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We study the problem of selecting a maximum-weight subgraph of a given graph such that the subgraph can be drawn within a prescribed drawing area subject to given non-uniform vertex sizes. We develop and analyze heuristics both for the…

The goal of this paper is to investigate the importance of providing visual "big pictures" in the teaching of economics. The plurality and variety of concepts, variables, diagrams, and models involved in economics can be a source of…

Students' difficulties in quantum mechanics may be the result of unproductive framing rather than a fundamental inability to solve the problems or misconceptions about physics content. Using the theoretical lens of epistemological framing,…

Decoder-only language models have the ability to dynamically switch between various computational tasks based on input prompts. Despite many successful applications of prompting, there is very limited understanding of the internal mechanism…

Introductory physics labs can be designed and studied using the Communities of Practice framework, where a group of members pursues a common set of goals by learning and implementing a set of practices. Studies of student preferences and…

I am a second-year cognitive science major, and as a student who has completed my physical science distribution requirements, I will likely never again encounter Gauss's law. So why do I feel that the time and effort I devoted to solving…

In this companion paper, we explore the use of isomorphic problem pairs (IPPs) to assess introductory physics students' ability to solve and successfully transfer problem-solving knowledge from one context to another in mechanics. We call…

We investigate the asymptotic number of induced subgraphs in power-law uniform random graphs. We show that these induced subgraphs appear typically on vertices with specific degrees, which are found by solving an optimization problem.…

Fundamental diagrams describe the relationship between speed, flow, and density for some roadway (or set of roadway) configuration(s). These diagrams typically do not reflect, however, information on how speed-flow relationships change as a…

Graphs are a natural representation for systems based on relations between connected entities. Combinatorial optimization problems, which arise when considering an objective function related to a process of interest on discrete structures,…

Reading scientific research papers is a skill that many students do not learn before entering PhD programs, but it is critical to their success. This paper describes our diagramming technique for teaching this skill, which helps them…

Introductory algebra-based physics courses frequently feature multiple student major populations in the same course section, however, different majors' requirements may impact students' motivations towards different aspects of the course…

Physics graduate teaching assistants (TAs) are often responsible for grading. Physics education research suggests that grading practices that place the burden of proof for explicating the problem solving process on students can help them…

Many students in upper-division physics courses struggle with the mathematically sophisticated tools and techniques that are required for advanced physics content. We have developed an analytical framework to assist instructors and…

Pencasts are videos of problem solving with narration by the problem solver. Pedagogically, students can create pencasts to illustrate their own problem solving to the instructor or to their peers. Pencasts have implications for teaching at…

Automating the creation of scientific diagrams from academic papers can significantly streamline the development of tutorials, presentations, and posters, thereby saving time and accelerating the process. Current text-to-image models…

Large-scale "pre-train and prompt learning" paradigms have demonstrated remarkable adaptability, enabling broad applications across diverse domains such as question answering, image recognition, and multimodal retrieval. This approach fully…

Given a physics scenario, different problem types presenting that scenario in various ways can emphasize different instructional goals. In this investigation, we examined the views of physics graduate teaching assistants (TAs) about the…

Identifying the relevant physics principles is a central component of problem solving. A major goal of most introductory physics courses is to help students discern the deep similarities between problems based upon the physics principles so…

Deep learning algorithms are responsible for a technological revolution in a variety of tasks including image recognition or Go playing. Yet, why they work is not understood. Ultimately, they manage to classify data lying in high dimension…