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The pursuit of knowledge in particle physics requires constant learning. As new tools become available, new theories are developed, and physicists search for new answers with ever-evolving methods. However, it is the case that formal…
As more neurodivergent students enter college, discussion on neurodiversity in higher education is gaining momentum. It is increasingly imperative that we understand how neurodivergent individuals construct their identities within the…
Distance metric learning is a branch of machine learning that aims to learn distances from the data, which enhances the performance of similarity-based algorithms. This tutorial provides a theoretical background and foundations on this…
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…
Differentiable simulation enables gradients to be back-propagated through physics simulations. In this way, one can learn the dynamics and properties of a physics system by gradient-based optimization or embed the whole differentiable…
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…
Making meaning with math in physics requires blending physical conceptual knowledge with mathematical symbology. Students in introductory physics classes often struggle with this, but it is an essential component of learning how to think…
The manifold hypothesis is a core mechanism behind the success of deep learning, so understanding the intrinsic manifold structure of image data is central to studying how neural networks learn from the data. Intrinsic dataset manifolds and…
In this article we discuss an important students' misconception about derivatives, that the expression of the derivative of the function contains the information as to whether the function is differentiable or not where the expression is…
We introduce the Primary Gasing Triangle, a right triangle with a hypotenuse of 1 unit, to define the primary trigonometric functions: sine and cosine. This triangle serves as the foundational element in a new approach to learning…
Recognition is the fundamental task of visual cognition, yet how to formalize the general recognition problem for computer vision remains an open issue. The problem is sometimes reduced to the simplest case of recognizing matching pairs,…
Students' sometimes contradictory ideas about ATP (adenosine triphosphate) and the nature of chemical bonds have been studied in the biology and chemistry education literatures, but these topics are rarely part of the introductory physics…
Non-Euclidean constraints are inherent in many kinds of data in computer vision and machine learning, typically as a result of specific invariance requirements that need to be respected during high-level inference. Often, these geometric…
A fixed set of vertices in the plane may have multiple planar straight-line triangulations in which the degree of each vertex is the same. As such, the degree information does not completely determine the triangulation. We show that even if…
Symbolic equations are one of the many representations used in physics. Understanding these representations is important for students because they are how students access knowledge in physics. In this paper I build off of the work by Redish…
An analysis of longitudinal student Physics practicals data over a period of three semesters is conducted. In particular, we study the association of the gender of students and their Physics practicals marks in mechanics, thermodynamics,…
Relating two quantities to describe a physical system or process is at the heart of "doing physics" for novices and experts alike. In this paper, we explore the ways in which experts use covariational reasoning when solving introductory…
Multimodal learning plays a pivotal role in advancing artificial intelligence systems by incorporating information from multiple modalities to build a more comprehensive representation. Despite its importance, current state-of-the-art…
The derivative expansion approach to the calculation of the interaction between two surfaces, is a generalization of the proximity force approximation, a technique of widespread use in different areas of physics. The derivative expansion…
This manuscript, titled Differential Geometry of Curves and Surfaces in Three-dimensional Euclidean Space, is intended for undergraduate students of mathematics and other sciences with the need of use of Euclidean differential geometry. We…