Multiple Perspectives on Student Solution Methods for Air Resistance Problems

Physics education researchers use many frameworks to observe and analyze student understanding in physics - each is useful for understanding and explaining particular student behaviors. In this dissertation, I focus on two: difficulties and knowledge in pieces. In the difficulties paradigm, researchers focus on identifying specific topics or questions that pose challenges to students without making claims regarding underlying cognition. In the pieces paradigm, the focus is on describing the structure of student ideas, which are often found to be developed on-the-fly, easy to change, and can be described as made up of chunks of knowledge that are not inherently correct or incorrect. I use both video and written data collection methods and the difficulties and pieces theoretical frameworks to examine aspects of students\u27 solutions to first-order separable differential equations in an air-resistance context. I uncover several difficulties students have when applying boundary conditions, and develop a new graphic, the consistency plot, that allows researchers to track individual student responses over time. Additionally, using air resistance as a context, I expand upon resources, a model of student thinking that falls into the pieces paradigm. I both expand the resources model directly and make connections between it and other modes of analysis present but less common in physics education research: epistemic games, gesture analysis, conceptual blending, and Process/Object theory. Introducing procedural resources as a type of resource allows the resources model to better describe students\u27 problem-solving activities. I give several examples of procedural resources used in the incorporation of boundary conditions, and I show how procedural resources can be organized into facets of epistemic games. I also examine the creation of procedural resources. Drawing from the traditions of gesture analysis, conceptual blending, and Process/Object theory, I consider the internal structure of two procedural resources, Group and Move, and give a plausible path for the creation of the resource Separate Variables