Search for: All records

Exponential functions are foundational to modeling dynamic phenomena in physics, yet students often strug- gle to integrate their mathematical form with corresponding physical interpretations. This study reports on upper-division physics students’ reasoning about exponential decay in the context of projectile motion with drag. Using the knowledge in pieces framework, we analyze how students activate and coordinate mathematical and conceptual resources during problem-solving. Case studies reveal that while participants demonstrated pro- cedural fluency with exponential expressions, they did not construe these forms as meaningful representations of physical systems. In contrast, polynomial forms elicited stronger conceptual associations, suggesting that curricular familiarity plays a role in resource coordination. These findings underscore a persistent disconnect between symbolic manipulation and physical interpretation in students’ reasoning. We argue for instructional designs that explicitly foster connections between mathematical structure (e.g., ekt) and mechanistic models (e.g., velocity-dependent drag), thereby supporting more integrated and expert-like engagement with exponen- tial functions in physics contexts. 

Symbolic representation is a cornerstone of mathematics and science. While much research has explored student understanding of various mathematical symbols, there is very little known about the way students con- ceptualize the use of Greek letters in scientific notation. In this work, we share excerpts from interviews with upper-division physics students, which illuminate their experience with Greek symbol use. The students re- ported frequently mistaking pairs of similar-looking Greek and Latin letters. They also felt that their texts and instructors had not sufficiently introduced novel Greek letters or explained what they represented in the equa- tions. The students also disliked how often a single Greek letter would be used in multiple contexts – or that different texts and instructors would not follow the same convention for which letter to use in a single context. These observations suggest that educators should devote additional time to introducing and discussing Greek letters in scientific contexts. 

Keystroke data collected from CS1 student participants during spring 2024 semester at Utah State University. See readme.txt for detailed information. This dataset has undergone deidentification, though it is possible, being a complex, temporal, and ephemeral dataset, that identifying keystrokes may have been missed. Ethical use of this dataset includes avoiding attempts at reconstructing identities. That said, if researchers discover anything identifiable in the data, they are encouraged to contact the dataset authors (john.edwards@usu.edu). 

Digital simulations are powerful instructional tools for physics education. They are often designed to visualize canonical physical phenomena, with adjustable parameters for influencing the system. While this is sufficient for developing conceptual and qualitative intuitions, it does little to help physics students build connections between physical systems and the mathematical models and equations that represent them. We present PhysMath, a suite of interactive physics simulations for use in upper-division courses. These simulations allow students to explore connections between mathematical equations and the phenomena they represent by inputting, modifying, and observing changes in system behavior. In this paper, we describe our first simulation—the Bead-On-Hoop for Classical Mechanics—and report findings from pilot interviews with intermediate physics students interacting with the simulation. Our findings validate the simulations’ design and highlight its potential for scaffolding students’ mathematical sensemaking. 

Digital simulations are especially helpful in physics education, but most simulations provide only a visual- ization of a phenomenon while obscuring the mathematical relationships that model its behavior. Our team is developing a suite of online simulations called DynamicsLab, which combine visual representations with an ability to input and alter the governing physics equations. Here, we share excerpts from a group of clinical interviews, in which intermediate physics students explored the first iterations of a DynamicsLab simulation of a characteristic problem in Classical Mechanics: the bead on a spinning hoop. The students were given predict- observe-explain prompts to investigate the way they connected the mathematical representation to the physical phenomenon. We highlight three episodes in which students had to revise unsuccessful predictions, and how these instances indicate that engaging with the DynamicsLab simulation encouraged the students to draw upon a more diverse range of knowledge elements to support their physical and mathematical reasoning. 

Pausing behavior in introductory Computer Science (CS1) courses has been related to course outcomes and could be linked to a student’s cognitive load. Using Cognitive Load Theory and Vygotsky’s Zone of Proximal Development as a theoretical framework, this study empirically analyzes keystroke latencies, or pause times between keystrokes, with the goal of better understanding what types of assignments need more scaffolding than others. We report the characteristics of eleven assignments, introduce a method to analyze pausing behavior, and investigate how pausing behavior changes with assignment characteristics (e.g., introducing new programming constructs, engaging creativity through Turtle graphics, etc). We find evidence that pausing behavior does change based on the assignment characteristics and that assignments with particular characteristics, such as object-oriented principles, may be more likely to have excessive demands on student working memory. We also find evidence that assignment completion time may not be an accurate measure of assignment difficulty. 

As seen by an observer in the rotating frame, the earth’s small spheroidal deformations neutralize the centrifugal force, leaving only the smaller Coriolis force to govern the “inertial” motion of objects that move on its surface, assumed smooth and frictionless. Previous studies of inertial motion employ weakly spheroidal equations of motion that ignore the influence of the centrifugal force and yet treat the earth as a sphere. The latitude dependence of these equations renders them strongly nonlinear. We derive and justify these equations and use them to identify, classify, name, describe, and illustrate all possible classes of inertial motion, including a new class of motion called circumpolar waves, which encircle both poles during each cycle of the motion. We illustrate these classes using CorioVis, our freely available Coriolis visualization software. We identify a rotational/time-reversal symmetry for motion on the earth’s surface and use this symmetry to develop and validate closed-form small-amplitude approximations for the four main classes and one degenerate class of inertial motion. For these five classes, we supply calculations of experimentally relevant frequencies, zonal drifts, and latitude ranges.