AAPT Winter Meeting 2018 Special Collection

Here we discuss blackbody radiation within the context of classical theory. We note that nonrelativistic classical mechanics and relativistic classical electrodynamics have contrasting scaling symmetries which influence the scattering of radiation. Also, nonrelativistic mechanical systems can be accurately combined with relativistic electromagnetic radiation only provided the nonrelativistic mechanical systems are the low-velocity limits of fully relativistic systems. Application of the no-interaction theorem for relativistic systems limits the scattering mechanical systems for thermal radiation to relativistic classical electrodynamic systems, which involve the Coulomb potential. Whereas the naive use of nonrelativistic scatterers or nonrelativistic classical statistical mechanics leads to the Rayleigh–Jeans spectrum, the use of fully relativistic scatterers leads to the Planck spectrum for blackbody radiation within classical physics.

Suppose that a piston of nonzero mass encloses an ideal gas in a vertical cylinder. The piston and cylinder are thermally insulated so that no energy is lost by heat transfer to the surroundings. If the piston is set into motion, it oscillates like a block on a spring. However, the motion is damped because the gas density and pressure immediately adjacent to the piston are higher or lower than the bulk values, depending on whether the piston is compressing or expanding the gas, respectively. That automatically gives rise to a drag force linear in the velocity of the piston. It is not necessary to add extra dissipative terms such as kinetic friction between the piston and cylinder, or viscosity of the gas, to damp out the motion of the piston. The ideas should thus be helpful to undergraduate students performing a Rüchardt experiment to measure the ratio of the heat capacities of a gas.

This study used eye-tracking technology to investigate students' visual attention while taking the Force Concept Inventory (FCI) in a web-based interface. Eighty nine university students were randomly selected into a pre-test group and a post-test group. Students took the 30-question FCI on a computer equipped with an eye-tracker. There were seven weeks of instruction between the pre- and post-test data collection. Students' performance on the FCI improved significantly from pre-test to post-test. Meanwhile, the eye-tracking results reveal that the time students spent on taking the FCI test was not affected by student performance and did not change from pre-test to post-test. Analysis of students' attention to answer choices shows that on the pre-test students primarily focused on the naïve choices and ignored the expert choices. On the post-test, although students had shifted their primary attention to the expert choices, they still kept a high level of attention to the naïve choices, indicating significant conceptual mixing and competition during problem solving. Outcomes of this study provide new insights on students' conceptual development in learning physics.

We explore the similarities and differences between the electric dipole studied in introductory physics and the purportedly equivalent elementary experiment in which the electric potential is measured on a conductive sheet as a current flows. The former is a three-dimensional electrostatic dipole while the latter is a two-dimensional steady-state dipole. In spite of these differences, and as shown in this work, the potentials due to these dipoles look very similar. This may be misleading to either students or unaware instructors.

This is the first part of a broader study, exploring the contextual variations of the responses of 149 first year (non-physics major) university students at two South African universities in Cape Town. The data analysis was done in terms of the (i) forced choice responses (FCR), (ii) free written responses and (iii) personal interviews. This paper presents the development of the instrument (aspects of circuits questionnaire, or ACQ) used in the exploratory study and the results obtained from the FCR analysis of 60 students. The results showed that the student responses are triggered by the context framed by the questions and the results obtained from investigations using light bulbs cannot be generalised and may be reinterpreted.

Traditional lab sections in introductory physics courses at Mount Royal University were replaced by a new style of lab called 'labatorials' developed by the Physics Education Development Group at the University of Calgary. Using labatorials in introductory physics courses has lowered student anxiety and strengthened student engagement in lab sessions. Labatorials provide instant feedback to the students and instructors. Interviews with students who had completed Introductory Physics labatorials as well as the anonymous comments left by them showed that labatorials have improved student satisfaction. Students improved their understanding of concepts compared to students who had taken traditional labs in earlier years. Moreover a combination of labatorials and reflective writing can promote positive change in students' epistemological beliefs.

There has been an increased focus on the integration of practices into physics curricula, with a particular emphasis on integrating computation into the undergraduate curriculum of scientists and engineers. In this paper, we present a university-level, introductory physics course for science and engineering majors at Michigan State University called P³ (projects and practices in physics) that is centred around providing introductory physics students with the opportunity to appropriate various science and engineering practices. The P³ design integrates computation with analytical problem solving and is built upon a curriculum foundation of problem-based learning, the principles of constructive alignment and the theoretical framework of community of practice. The design includes an innovative approach to computational physics instruction, instructional scaffolds, and a unique approach to assessment that enables instructors to guide students in the development of the practices of a physicist. We present the very positive student related outcomes of the design gathered via attitudinal and conceptual inventories and research interviews of students' reflecting on their experiences in the P³ classroom.

Inquiry-based learning is a pedagogical approach where students are motivated to pose their own questions when facing problems or scenarios. In physics learning, students are turned into scientists who carry out experiments, collect and analyze data, formulate and evaluate hypotheses, and so on. Lab experimentation is essential for inquiry-based learning, yet there is a drawback with traditional hands-on labs in the high costs associated with equipment, space, and maintenance staff. Virtual laboratories are helpful to reduce these costs. This paper enriches the virtual lab ecosystem by providing an integrated environment to automate experimentation tasks. In particular, our environment supports: (i) scripting and running experiments on virtual labs, and (ii) collecting and analyzing data from the experiments. The current implementation of our environment supports virtual labs created with the authoring tool Easy Java/Javascript Simulations. Since there are public repositories with hundreds of freely available labs created with this tool, the potential applicability to our environment is considerable.

We propose an epistemic measure of physics in terms of the ability to discriminate between the purely mathematical, physical (i.e. dependent on empirical inputs) and nominal (i.e. empty of mathematical or physical content) propositions appearing in a typical derivation in physics. The measure can be relevant in understanding the maths–physics link hurdles among college students. To illustrate the idea, we construct a tool for a familiar derivation (involving specific heats of an ideal gas), and use it for a sample of students from three different institutes. The reliability of the tool is examined. The results indicate, as intuitively expected, that epistemic clarity correlates with content clarity. Data yield several significant trends on the extent and kinds of epistemic pitfalls prevalent among physics undergraduates.

The Mach–Zehnder interferometer has played an important role both in quantum and classical physics research over the years. In physics education, it has been used as a didactic tool for quantum physics teaching, allowing fundamental concepts, such as particle–wave duality, to be addressed from the very beginning. For a student to understand the novelties of the quantum scenario, it is first worth introducing the classical picture. In this paper, we introduce a new version of the software developed by our research group to deepen the discussion on the classical picture of the Mach–Zehnder interferometer. We present its equivalence with the double slit experiment and we derive the mathematical expressions relating to the interference pattern. We also explore the concept of visibility (which is very important for understanding wave–particle complementarity in quantum physics) to help students become familiar with this experiment and to enhance their knowledge of its counterintuitive aspects. We use the software articulated by the mathematical formalism and phenomenological features. We also present excerpts of the discursive interactions of students using the software in didactic situations.

Particle–wave duality is a central tenet of quantum physics, and an electron has wave-like properties. Introductory texts discuss the wavelength–momentum relationship $\lambda =h/p$, but do not discuss the frequency–energy relationship. This is curious since a wave is periodic both in space and time. The discussion in more advanced texts is not satisfactory either since two different expressions for the frequency are given based on the relativistic and non-relativistic expression for the electron energy. The relativistic expression yields the correct frequency, and we explain why the expression based on the Schrödinger equation gives the incorrect expression. We argue that the electron frequency should be discussed at the introductory level.

One key objective of physics teaching is the promotion of conceptual understanding. Additionally, the critical faculty is universally seen as a central quality to be developed in students. In recent years, however, teaching objectives have placed stronger emphasis on skills than on concepts, and there is a risk that conceptual structuring may be disregarded. The question therefore arises as to whether it is possible for students to develop a critical stance without a conceptual basis, leading in turn to the issue of possible links between the development of conceptual understanding and critical attitude. In an in-depth study to address these questions, the participants were seven prospective physics and chemistry teachers. The methodology included a 'teaching interview', designed to observe participants' responses to limited explanations of a given phenomenon and their ensuing intellectual satisfaction or frustration. The explanatory task related to the physics of how a survival blanket works, requiring a full and appropriate system analysis of the blanket. The analysis identified five recurrent lines of reasoning and linked these to judgments of adequacy of explanation, based on metacognitive/affective (MCA) factors, intellectual (dis)satisfaction and critical stance. Recurrent themes and MCA factors were used to map the intellectual dynamics that emerged during the interview process. Participants' critical attitude was observed to develop in strong interaction with their comprehension of the topic. The results suggest that most students need to reach a certain level of conceptual mastery before they can begin to question an oversimplified explanation, although one student's replies show that a different intellectual dynamics is also possible. The paper ends with a discussion of the implications of these findings for future research and for decisions concerning teaching objectives and the design of learning environments.

In this article we characterize transient learning challenges as learning challenges that arise out of teaching situations rather than conflicts with prior knowledge. We propose that these learning challenges can be identified by paying careful attention to the representations that students produce. Once a transient learning challenge has been identified, teachers can create interventions to address it. By illustration, we argue that an appropriate way to design such interventions is to create variation around the disciplinary-relevant aspects associated with the transient learning challenge.

Since the pioneering experiments of Forrester et al (1955 Phys. Rev. 99 1691) and Hanbury Brown and Twiss (1956 Nature 177 27; Nature 178 1046), along with the introduction of the laser in the 1960s, the systematic analysis of random fluctuations of optical fields has developed to become an indispensible part of physical optics for gaining insight into features of the fields. In 1985 Joseph W Goodman prefaced his textbook on statistical optics with a strong commitment to the 'tools of probability and statistics' (Goodman 2000 Statistical Optics (New York: John Wiley & Sons Inc.)) in the education of advanced optics. Since then a wide range of novel undergraduate optical counting experiments and corresponding pedagogical approaches have been introduced to underpin the rapid growth of the interest in coherence and photon statistics. We propose low cost experimental steps that are a fair way off 'real' quantum optics, but that give deep insight into random optical fluctuation phenomena: (1) the introduction of statistical methods into undergraduate university optical lab work, and (2) the connection between the photoelectrical signal and the characteristics of the light source. We describe three experiments and theoretical approaches which may be used to pave the way for a well balanced growth of knowledge, providing students with an opportunity to enhance their abilities to adapt the 'tools of probability and statistics'.

Frequently, in university-level general physics courses, after explaining the theory, exercises are set based on examples that illustrate the application of concepts and laws. Traditionally formulated numerical exercises are usually solved by the teacher and students through direct replacement of data in formulae. It is our contention that such strategies can lead to the superficial and erroneous resolution of such exercises. In this paper, we provide an example that illustrates that students tend to solve problems in a superficial manner, without applying fundamental problem-solving strategies such as qualitative analysis, hypothesis-forming and analysis of results, which prevents them from arriving at a correct solution. We provide evidence of the complexity of an a priori simple exercise in physics, although the theory involved may seem elementary at first sight. Our aim is to stimulate reflection among instructors to follow these results when using examples and solving exercises with students.

In undergraduate statistical mechanics courses the Ising model always plays an important role because it is the simplest non-trivial model used to describe magnetic systems. The one-dimensional model is easily solved analytically, while the two-dimensional one can be solved exactly by the Onsager solution. For this reason, numerical simulations are usually used to solve the two-dimensional model. Keeping in mind that the two-dimensional model is the platform for studying phase transitions, it is usually an exercise in computational undergraduate courses because its numerical solution is relatively simple to implement and its critical exponents are perfectly known. The purpose of this article is to present a detailed numerical study of the second-order phase transition in the two-dimensional Ising model at an undergraduate level, allowing readers not only to compare the mean-field solution, the exact solution and the numerical one through a complete study of the order parameter, the correlation function and finite-size scaling, but to present the techniques, along with hints and tips, for solving it themselves. We present the elementary theory of phase transitions and explain how to implement Markov chain Monte Carlo simulations and perform them for different lattice sizes with periodic boundary conditions. Energy, magnetization, specific heat, magnetic susceptibility and the correlation function are calculated and the critical exponents determined by finite-size scaling techniques. The importance of the correlation length as the relevant parameter in phase transitions is emphasized.

The higher derivatives of motion are rarely discussed in the teaching of classical mechanics of rigid bodies; nevertheless, we experience the effect not only of acceleration, but also of jerk and snap. In this paper we will discuss the third and higher order derivatives of displacement with respect to time, using the trampolines and theme park roller coasters to illustrate this concept. We will also discuss the effects on the human body of different types of acceleration, jerk, snap and higher derivatives, and how they can be used in physics education to further enhance the learning and thus the understanding of classical mechanics concepts.

Within the context of higher education for science or engineering undergraduates, we present an inquiry-driven learning path aimed at developing a more meaningful conceptual understanding of the electron dynamics in semiconductors in the presence of applied electric fields. The electron transport in a nondegenerate n-type indium phosphide bulk semiconductor is modelled using a multivalley Monte Carlo approach. The main characteristics of the electron dynamics are explored under different values of the driving electric field, lattice temperature and impurity density. Simulation results are presented by following a question-driven path of exploration, starting from the validation of the model and moving up to reasoned inquiries about the observed characteristics of electron dynamics. Our inquiry-driven learning path, based on numerical simulations, represents a viable example of how to integrate a traditional lecture-based teaching approach with effective learning strategies, providing science or engineering undergraduates with practical opportunities to enhance their comprehension of the physics governing the electron dynamics in semiconductors. Finally, we present a general discussion about the advantages and disadvantages of using an inquiry-based teaching approach within a learning environment based on semiconductor simulations.

In this paper, we present an interesting experiment to turn the vibratory light from an incandescent light bulb into audible sound. Inspired by research on the photoacoustic effect (PAE) using lasers, we construct a similar device in an undergraduate physics laboratory with everyday articles including light bulbs, glass beakers and soot. Using our device, a distinct sound is detected and analysed experimentally. Particular attention is paid to the attenuation effect of the acoustic signal, which can be explained by modifying the existing theory and using the adiabatic boundary condition according to the incident light source we use. This demonstration is a comprehensive experiment with the combination of sound, light and heat. The modification on the model can help undergraduate students gain an intuitive understanding of different boundary conditions.

We have developed a new introductory physics/chemistry programme that teaches advanced science topics and practical laboratory skills to freshmen undergraduate students through the use of student-led, bona fide research activities. While many recent attempts to improve college-level physics education have focused on integrating interactive demonstrations and activities into traditional passive lectures, we have taken the idea of active-learning several steps further. Working in conjunction with several research faculty at Binghamton University, we have created a programme that puts undergraduate students on an accelerated path towards working in real research laboratories performing publishable research. Herein, we describe in detail the programme goals, structure, and educational content, and report on our promising initial student outcomes.

Although he is best known as an American statesman, Benjamin Franklin also made important contributions to electrical science in the mid-18th century. At the time, the Leyden jar, the first capacitor, had just been invented, and Franklin performed experiments to determine the source of the spark and shock that occurred on discharge of the jar. In these experiments, he used Leyden jars and Franklin squares (parallel-plate capacitors) that could be disassembled and reassembled. These devices later became known as dissectible capacitors. One of the more interesting results Franklin obtained was that an electrified capacitor containing a dielectric could be disassembled, the electrodes discharged, and the capacitor reassembled without sacrificing its ability to produce a spark and shock. This result is contrary to what one expects from today's theory for capacitors involving ideal dielectrics (those possessing polarization and no other special properties such as surface effects): all charge is on the electrodes, and once they are discharged the capacitor is no longer electrified. During the years since Franklin's observations, additional experiments have been performed and various explanations offered for the cause of Franklin's results. In this paper, we first review the details for Franklin's experiments, and then we describe a very simple experiment that can be performed today with a parallel-plate capacitor that gives results similar to Franklin's. Next we discuss the experiments of Addenbrooke and Zeleny, performed in the first half of the 20th century, which provide plausible explanations for Franklin's observations. Finally we describe the relationship of Franklin's dissectible parallel-plate capacitor to another important 18th century invention—Volta's generator of static electricity, the electrophorus.

When connections between related observations and facts are not being made, introductory science classes can be perceived as an accumulation of disjointed equations with the risk of losing both students' interest as well as their grasp of the materials. In astronomy we have to walk a tightrope between being complete in our presentation of modern-day findings and skirting the surface of quantum mechanics. We introduce Wien's displacement law, Stefan–Boltzmann's law, Hubble's law, and we talk about the age of the Universe and when it first became transparent. The derivation of all these laws and their applications to get numbers out of observations requires knowledge of modern physics, knowledge that students have not acquired (yet), so we tend to choose to not make connections between them. In here, we offer an alternative approach to overcome these drawbacks: we make connections between the main tenets of the laws, such as the temperature dependence that enters Stefan–Boltzmann's law, and processes that students are familiar with, such as the acceleration of electrons. In doing so we reduce the number of disjointed facts presented to students, and we are able to relate equations to imagery that does not rely on faulty representations.