相关论文: Exploring Students' Understanding of Linear and Qu…

University students taking introductory physics are generally successful executing mathematical procedures in context, but often struggle with the use of mathematical concepts for sense making. Physics instructors note that their students…

This paper proposes a novel approach to analyzing multi-hop reasoning in language models through Hamiltonian mechanics. We map reasoning chains in embedding spaces to Hamiltonian systems, defining a function that balances reasoning…

The capability of making explainable inferences regarding physical processes has long been desired. One fundamental physical process is object motion. Inferring what causes the motion of a group of objects can even be a challenging task for…

Deep learning has revolutionized the field of artificial intelligence. Based on the statistical correlations uncovered by deep learning-based methods, computer vision has contributed to tremendous growth in areas like autonomous driving and…

Six specific modes of reasoning about ratio and proportion have been delineated as a means of operationalizing expert practice. These modes stem from consideration of how physicists reason in context, are informed by prior work in physics…

Charts used for persuasion can easily veer into being outright misleading when, for instance, cherry-picked data is paired with a deceptive caption, as is commonly encountered on social media. The rise of interactive time-series data…

Compared with introductory physics, relatively little is known about the development of expertise in advanced physics courses, especially in the case of quantum mechanics. Here, we describe a framework for understanding the patterns of…

Many studies have investigated students' epistemological framing when solving physics problems. Framing supports students' problem solving as they decide what knowledge to employ and the necessary steps to solve the problem. Students may…

Investigations into using visualization to improve Bayesian reasoning and advance risk communication have produced mixed results, suggesting that cognitive ability might affect how users perform with different presentation formats. Our work…

We investigated the common difficulties that students have with concepts related to rotational and rolling motion covered in the introductory physics courses. We compared the performance of calculus- and algebra-based introductory physics…

Science is an inherently quantitative endeavor, and general education science courses are taken by a majority of college students. As such, they are a powerful venue for advancing students' skills and attitudes toward mathematics. This…

Previous research indicates that after standard instruction students at all academic levels often construct a conceptual framework in which the ideas of absolute simultaneity and the relativity of simultaneity co-exist. This article…

Multivariate spatial field data are increasingly common and whose modeling typically relies on building cross-covariance functions to describe cross-process relationships. An alternative viewpoint is to model the matrix of spectral…

Expanding our knowledge of student difficulties in advanced undergraduate electromagnetism is essential if we are to develop effective instructional interventions. Drawing on an analysis of course materials, in-class observations and…

In this thesis, a Bayes linear methodology for the adjustment of covariance matrices is presented and discussed. A geometric framework for quantifying uncertainties about covariance matrices is set up, and an inner-product for spaces of…

This note presents reflections drawn from my recent experiences in teaching a course on mathematics and sustainability, with a particular emphasis on raising awareness of the topic and its broader implications. The lectures were structured…

This article reports on an investigation of student understanding of the concept of time in special relativity. A series of research tasks are discussed that illustrate, step-by-step, how student reasoning of fundamental concepts of…

Physics education researchers have argued that authentic physics education includes computation as part of a physics student's training, and many parties have made efforts towards this goal. However, most research on this teaching modality…

In a first course of general relativity it is usually quite difficult for students to grasp the concept of a geodesic. It is supposed to be straight (auto-parallel) and yet it 'looks' curved. In these situations it is very useful to have…

Despite being used in many engineering and scientific areas such as physics and mathematics and often taught in high school, graphical vector addition turns out to be a topic prone to misconceptions in understanding even at university-level…