Related papers: Unpacking Symbolic Equations in Introductory Physi…
During the last decade we have witnessed an impressive development in so-called interpreted languages and computational environments such as Maple, Mathematica, IDL, Matlab etc. Problems which until recently were typically solved on…
Undergraduate physics education has greatly benefited from the introduction of computational activities. However, despite the benefits computation has delivered, we still lack a complete understanding of the computationally integrated…
Upper-division physics students spend much of their time solving problems. In addition to their basic skills and background, their epistemic framing can form an important part of their ability to learn physics from these problems.…
Differentiable physics provides a new approach for modeling and understanding the physical systems by pairing the new technology of differentiable programming with classical numerical methods for physical simulation. We survey the rapidly…
When neural networks are used to solve differential equations, they usually produce solutions in the form of black-box functions that are not directly mathematically interpretable. We introduce a method for generating symbolic expressions…
We describe the development of a junior-senior level course for Physics majors designed to teach Mathematica skills in support of their undergraduate coursework, but also to introduce students to modern research level results. Standard…
Prior research has demonstrated how the realist perspectives of classical physics students can translate into specific beliefs about quantum phenomena when taking an introductory modern physics course. Student beliefs regarding the…
In the rapidly evolving interdisciplinary field of quantum information science and technology, a major obstacle is the need to understand advanced mathematics to solve complex problems. Current findings in educational research suggest that…
Most introductory quantum physics instructors would agree that transitioning students from classical to quantum thinking is an important learning goal, but may disagree on whether or how this can be accomplished. Although (and perhaps…
The mathematical representation of the physical objects determines which mathematical branch will be applied during the physical analysis in the systems studied. The difference among non-quantum physics, like classic or relativistic…
The ability to flexibly transform between different representations (e.g., from mathematical to graphical representations) of the same concept is a hallmark of expertise. Prior research suggests that many introductory physics students show…
We designed three color-coding schemes to identify related information across representations and to differentiate distinct information within a representation in slide-based instruction for calculus-based introductory mechanics. We found…
In order to describe natural phenomena, science develops sophisticated models that use mathematical and formal languages which seem, and often are, very far from common experience. When a phenomenon is not accessible to our senses, its…
What kind of problem-solving instruction can help students apply what they have learned to solve the new and unfamiliar problems they will encounter in the future? We propose that mathematical sensemaking, the practice of seeking coherence…
Investigations related to expertise in problem solving and ability to transfer learning from one context to another are important for developing strategies to help students perform more expert-like tasks. Here we analyze written responses…
Machine-learning methods are gradually being adopted in a wide variety of social, economic, and scientific contexts, yet they are notorious for struggling with exact mathematics. A typical example is computer algebra, which includes tasks…
Diagrams are ubiquitous in physics, especially in physics education and physics problem solving. Problem solvers may generate diagrams to orient to a scenario, to organize information, to directly extract an answer, or as a tool of…
Symbolic equations are at the core of scientific discovery. The task of discovering the underlying equation from a set of input-output pairs is called symbolic regression. Traditionally, symbolic regression methods use hand-designed…
Separation of variables can be a powerful technique for solving many of the partial differential equations that arise in physics contexts. Upper-division physics students encounter this technique in multiple topical areas including…
Partial differential equations (PDEs) are ubiquitous in the world around us, modelling phenomena from heat and sound to quantum systems. Recent advances in deep learning have resulted in the development of powerful neural solvers; however,…