such a framework and contemplating the parallels between the difficulties in these two knowledge domains can enable researchers to leverage the extensive literature for introductory physics education research to guide the design of teaching and learning tools for helping students develop expertise in quantum mechanics.

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