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...
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....
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...
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...