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Learning advanced physics, in general, is challenging not only due to the increased mathematical sophistication but also because one must continue to build on all of the prior knowledge acquired at the introductory and intermediate levels.…
Instruction in quantum mechanics is becoming increasingly important as the field is not only a key part of modern physics research, but is also important for emerging technologies. However, many students regard quantum mechanics as a…
Advances in reinforcement learning research have demonstrated the ways in which different agent-based models can learn how to optimally perform a task within a given environment. Reinforcement leaning solves unsupervised problems where…
Asymptotic analysis provides powerful insights into physical systems by examining their behavior in limiting cases. This paper explores how extending this advanced methodology to high school physics education can deepen conceptual…
Most physics theories are deterministic, with the notable exception of quantum mechanics which, however, comes plagued by the so-called measurement problem. This state of affairs might well be due to the inability of standard mathematics to…
A perplexing problem in understanding physical reality is why the universe seems comprehensible, and correspondingly why there should exist physical systems capable of comprehending it. In this essay I explore the possibility that rather…
As we typically teach in an introductory mechanics course, choosing a "good" reference frame with convenient axes may present a major simplification to a problem. Additionally, knowing some conserved quantities provides an extremely…
Helping students learn from their own mistakes can help them develop habits of mind while learning physics content. Based upon cognitive apprenticeship model, we asked students to self-diagnose their mistakes and learn from reflecting on…
Well-developed problem-solving skills are essential for any student enrolled in a science, technology, engineering or mathematics (STEM) course as well as for graduates in the workforce. One of the most essential skills is the ability to…
In this study, we explored the extent to which problems and instructional strategies affect social cohesion and interactions for information seeking in physics classrooms. Three sections of a mechanics physics course taught at a Chilean…
Symbolic calculators like Mathematica are becoming more commonplace among upper level physics students. The presence of such a powerful calculator can couple strongly to the type of mathematical reasoning students employ. It does not merely…
Can we learn the physics of matter in motion directly from images and video--and trust it? Answering this question requires integrating experiments, physics-based simulation, and data across traditionally separate disciplines. Much of this…
With the rise of large language models such as ChatGPT, interest has grown in understanding how these tools influence learning in STEM education, including physics. This study explores how students use ChatGPT during a physics…
Computation is a central aspect of 21st century physics practice; it is used to model complicated systems, to simulate impossible experiments, and to analyze mountains of data. Physics departments and their faculty are increasingly…
Computation is a central aspect of modern science and engineering work, and yet, computational instruction has yet to fully pervade university STEM curricula. In physics, we have begun to integrate computation into our courses in a variety…
Form a pure mathematical point of view, common functional forms representing different physical phenomena can be defined. For example, rates of chemical reactions, diffusion and heat transfer are all governed by exponential-type…
Many have wondered how mathematics, which appears to be the result of both human creativity and human discovery, can possibly exhibit the degree of success and seemingly-universal applicability to quantifying the physical world as…
Integrating computation into physics teaching is a curricular move that, at present, has been predominately studied for its cognitive impacts. However, if this modality of instruction shifts how students engage with physics, we argue there…
Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space. The topic of this paper is the numerical approximation of functions using…
A pedagogical approach of problem-based learning with embedded librarianship in several undergraduate mathematics courses is implemented in this educational research. The students are assigned to work on several projects on various…