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12535Characterizing representational learning: A combined simulation and tutorial on perturbation theory
https://www.compadre.org/portal/items/detail.cfm?ID=15688
Analyzing, constructing, and translating between graphical, pictorial, and mathematical representations of physics ideas and reasoning flexibly through them (“representational competence”) is a key characteristic of expertise in physics but is a challenge for learners to develop. Interactive computer simulations and University of Washington style tutorials both have affordances to support representational learning. This article describes work to characterize students’ spontaneous use of representations before and after working with a combined simulation and tutorial on first-order energy corrections in the context of quantum-mechanical time-independent perturbation theory. Data were collected from two institutions using pre-, mid-, and post-tests to assess short- and long-term gains. A representational competence level framework was adapted to devise level descriptors for the assessment items. The results indicate an increase in the number of representations used by students and the consistency between them following the combined simulation tutorial. The distributions of representational competence levels suggest a shift from perceptual to semantic use of representations based on their underlying meaning. In terms of activity design, this study illustrates the need to support students in making sense of the representations shown in a simulation and in learning to choose the most appropriate representation for a given task. In terms of characterizing representational abilities, this study illustrates the usefulness of a framework focusing on perceptual, syntactic, and semantic use of representations.Education Foundations/Problem Solving/Representational Usehttps://www.compadre.org/portal/bulletinboard/Thread.cfm?ID=15688Wed, 12 May 2021 10:32:13 ESThttps://www.compadre.org/portal/items/detail.cfm?ID=15688Characterizing representational learning: A combined simulation and tutorial on perturbation theory
https://www.compadre.org/portal/items/detail.cfm?ID=15688
Analyzing, constructing, and translating between graphical, pictorial, and mathematical representations of physics ideas and reasoning flexibly through them (“representational competence”) is a key characteristic of expertise in physics but is a challenge for learners to develop. Interactive computer simulations and University of Washington style tutorials both have affordances to support representational learning. This article describes work to characterize students’ spontaneous use of representations before and after working with a combined simulation and tutorial on first-order energy corrections in the context of quantum-mechanical time-independent perturbation theory. Data were collected from two institutions using pre-, mid-, and post-tests to assess short- and long-term gains. A representational competence level framework was adapted to devise level descriptors for the assessment items. The results indicate an increase in the number of representations used by students and the consistency between them following the combined simulation tutorial. The distributions of representational competence levels suggest a shift from perceptual to semantic use of representations based on their underlying meaning. In terms of activity design, this study illustrates the need to support students in making sense of the representations shown in a simulation and in learning to choose the most appropriate representation for a given task. In terms of characterizing representational abilities, this study illustrates the usefulness of a framework focusing on perceptual, syntactic, and semantic use of representations.Education Foundations/Problem Solving/Representational Usehttps://www.compadre.org/portal/bulletinboard/Thread.cfm?ID=15688Wed, 12 May 2021 10:31:54 ESThttps://www.compadre.org/portal/items/detail.cfm?ID=15688Characterizing representational learning: A combined simulation and tutorial on perturbation theory
https://www.compadre.org/portal/items/detail.cfm?ID=15688
Analyzing, constructing, and translating between graphical, pictorial, and mathematical representations of physics ideas and reasoning flexibly through them (“representational competence”) is a key characteristic of expertise in physics but is a challenge for learners to develop. Interactive computer simulations and University of Washington style tutorials both have affordances to support representational learning. This article describes work to characterize students’ spontaneous use of representations before and after working with a combined simulation and tutorial on first-order energy corrections in the context of quantum-mechanical time-independent perturbation theory. Data were collected from two institutions using pre-, mid-, and post-tests to assess short- and long-term gains. A representational competence level framework was adapted to devise level descriptors for the assessment items. The results indicate an increase in the number of representations used by students and the consistency between them following the combined simulation tutorial. The distributions of representational competence levels suggest a shift from perceptual to semantic use of representations based on their underlying meaning. In terms of activity design, this study illustrates the need to support students in making sense of the representations shown in a simulation and in learning to choose the most appropriate representation for a given task. In terms of characterizing representational abilities, this study illustrates the usefulness of a framework focusing on perceptual, syntactic, and semantic use of representations.Education Foundations/Problem Solving/Representational Usehttps://www.compadre.org/portal/bulletinboard/Thread.cfm?ID=15688Wed, 12 May 2021 10:29:34 ESThttps://www.compadre.org/portal/items/detail.cfm?ID=15688Enhancing student learning of two-level quantum systems with interactive simulations
https://www.compadre.org/portal/items/detail.cfm?ID=15589
The QuVis Quantum Mechanics Visualization project aims to address challenges of quantum mechanics instruction through the development of interactive simulations for the learning and teaching of quantum mechanics. In this article, we describe the evaluation of simulations focusing on two-level systems developed as part of the Institute of Physics Quantum Physics resources. Simulations are research-based and have been iteratively refined using student feedback in individual observation sessions and in-class trials. We give evidence that these simulations are helping students learn quantum mechanics concepts at both the introductory and advanced undergraduate level, and that students perceive simulations to be beneficial to their learning.Quantum Physics/Spin and Finite Dimensional Systems/Two-Level Systemhttps://www.compadre.org/portal/bulletinboard/Thread.cfm?ID=15589Tue, 11 May 2021 15:16:37 ESThttps://www.compadre.org/portal/items/detail.cfm?ID=15589Enhancing student learning of two-level quantum systems with interactive simulations
https://www.compadre.org/portal/items/detail.cfm?ID=15589
The QuVis Quantum Mechanics Visualization project aims to address challenges of quantum mechanics instruction through the development of interactive simulations for the learning and teaching of quantum mechanics. In this article, we describe the evaluation of simulations focusing on two-level systems developed as part of the Institute of Physics Quantum Physics resources. Simulations are research-based and have been iteratively refined using student feedback in individual observation sessions and in-class trials. We give evidence that these simulations are helping students learn quantum mechanics concepts at both the introductory and advanced undergraduate level, and that students perceive simulations to be beneficial to their learning.Quantum Physics/Spin and Finite Dimensional Systems/Two-Level Systemhttps://www.compadre.org/portal/bulletinboard/Thread.cfm?ID=15589Tue, 11 May 2021 15:16:22 ESThttps://www.compadre.org/portal/items/detail.cfm?ID=15589Enhancing student learning of two-level quantum systems with interactive simulations
https://www.compadre.org/portal/items/detail.cfm?ID=15589
The QuVis Quantum Mechanics Visualization project aims to address challenges of quantum mechanics instruction through the development of interactive simulations for the learning and teaching of quantum mechanics. In this article, we describe the evaluation of simulations focusing on two-level systems developed as part of the Institute of Physics Quantum Physics resources. Simulations are research-based and have been iteratively refined using student feedback in individual observation sessions and in-class trials. We give evidence that these simulations are helping students learn quantum mechanics concepts at both the introductory and advanced undergraduate level, and that students perceive simulations to be beneficial to their learning.Education Practices/Instructional Material Design/Simulationhttps://www.compadre.org/portal/bulletinboard/Thread.cfm?ID=15589Tue, 11 May 2021 15:16:01 ESThttps://www.compadre.org/portal/items/detail.cfm?ID=15589The Difference Between a Probability and a Probability Density
https://www.compadre.org/portal/items/detail.cfm?ID=15585
Learning introductory quantum physics is challenging, in part due to the different paradigms in classical mechanics and quantum physics. Classical mechanics is deterministic in that the equations of motion and the initial conditions fully determine a particle’s trajectory. Quantum physics is an inherently probabilistic theory in that only probabilities for measurement outcomes can be determined. Prior to studying quantum physics, students will typically have little experience with probabilistic analyses of physical systems, and thus probability may be a conceptual hurdle for introductory quantum physics students. This article describes two interactive simulations developed as part of the QuVis Quantum Mechanics Visualization Project that aim to bridge the gap between classical mechanics and quantum physics using probabilistic analyses of classical systems. The simulations illustrate how a probability density can be obtained for two classical systems well known to students. The key learning goals of the simulations are to introduce students to probability densities and to help students distinguish between a probability and a probability density. The simulations build on previous work by Bao and Redish, who developed an activity that used pseudo-random video frames of a glider in harmonic motion to derive a classical probability density for this system, and a University of Washington quantum mechanics tutorial focusing on probability and probability density for a classical system. Interactive simulations allow students to easily carry out experiments and change variables that would be difficult to do with real equipment, and help students connect multiple representations by showing explicitly how they are linked. The simulations described here only require basic knowledge of algebra and classical mechanics. They run on touchscreen devices as well as desktop computers, and can be run in a standard web browser from the QuVis website or downloaded for offline use.Quantum Physics/Probability, Waves, and Interferencehttps://www.compadre.org/portal/bulletinboard/Thread.cfm?ID=15585Tue, 11 May 2021 15:06:41 ESThttps://www.compadre.org/portal/items/detail.cfm?ID=15585The Difference Between a Probability and a Probability Density
https://www.compadre.org/portal/items/detail.cfm?ID=15585
Learning introductory quantum physics is challenging, in part due to the different paradigms in classical mechanics and quantum physics. Classical mechanics is deterministic in that the equations of motion and the initial conditions fully determine a particle’s trajectory. Quantum physics is an inherently probabilistic theory in that only probabilities for measurement outcomes can be determined. Prior to studying quantum physics, students will typically have little experience with probabilistic analyses of physical systems, and thus probability may be a conceptual hurdle for introductory quantum physics students. This article describes two interactive simulations developed as part of the QuVis Quantum Mechanics Visualization Project that aim to bridge the gap between classical mechanics and quantum physics using probabilistic analyses of classical systems. The simulations illustrate how a probability density can be obtained for two classical systems well known to students. The key learning goals of the simulations are to introduce students to probability densities and to help students distinguish between a probability and a probability density. The simulations build on previous work by Bao and Redish, who developed an activity that used pseudo-random video frames of a glider in harmonic motion to derive a classical probability density for this system, and a University of Washington quantum mechanics tutorial focusing on probability and probability density for a classical system. Interactive simulations allow students to easily carry out experiments and change variables that would be difficult to do with real equipment, and help students connect multiple representations by showing explicitly how they are linked. The simulations described here only require basic knowledge of algebra and classical mechanics. They run on touchscreen devices as well as desktop computers, and can be run in a standard web browser from the QuVis website or downloaded for offline use.Quantum Physics/Probability, Waves, and Interferencehttps://www.compadre.org/portal/bulletinboard/Thread.cfm?ID=15585Tue, 11 May 2021 15:06:21 ESThttps://www.compadre.org/portal/items/detail.cfm?ID=15585The Difference Between a Probability and a Probability Density
https://www.compadre.org/portal/items/detail.cfm?ID=15585
Learning introductory quantum physics is challenging, in part due to the different paradigms in classical mechanics and quantum physics. Classical mechanics is deterministic in that the equations of motion and the initial conditions fully determine a particle’s trajectory. Quantum physics is an inherently probabilistic theory in that only probabilities for measurement outcomes can be determined. Prior to studying quantum physics, students will typically have little experience with probabilistic analyses of physical systems, and thus probability may be a conceptual hurdle for introductory quantum physics students. This article describes two interactive simulations developed as part of the QuVis Quantum Mechanics Visualization Project that aim to bridge the gap between classical mechanics and quantum physics using probabilistic analyses of classical systems. The simulations illustrate how a probability density can be obtained for two classical systems well known to students. The key learning goals of the simulations are to introduce students to probability densities and to help students distinguish between a probability and a probability density. The simulations build on previous work by Bao and Redish, who developed an activity that used pseudo-random video frames of a glider in harmonic motion to derive a classical probability density for this system, and a University of Washington quantum mechanics tutorial focusing on probability and probability density for a classical system. Interactive simulations allow students to easily carry out experiments and change variables that would be difficult to do with real equipment, and help students connect multiple representations by showing explicitly how they are linked. The simulations described here only require basic knowledge of algebra and classical mechanics. They run on touchscreen devices as well as desktop computers, and can be run in a standard web browser from the QuVis website or downloaded for offline use.Education Practices/Technology/Multimediahttps://www.compadre.org/portal/bulletinboard/Thread.cfm?ID=15585Tue, 11 May 2021 15:05:54 ESThttps://www.compadre.org/portal/items/detail.cfm?ID=15585Enhancing student visual understanding of the time evolution of quantum systems
https://www.compadre.org/portal/items/detail.cfm?ID=14999
Time dependence is of fundamental importance for the description of quantum systems, but is particularly difficult for students to master. We describe the development and evaluation of a combined simulation-tutorial to support the development of visual understanding of time dependence in quantum mechanics. The associated interactive simulation shows the time dependence of an energy eigenstate and a superposition state, and how the time dependence of the probability density arises from that of the wave function. In order to assess transitions in student thinking, we developed a framework to characterize student responses in terms of real and complex mathematical reasoning and classical and quantum visual reasoning. The results of pre-, mid-, and post-tests indicate that the simulation-tutorial supports the development of visual understanding of time dependence, and that visual reasoning is correlated with improved student performance on a question relating to the time evolution of the wave function and the probability density. The results also indicate that the analogy of a classical standing wave for the infinite well energy eigenfunctions may be problematic in cueing incorrect ideas of time dependence.Quantum Physics/Foundations and Measurements/Time Dependencehttps://www.compadre.org/portal/bulletinboard/Thread.cfm?ID=14999Tue, 11 May 2021 15:00:17 ESThttps://www.compadre.org/portal/items/detail.cfm?ID=14999Enhancing student visual understanding of the time evolution of quantum systems
https://www.compadre.org/portal/items/detail.cfm?ID=14999
Time dependence is of fundamental importance for the description of quantum systems, but is particularly difficult for students to master. We describe the development and evaluation of a combined simulation-tutorial to support the development of visual understanding of time dependence in quantum mechanics. The associated interactive simulation shows the time dependence of an energy eigenstate and a superposition state, and how the time dependence of the probability density arises from that of the wave function. In order to assess transitions in student thinking, we developed a framework to characterize student responses in terms of real and complex mathematical reasoning and classical and quantum visual reasoning. The results of pre-, mid-, and post-tests indicate that the simulation-tutorial supports the development of visual understanding of time dependence, and that visual reasoning is correlated with improved student performance on a question relating to the time evolution of the wave function and the probability density. The results also indicate that the analogy of a classical standing wave for the infinite well energy eigenfunctions may be problematic in cueing incorrect ideas of time dependence.Education Practices/Instructional Material Design/Tutorialhttps://www.compadre.org/portal/bulletinboard/Thread.cfm?ID=14999Tue, 11 May 2021 14:59:55 ESThttps://www.compadre.org/portal/items/detail.cfm?ID=14999Enhancing student visual understanding of the time evolution of quantum systems
https://www.compadre.org/portal/items/detail.cfm?ID=14999
Time dependence is of fundamental importance for the description of quantum systems, but is particularly difficult for students to master. We describe the development and evaluation of a combined simulation-tutorial to support the development of visual understanding of time dependence in quantum mechanics. The associated interactive simulation shows the time dependence of an energy eigenstate and a superposition state, and how the time dependence of the probability density arises from that of the wave function. In order to assess transitions in student thinking, we developed a framework to characterize student responses in terms of real and complex mathematical reasoning and classical and quantum visual reasoning. The results of pre-, mid-, and post-tests indicate that the simulation-tutorial supports the development of visual understanding of time dependence, and that visual reasoning is correlated with improved student performance on a question relating to the time evolution of the wave function and the probability density. The results also indicate that the analogy of a classical standing wave for the infinite well energy eigenfunctions may be problematic in cueing incorrect ideas of time dependence.Quantum Physics/Foundations and Measurements/Time Dependencehttps://www.compadre.org/portal/bulletinboard/Thread.cfm?ID=14999Tue, 11 May 2021 14:59:03 ESThttps://www.compadre.org/portal/items/detail.cfm?ID=14999Uniformly Accelerated Reference Frames JS Model
https://www.compadre.org/portal/items/detail.cfm?ID=15584
The Uniformly Accelerated Reference Frames JavaScrip model shows the world lines for six particles. The these point mass particles move in a Cartesian, inertial coordinate system in a Minkowski space M with constant velocity u along straight lines which are parallel to the x-axis of the coordinate system. The user can set the initial x-position and the initial velocity of the particles, as well as the acceleration of the reference frame.
Consider a uniformly accelerated frame (UAF) moving along the positive y-axis. In the simulation the world line of each particle is depicted from the relativistic and the Newtonian point of view. The model shows an “event horizon” in the relativistic model and the difference rate of time measured by two clocks attached at the referenced frame origin and a selected moving particle.
Relativity/Reference Frames/Inertialhttps://www.compadre.org/portal/bulletinboard/Thread.cfm?ID=15584Wed, 05 May 2021 15:07:27 ESThttps://www.compadre.org/portal/items/detail.cfm?ID=15584Tracker Video Analysis and Modeling JS (Beta)
https://www.compadre.org/portal/items/detail.cfm?ID=15557
The JavaScript implementation of the Tracker Video Analysis and Modeling Tool is now available for beta testing. This online program runs within a web browser that supports HTML5 + JavaScript. It allows users to drag and drop Tracker Experiment files or video clips onto the web page to analyze the motion of objects in videos. By overlaying simple dynamical models directly onto videos, students may see how well a model matches the real world. Interference patterns and spectra can also be analyzed.
The original Tracker Java program was written by Doug Brown at Cabrillo College using portions of the the Open Source Physics code library developed by Wolfgang Christian at Davidson College. Tracker was later converted from Java to JavaScript by Doug Brown, Wolfgang Christian and Robert Hanson using the SwingJS system developed by Hanson and his students at St. Olaf College.
Additional Tracker resources, including Tracker help and sample videos, are available from the <a href="https://physlets.org/tracker/">Tracker website</a>.Education Practices/Curriculum Development/Laboratoryhttps://www.compadre.org/portal/bulletinboard/Thread.cfm?ID=15557Tue, 04 May 2021 09:40:23 ESThttps://www.compadre.org/portal/items/detail.cfm?ID=15557Tracker Video Analysis and Modeling JS (Beta)
https://www.compadre.org/portal/items/detail.cfm?ID=15557
The JavaScript implementation of the Tracker Video Analysis and Modeling Tool is now available for beta testing. This online program runs within a web browser that supports HTML5 + JavaScript. It allows users to drag and drop Tracker Experiment files or video clips onto the web page to analyze the motion of objects in videos. By overlaying simple dynamical models directly onto videos, students may see how well a model matches the real world. Interference patterns and spectra can also be analyzed.
The original Tracker Java program was written by Doug Brown at Cabrillo College using portions of the the Open Source Physics code library developed by Wolfgang Christian at Davidson College. Tracker was later converted from Java to JavaScript by Doug Brown, Wolfgang Christian and Robert Hanson using the SwingJS system developed by Hanson and his students at St. Olaf College.
Additional Tracker resources, including Tracker help and sample videos, are available from the <a href="https://physlets.org/tracker/">Tracker website</a>.Education Practices/Curriculum Development/Laboratoryhttps://www.compadre.org/portal/bulletinboard/Thread.cfm?ID=15557Tue, 04 May 2021 09:40:04 ESThttps://www.compadre.org/portal/items/detail.cfm?ID=15557Tracker Video Analysis and Modeling JS (Beta)
https://www.compadre.org/portal/items/detail.cfm?ID=15557
The JavaScript implementation of the Tracker Video Analysis and Modeling Tool is now available for beta testing. This online program runs within a web browser that supports HTML5 + JavaScript. It allows users to drag and drop Tracker Experiment files or video clips onto the web page to analyze the motion of objects in videos. By overlaying simple dynamical models directly onto videos, students may see how well a model matches the real world. Interference patterns and spectra can also be analyzed.
The original Tracker Java program was written by Doug Brown at Cabrillo College using portions of the the Open Source Physics code library developed by Wolfgang Christian at Davidson College. Tracker was later converted from Java to JavaScript by Doug Brown, Wolfgang Christian and Robert Hanson using the SwingJS system developed by Hanson and his students at St. Olaf College.
Additional Tracker resources, including Tracker help and sample videos, are available from the <a href="https://physlets.org/tracker/">Tracker website</a>.Education Practices/Curriculum Development/Laboratoryhttps://www.compadre.org/portal/bulletinboard/Thread.cfm?ID=15557Tue, 04 May 2021 09:38:58 ESThttps://www.compadre.org/portal/items/detail.cfm?ID=15557Tracker Video Analysis and Modeling JS (Beta)
https://www.compadre.org/portal/items/detail.cfm?ID=15557
The JavaScript implementation of the Tracker Video Analysis and Modeling Tool is now available for beta testing. This online program runs within a web browser that supports HTML5 + JavaScript. It allows users to drag and drop Tracker Experiment files or video clips onto the web page to analyze the motion of objects in videos. By overlaying simple dynamical models directly onto videos, students may see how well a model matches the real world. Interference patterns and spectra can also be analyzed.
The original Tracker Java program was written by Doug Brown at Cabrillo College using portions of the the Open Source Physics code library developed by Wolfgang Christian at Davidson College. Tracker was later converted from Java to JavaScript by Doug Brown, Wolfgang Christian and Robert Hanson using the SwingJS system developed by Hanson and his students at St. Olaf College.
Additional Tracker resources, including Tracker help and sample videos, are available from the <a href="https://physlets.org/tracker/">Tracker website</a>.Education Practices/Curriculum Development/Laboratoryhttps://www.compadre.org/portal/bulletinboard/Thread.cfm?ID=15557Tue, 04 May 2021 09:38:25 ESThttps://www.compadre.org/portal/items/detail.cfm?ID=15557A new multimedia resource for teaching quantum mechanics concepts
https://www.compadre.org/portal/items/detail.cfm?ID=12965
We describe a collection of interactive animations and visualizations for teaching quantum mechanics. The animations can be used at all levels of the undergraduate curriculum. Each animation includes a step-by-step exploration that explains the key points. The animations and instructor resources are freely available. By using a diagnostic survey, we report substantial learning gains for students who have worked with the animations.Education Practices/Instructional Material Design/Simulationhttps://www.compadre.org/portal/bulletinboard/Thread.cfm?ID=12965Tue, 04 May 2021 09:21:51 ESThttps://www.compadre.org/portal/items/detail.cfm?ID=12965A new multimedia resource for teaching quantum mechanics concepts
https://www.compadre.org/portal/items/detail.cfm?ID=12965
We describe a collection of interactive animations and visualizations for teaching quantum mechanics. The animations can be used at all levels of the undergraduate curriculum. Each animation includes a step-by-step exploration that explains the key points. The animations and instructor resources are freely available. By using a diagnostic survey, we report substantial learning gains for students who have worked with the animations.Education Practices/Instructional Material Design/Simulationhttps://www.compadre.org/portal/bulletinboard/Thread.cfm?ID=12965Tue, 04 May 2021 09:21:20 ESThttps://www.compadre.org/portal/items/detail.cfm?ID=12965A new multimedia resource for teaching quantum mechanics concepts
https://www.compadre.org/portal/items/detail.cfm?ID=12965
We describe a collection of interactive animations and visualizations for teaching quantum mechanics. The animations can be used at all levels of the undergraduate curriculum. Each animation includes a step-by-step exploration that explains the key points. The animations and instructor resources are freely available. By using a diagnostic survey, we report substantial learning gains for students who have worked with the animations.Education Practices/Instructional Material Design/Simulationhttps://www.compadre.org/portal/bulletinboard/Thread.cfm?ID=12965Tue, 04 May 2021 09:20:56 ESThttps://www.compadre.org/portal/items/detail.cfm?ID=12965