The aim of this Physics Education Research project was to implement a modified version
of Calibrated Peer Review and measure the impacts in junior-level students' scientific
writing. The project developed and implemented a set of guiding questions, instructor
written examples, and a rubric which were implemented in a multi-staged process,...
One source of di culty for students in Thermodynamics courses is their unfamiliarity with partial derivatives and the associated mathematical procedures. At Oregon State University, a mechanical analogue of thermodynamic systems, called the Partial Derivative Machine (PDM), has been designed. The PDM represents an attempt to make the mathematics of...
A combination of theoretical perspectives is used to create a rich description of student reasoning when facing a highly-geometric electricity and magnetism problem in an upper-division active-engagement physics classroom at Oregon State University. Geometric reasoning as students encounter problem situations ranging from familiar to novel is described using van Zee...
Chain rules are critical to the process of solving many thermodynamics-related partial derivatives. This study evaluates the solution method and error evolution of students’ responses to a pair of chain rule problems in an upper-level undergraduate thermodynamics course. Students’ responses were categorized by solution method. Students’ solution methods included implicit...
Presented here is a case study of the problem-solving behaviors of upper-division undergraduate physics majors. This study explores the role of visual representations in students' problem solving and provides a foundation for investigating how students' use of visualization changes in the upper-division physics major. Three independent studies were conducted on...
Mathematical sophistication increases rapidly as students transition from lower- to upper-division physics courses. Complex algebra is one of the mathematical tools that is not introduced or used in lower-division physics courses but is pervasive throughout upper-division courses. In this dissertation, I study middle-division physics students' developing fluency with complex number...
This thesis explores student understanding of divergence in physics settings. The various uses of divergence in physics are detailed. Textbook approaches to divergence are categorized as geometric, curvilinear coordinate, discussion-based, and algebraic statement. Textbook approaches to the divergence theorem are categorized as geometric, equivalent integrals, mathematical statement with explanation, and...
Junior level physics students are familiar with a few types of vector field derivatives, such as divergence and curl, but are typically unfamiliar with how to take a general derivative of a vector field. Three junior-level physics students were interviewed with the open-ended prompt, “How would you think about taking...
[This paper is part of the Focused Collection on Upper Division Physics Courses.] Standardized assessment tests that allow researchers to compare the performance of students under various curricula are highly desirable. There are several research-based conceptual tests that serve as instruments to assess and identify students' difficulties in lower-division courses....
Anderson and DeWitt considered the quantization of a massless scalar field in a spacetime whose spacelike hypersurfaces change topology and concluded that the topology change gives rise to infinite particle and energy production. We show here that their calculations are insufficient and that their propagation rule is unphysical. However, our...
We introduce a series of activities to help students understand the partial derivatives that arise in thermodynamics. Students construct thought experiments that would allow them to measure given partial derivatives. These activities are constructed with a number of learning goals in mind, beginning with helping students to learn to think...
Representations of SO(4,2;R) are constructed using 4 x 4 and 2 x 2 matrices with elements in H' ⊗ C . Using 2 x 2 matrix representations of C and H', the 4 x 4 representation is interpreted in terms of 16 x 16 real matrices. Finally, the known isomorphism...
Physics problems that require integration, such as finding the center of mass of an object or finding the electric field from a continuous distribution of charge, are one type of problem that is difficult for introductory physics students to solve. These problems require students to define a coordinate system in...
Physicists seek to understand the world and often use mathematics to aid in attaining that goal. Thus when doing mathematics they often interrogate their results in order to ensure that they align with their expectations and to gain new insight into how the world works. This seeking of coherence between...
In this dissertation we study the electromagnetic properties of planar waveguides
with non-magnetic strongly anisotropic dielectric cores. We develop an analytical
description of the mode propagation in these systems and show that the index
of refraction can be either positive or negative depending on the specific material
parameters. Propagating modes...
Several studies in recent years have demonstrated that upper-division students struggle with partial derivatives
and the complicated chain rules ubiquitous in thermodynamics. We asked several experts (primarily faculty who teach
thermodynamics) to solve a challenging and novel thermodynamics problem in order to understand how they navigate through
this maze. What...
Several studies in recent years have demonstrated that upper-division students struggle with the
mathematics of thermodynamics. This paper presents a task analysis based on several expert attempts
to solve a challenging mathematics problem in thermodynamics. The purpose of this paper is twofold.
First, we highlight the importance of cognitive task...
We consider the (massless) scalar field on a two-dimensional manifold with metric that changes signature from Lorentzian to Euclidean. Requiring a conserved momentum in the spatially homogeneous case leads to a particular choice of propagation rule. The resulting mix of positive and negative frequencies depends only on the total (conformal)...
We derive conditions for rotating particle detectors to respond in a variety of bounded spacetimes and
compare the results with the folklore that particle detectors do not respond in the vacuum state appropriate to
their motion. Applications involving possible violations of the second law of thermodynamics are briefly
addressed.