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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…
The electrostatic potential in certain types of boundary value problems can be found by solving Laplace's Equation (LE). To develop students' ability for solving problems that can be solved effectively using Laplace's equation in an…
The widespread dissemination of machine learning tools in science, particularly in astronomy, has revealed the limitation of working with simple single-task scenarios in which any task in need of a predictive model is looked in isolation,…
The ability to categorize problems based upon underlying principles, rather than surface features or contexts, is considered one of several proxy predictors of expertise in problem solving. With inspiration from the classic study by Chi,…
Development of conceptual multiple-choice tests related to a particular physics topic is important for designing research-based learning tools to reduce the difficulties. We explore the difficulties that the advanced undergraduate and…
A fundamental problem in manifold learning is to approximate a functional relationship in a data chosen randomly from a probability distribution supported on a low dimensional sub-manifold of a high dimensional ambient Euclidean space. The…
An appropriate diagram is a required element of a solution building process in physics problem solving and it can transform a given problem into a representation that is easier to exploit for solving the problem. A major focus while helping…
We investigate upper-division student difficulties with direct integration in multiple contexts involving the calculation of a potential from a continuous distribution (e.g., mass, charge, or current). Integration is a tool that has been…
We report on a large-scale study of student learning of quantum tunneling in 4 traditional and 4 transformed modern physics courses. In the transformed courses, which were designed to address student difficulties found in previous research,…
This article is devoted to the simultaneous resolution of three inverse problems, among the most important formulation of inverse problems for partial differential equations, stated for some class of diffusion equations from a single…
Assessments are usually thought of as ways for instructors to get information from students. In this work, we flip this perspective and explore how assessments communicate information to students. Specifically, we consider how assessments…
This paper reports on a study of student understanding of induced EMF. Students enrolled in a physics lab course completed a pretest and posttest that included questions about induced EMF. Following the posttest, some of those students…
In the current work, a problem-splitting approach and a scheme motivated by transfer learning is applied to a structural health monitoring problem. The specific problem in this case is that of localising damage on an aircraft wing. The…
Diffusion models have recently shown considerable potential in solving Bayesian inverse problems when used as priors. However, sampling from the resulting denoising posterior distributions remains a challenge as it involves intractable…
Continual learning of a stream of tasks is an active area in deep neural networks. The main challenge investigated has been the phenomenon of catastrophic forgetting or interference of newly acquired knowledge with knowledge from previous…
Cognitive diagnosis, the goal of which is to obtain the proficiency level of students on specific knowledge concepts, is an fundamental task in smart educational systems. Previous works usually represent each student as a trainable…
Helping students become proficient problem-solvers is one of the primary goals of physics courses. In part 1 of this article, we summarized the vast research on problem-solving relevant for physics instruction, and here we discuss a…
We introduce Mediffusion -- a new method for semi-supervised learning with explainable classification based on a joint diffusion model. The medical imaging domain faces unique challenges due to scarce data labelling -- insufficient for…
As research-based self-paced e-learning tools become increasingly available, a critical issue educators encounter is implementing strategies to ensure that all students engage with them as intended. Here, we discuss the effectiveness of…
This article outlines a comprehensive redesign of an introductory physics laboratory course aimed at promoting active student engagement, enhancing scientific experimental skills and the development of expert-like attitudes. The redesign…