# Processes of problem-solving and instructional change in physics

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This research presents an investigation of how students solve physics problems and how physics instructors approach changes in their teaching. In particular, the first part of this dissertation focuses on three major projects looking at students' processes of problem-solving in upper-division physics courses. The second part focuses on the processes of instructional change. In the first project described in part I, I discuss the clusters of resources that emerge when upper-division students write about electromagnetic fields in linear materials. I use a resource theory perspective to describe the ways students link pieces of information (or resources) to form more complex ideas, improve their understanding, and solve physics problems. The evidence shows that students benefit from activating resources related to the internal structure of the atom when thinking about electric fields to complete their mental model. Physics as a discipline embeds conceptual meaning about the physical world in mathematical formalism. In the second project, I use Sherin's symbolic forms theory to present an analysis of the different physical meanings associated with the equal signs across a physics context. Sherin's symbolic forms framework links mathematical equations to intuitive conceptual ideas. I delineate types of equal signs as used in five undergraduate level physics textbooks and develop a categorization scheme. Six distinct meanings are identified: causality, balancing, definitional, assignment, hybrid, and calculation. After considering five physics textbooks, I then analyze students' solutions in their written homework in an upper-division electrostatics course and compare them to textbook solutions. In doing so, I am able to look for patterns and compare the ways students use the equal signs to the textbook solution manual. In the last section of Part I, I examine students' epistemological framing when solving physics problems as a group. I analyze videos of students solving electrodynamics problems. I consider two epistemic frames which are common in students' discussions during problem solving in group: sense-making and answer-making. I first characterize the markers of each frame, focusing on analyzing students' group frame. Then, I present a pair of examples that show how often students transition between these frames. I notice moments that students change their attitude towards the problem to move forward in their activities. While there are many ways to view how students practice physics, the results of this project provide deeper insight into students' problem-solving processes in an upper-division course. In Part II, I use phenomenography as a methodology to explain how physics instructors approach making changes in their teaching and the different kinds of support that they would like to have. The purpose of phenomenography is to describe the qualitative variation in people's experiences. For example, what are the ways in which physics instructors think and talk about their teaching practices? Our phenomenography study explored six different major categories: how instructors approach their teaching, their motivation to make changes, resources that they have used, how they have implemented those resources, challenges they experience during a semester, and their attitudes towards implementing new changes. We ultimately aim to use our findings to redesign the PhysPort website.