Related papers: Unpacking Symbolic Equations in Introductory Physi…
Basic principles of mathematical modeling are reviewed in this book, with the focus on physics and its practical applications, and examples of selected mathematical methods are presented. Most of the models have been imported from physics…
Writing and argumentation are critical to both professional physics and physics education. However, the skill of making an extended argument in writing is often overlooked in physics classrooms, apart from certain practices like lab…
In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…
The purpose of this paper (which, in many passages, I take the liberty of writing in the first person singular for bringing a personal experience) is to show how teachers of Physics and Mathematics in Basic Education can teach, through a…
We discuss how a class of difficult kinematic problems can play an important role in an introductory course in stimulating students' reasoning on more complex physical situations. The problems presented here have an elementary analysis once…
A core challenge for both physics and artificial intellicence (AI) is symbolic regression: finding a symbolic expression that matches data from an unknown function. Although this problem is likely to be NP-hard in principle, functions of…
In a companion paper, we discuss students' ability to take advantage of what they learn from a solved problem and transfer their learning to solve a quiz problem that has different surface features but the same underlying physics…
Drawing appropriate diagrams is a useful problem solving heuristic that can transform a problem into a representation that is easier to exploit for solving it. One major focus while helping introductory physics students learn effective…
This paper outlines a deceptively complex problem in classical mechanics which the paper names the "Falling Astronaut Problem," and it explores a method for teachers to implement this problem in an undergraduate classroom. The paper…
This article introduces a pedagogical method for {\it solving combinatorial problems} that frequently involve structures that are unfamiliar or less familiar. Indeed, an indirect method has been proposed in order to evade any possible…
In this paper, we discuss the question whether a physical "simplification" of a model makes it always easier to study, at least from a mathematical and numerical point of view. To this end, we give different examples showing that these…
Many students in upper-division physics courses struggle with the mathematically sophisticated tools and techniques that are required for advanced physics content. We have developed an analytical framework to assist instructors and…
In this note, I develop my personal view on the scope and relevance of symbolic computation in software science. For this, I discuss the interaction and differences between symbolic computation, software science, automatic programming,…
This document presents the material of two lectures on statistical physics and neural representations, delivered by one of us (R.M.) at the Fundamental Problems in Statistical Physics XIV summer school in July 2017. In a first part, we…
There is a substantial curricular overlap between calculus and physics, yet introductory physics students often struggle to connect the two. We introduce a quantity-based framing of the Fundamental Theorem of Calculus (FTC) to help unify…
The physics community explores and explains the physical world through a blend of theoretical and experimental studies. The future of physics as a discipline depends on training of students in both the theoretical and experimental aspects…
Explainability is an essential reason limiting the application of neural networks in many vital fields. Although neuro-symbolic AI hopes to enhance the overall explainability by leveraging the transparency of symbolic learning, the results…
This book is devoted to an informal discussion of patterns constructed for treating physical problems. Such patterns, when sufficiently formalized, are usually referred as "models", and tents to be applied not only in physics, but conquer…
Imitation learning is a popular method for teaching robots new behaviors. However, most existing methods focus on teaching short, isolated skills rather than long, multi-step tasks. To bridge this gap, imitation learning algorithms must not…
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…