Related papers: Using math in physics -- 1. Dimensional analysis
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.…
The large number of published articles in physics journals under the title "Comments on ..." and "Reply to ..." is indicative that the conceptual understanding of physical phenomena is very elusive and hard to grasp even to experts, but it…
The amount of published research in Physics Education Research (PER) shows, on one hand, an increasing interest in the design and development of high performance physics teaching strategies, and, on the other hand, it tries to understand…
Classical dimensional analysis is one of the cornerstones of qualitative physics and is also used in the analysis of engineering systems, for example in engineering design. The basic power product relationship in dimensional analysis is…
Symbolic dynamics is a coarse-grained description of dynamics. By taking into account the ``geometry'' of the dynamics, it can be cast into a powerful tool for practitioners in nonlinear science. Detailed symbolic dynamics can be developed…
The role of mathematics in physical sciences is discussed, particularly how higher mathematics found applications in empirical problems. Several examples are given to illustrate this role.
Many have argued that statistics students need additional facility to express statistical computations. By introducing students to commonplace tools for data management, visualization, and reproducible analysis in data science and applying…
Previous research has shown that students often struggle to develop an understanding of linear and quadratic relationships. Covariational reasoning has been identified as a way to support this development. This study aims to investigate how…
Over the past two decades, the rapid surge in data-intensive computational techniques for statistical modeling may have had the effect of diminishing the use of applied mathematics in causal scientific inquiry. In this paper, co-authored by…
Symbolic data analysis (SDA) is an emerging area of statistics concerned with understanding and modelling data that takes distributional form (i.e. symbols), such as random lists, intervals and histograms. It was developed under the premise…
What does it mean to "make sense" of physics? It's not a simple question. Most people have an intuitive feeling for when things do (or do not) make sense to them. But, putting this feeling into words--especially actionable words--is another…
The milq approach to quantum physics for high schools focuses on the conceptual questions of quantum physics. Students should be given the opportunity to engage with the world view of modern physics. The aim is to achieve a conceptually…
Current conceptions of expert problem solving depict physical/conceptual reasoning and formal mathematical reasoning as separate steps: a good problem solver first translates a physical Current conceptions of quantitative problem-solving…
We review the current status of dimensions, as the result of a long and controversial history that includes input from philosophy and physics. Our conclusion is that they are subjective but essential concepts which provide a kind of…
Data literacy has become a key learning objective in K-12 education, but it remains an ambiguous concept as teachers interpret it differently. When creating assessments, teachers turn broad ideas about "working with data" into concrete…
Computational thinking in physics has many different forms, definitions, and implementations depending on the level of physics, or the institution it is presented in. In order to better integrate computational thinking in introductory…
Developing and making sense of quantitative models is a core practice of physics. Covariational reasoning -- considering how the changes in one quantity affect changes in another, related quantity -- is an essential part of modeling…
Large Language Models (LLMs) have achieved remarkable progress on advanced reasoning tasks such as mathematics and coding competitions. Meanwhile, physics, despite being both reasoning-intensive and essential to real-world understanding,…
Students of quantum mechanics encounter discrete quantum numbers in a somewhat incoherent and bewildering number of ways. For each physical system studied, quantum numbers seem to be introduced in its own specific way, some enumerating from…
The centuries-long practice of the teaching turned mechanics into an academic construct detached from its underlying science, the physics of macroscopic bodies. In particular, the regularities that delineate the scope of validity of…