Reforming a large lecture modern physics course for engineering majors using a PER-based design

We have reformed a large lecture modern physics course for engineering majors by radically changing both the content and the learning techniques implemented in lecture and homework. Traditionally this course has been taught in a manner similar to the equivalent course for physics majors, focusing on mathematical solutions of abstract problems. Based on interviews with physics and engineering professors, we developed a syllabus and learning goals focused on content that was more useful to our actual student population: engineering majors. The content of this course emphasized reasoning development, model building, and connections to real world applications. In addition we implemented a variety of PER-based learning techniques, including peer instruction, collaborative homework sessions, and interactive simulations. We have assessed the effectiveness of reforms in this course using pre/post surveys on both content and beliefs. We have found significant improvements in both content knowledge and beliefs compared with the same course before implementing these reforms and a corresponding course for physics majors.Comment: To be published in the Proceedings of the Physics Education Research Conference 200

Assessing the Effectiveness of a Computer Simulation in Introductory Undergraduate Environments

We present studies documenting the effectiveness of using a computer simulation, specifically the Circuit Construction Kit (CCK) developed as part of the Physics Education Technology Project (PhET) [1, 2], in two environments: an interactive college lecture and an inquiry-based laboratory. In the first study conducted in lecture, we compared students viewing CCK to viewing a traditional demonstration during Peer Instruction [3]. Students viewing CCK had a 47% larger relative gain (11% absolute gain) on measures of conceptual understanding compared to traditional demonstrations. These results led us to study the impact of the simulation's explicit representation for visualizing current flow in a laboratory environment, where we removed this feature for a subset of students. Students using CCK with or without the explicit visualization of current performed similarly to each other on common exam questions. Although the majority of students in both groups favored the use of CCK over real circuit equipment, the students who used CCK without the explicit current model favored the simulation more than the other grou

Black Holes in Higher-Derivative Gravity

Extensions of Einstein gravity with higher-order derivative terms arise in string theory and other effective theories, as well as being of interest in their own right. In this paper we study static black-hole solutions in the example of Einstein gravity with additional quadratic curvature terms. A Lichnerowicz-type theorem simplifies the analysis by establishing that they must have vanishing Ricci scalar curvature. By numerical methods we then demonstrate the existence of further black-hole solutions over and above the Schwarzschild solution. We discuss some of their thermodynamic properties, and show that they obey the first law of thermodynamics.Comment: Typos corrected, discussion added, figure changed. 4 pages, 6 figure

Lichnerowicz Modes and Black Hole Families in Ricci Quadratic Gravity

A new branch of black hole solutions occurs along with the standard Schwarzschild branch in $n$-dimensional extensions of general relativity including terms quadratic in the Ricci tensor. The standard and new branches cross at a point determined by a static negative-eigenvalue eigenfunction of the Lichnerowicz operator, analogous to the Gross-Perry-Yaffe eigenfunction for the Schwarzschild solution in standard $n=4$ dimensional general relativity. This static eigenfunction has two r\^oles: both as a perturbation away from Schwarzschild along the new black-hole branch and also as a threshold unstable mode lying at the edge of a domain of Gregory-Laflamme-type instability of the Schwarzschild solution for small-radius black holes. A thermodynamic analogy with the Gubser and Mitra conjecture on the relation between quantum thermodynamic and classical dynamical instabilities leads to a suggestion that there may be a switch of stability properties between the old and new black-hole branches for small black holes with radii below the branch crossing point.Comment: 33 pages, 8 figure

Spherically Symmetric Solutions in Higher-Derivative Gravity

Extensions of Einstein gravity with quadratic curvature terms in the action arise in most effective theories of quantised gravity, including string theory. This article explores the set of static, spherically symmetric and asymptotically flat solutions of this class of theories. An important element in the analysis is the careful treatment of a Lichnerowicz-type `no-hair' theorem. From a Frobenius analysis of the asymptotic small-radius behaviour, the solution space is found to split into three asymptotic families, one of which contains the classic Schwarzschild solution. These three families are carefully analysed to determine the corresponding numbers of free parameters in each. One solution family is capable of arising from coupling to a distributional shell of matter near the origin; this family can then match on to an asymptotically flat solution at spatial infinity without encountering a horizon. Another family, with horizons, contains the Schwarzschild solution but includes also non-Schwarzschild black holes. The third family of solutions obtained from the Frobenius analysis is nonsingular and corresponds to `vacuum' solutions. In addition to the three families identified from near-origin behaviour, there are solutions that may be identified as `wormholes', which can match symmetrically on to another sheet of spacetime at finite radius.Comment: 57 pages, 6 figures; version appearing in journal; minor corrections and clarifications to v

Mapping the dynamic interactions between vortex species in highly anisotropic superconductors

Here we use highly sensitive magnetisation measurements performed using a Hall probe sensor on single crystals of highly anisotropic high temperature superconductors $Bi_{2}Sr_{2}CaCu_{2}O_{8}$ to study the dynamic interactions between the two species of vortices that exist in such superconductors. We observe a remarkable and clearly delineated high temperature regime that mirrors the underlying vortex phase diagram. Our results map out the parameter space over which these dynamic interaction processes can be used to create vortex ratchets, pumps and other fluxonic devices.Comment: 7 pages, 3 figures, to be published in Supercond. Sci. Techno

Correlating Student Beliefs With Student Learning Using The Colorado Learning Attitudes about Science Survey

A number of instruments have been designed to probe the variety of attitudes, beliefs, expectations, and epistemological frames taught in our introductory physics courses. Using a newly developed instrument -- the Colorado Learning Attitudes about Science Survey (CLASS)[1] -- we examine the relationship between students' beliefs about physics and other educational outcomes, such as conceptual learning and student retention. We report results from surveys of over 750 students in a variety of courses, including several courses modified to promote favorable beliefs about physics. We find positive correlations between particular student beliefs and conceptual learning gains, and between student retention and favorable beliefs in select categories. We also note the influence of teaching practices on student beliefs

A Study of Educational Simulations Part I - Engagement and Learning

Interactive computer simulations with complex representations and sophisticated graphics are a relatively new addition to the classroom, and research in this area is limited. We have conducted over 200 individual student interviews during which the students described what they were thinking as they interacted with simulations. These interviews were conducted as part of the research and design of simulations for the Physics Education Technology (PhET) project. PhET is an ongoing project that has developed over 60 simulations for use in teaching physics, chemistry, and physical science. These interviews are a rich source of information about how students interact with computer simulations and what makes an educationally effective simulation. We have observed that simulations can be highly engaging and educationally effective, but only if the student's interaction with the simulation is directed by the student's own questioning. Here we describe our design process, what features are effective for engaging students in educationally productive interactions and the underlying principles which support our empirically developed guidelines. In a companion paper we describe in detail the design features used to create an intuitive simulation for students to use

Developing and Researching PhET simulations for Teaching Quantum Mechanics

Quantum mechanics is difficult to learn because it is counterintuitive, hard to visualize, mathematically challenging, and abstract. The Physics Education Technology (PhET) Project, known for its interactive computer simulations for teaching and learning physics, now includes 18 simulations on quantum mechanics designed to improve learning of this difficult subject. Our simulations include several key features to help students build mental models and intuitions about quantum mechanics: visual representations of abstract concepts and microscopic processes that cannot be directly observed, interactive environments that directly couple students' actions to animations, connections to everyday life, and efficient calculations so students can focus on the concepts rather than the math. Like all PhET simulations, these are developed using the results of education research and feedback from educators, and are tested in student interviews and classroom studies. This article provides an overview of the PhET quantum simulations and their development. We also describe research demonstrating their effectiveness and share some insights about student thinking that we have gained from our research on quantum simulations.Comment: accepted by American Journal of Physics; v2 includes an additional study, more explanation of research behind claims, clearer wording, and more reference