Related papers: Analysing the Competency of Mathematical Modelling…
Helping students become proficient problem solvers is a major goal of many physics courses from introductory to advanced levels. In fact, physics has often been used by cognitive scientists to investigate the differences between the…
Throughout all years of study, students of physics are confronted with the question 'what exactly is light?' - a question that is impossible to answer correctly and, therefore, continuously discussed within the framework of models. Numerous…
The ability to develop, use, and refine models of experimental systems is a nationally recognized learning outcome for undergraduate physics lab courses. However, no assessments of students' model-based reasoning exist for upper-division…
In recent years, promising mathematical models have been suggested which aim to describe conscious experience and its relation to the physical domain. Whereas the axioms and metaphysical ideas of these theories have been carefully…
An introduction to applied mathematics written for students in engineering and science. Focus is on a rigorous presentation that also builds understanding by discussion, analogy, and examples. Discussion of concepts involved in modeling…
Over the past few decades the notion of symmetry has played a major role in physics and in the philosophy of physics. Philosophers have used symmetry to discuss the ontology and seeming objectivity of the laws of physics. We introduce…
Machine learning is rapidly making its pathway across all of the natural sciences, including physical sciences. The rate at which ML is impacting non-scientific disciplines is incomparable to that in the physical sciences. This is partly…
Education is a goal-oriented field. But if we want to treat education scientifically so we can accumulate, evaluate, and refine what we learn, then we must develop a theoretical framework that is strongly rooted in objective observations…
We describe a way to introduce physics high school students with no background in programming to computational problem-solving experiences. Our approach builds on the great strides made by the Modeling Instruction reform curriculum. This…
Problem solving is central to physics instruction. Results from Physics Education Research (PER), however, demonstrate that traditional ways of teaching with problem solving are inefficient and ineffective for promoting true physics…
We review and extend existing frameworks on modeling to develop a new framework that describes model-based reasoning in upper-division physics labs. Constructing and using models are core scientific practices that have gained significant…
The human mind is endowed with innate primordial perceptions such as space, distance, motion, change, flow of time, matter. The field of cognitive science argues that the abstract concepts of mathematics are not Platonic, but are built in…
Courses in mathematical methods for physics students are not known for including too much in the way of mathematical rigour and, in some ways, understandably so. However, the conditions under which some quite commonly used mathematical…
Current concerns over reforming engineering education have focused attention on helping students develop skills and an adaptive expertise. Phenomenological guidelines for instruction along these lines can be understood as arising out of an…
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,…
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…
Developing expertise in physics entails learning to use mathematics effectively and efficiently as applied to the context of physical situations. Doing so involves coordinating a variety of concepts and skills including mathematical…
Developing expertise in physics requires appropriate integration and assimilation of physics and mathematics. Instructors and students often describe physics courses in terms of their emphasis on conceptual and quantitative problem-solving.…
Many mathematicians find mathematics aesthetically beautiful and even comparable to art forms such as music or painting. On the other hand, every year a great number of school students leave mathematics with total disillusionment and…
In this paper we present a step forward to improve general physics as an educational experience: the implementation of a new course component composed by innovative workshop activities based on computational modelling in the general physics…