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Physics Education Research (PER) applies a scientific approach to the question, "How do our students think about and learn physics?" PER allows us to explore such intellectually engaging questions as, "What does it mean to understand…
Learning to use math in physics involves combining (blending) our everyday experiences and the conceptual ideas of physics with symbolic mathematical representations. Graphs are one of the best ways to learn to build the blend. They are a…
We present a research mathematician's perspective on current developments around in K-12 mathematics. We share activities, and highlight the different ways in which students' reasoning can progress, such as amount of abstraction,…
The key difference between math as math and math in science is that in science we blend our physical knowledge with our knowledge of math. This blending changes the way we put meaning to math and even to the way we interpret mathematical…
The magnetic field is traditionally presented as a (pseudo)vector quantity, tied closely to the cross product. Though familiar to experts, many students find these ideas challenging and full of subtleties. Building on earlier work in…
We characterize the class of quantum measurements that matches the applications of quantum theory to cognition (and decision making) - quantum-like modeling. Projective measurements describe the canonical measurements of the basic…
The problem of how mathematics and physics are related at a foundational level is of much interest. One approach is to work towards a coherent theory of physics and mathematics together. Here steps are taken in this direction by first…
Computational thinking has been a recent focus of education research within the sciences. However, there is a dearth of scholarly literature on how best to teach and to assess this topic, especially in disciplinary science courses. Physics…
Researchers working within knowledge-in-pieces traditions have often employed observational approaches to investigate micro-processes of learning. There is growing evidence from this line of work that students' intuitive thinking about…
Comparing abstract concepts (such as electric circuits) with familiar ideas (plumbing systems) through analogies is central to practice and communication of physics. Contemporary research highlights self-generated analogies to better…
Incorporating computer programming exercises into introductory physics is a delicate task that involves a number of choices that may have an effect on student learning. We present a "hybrid" approach that speaks to a number of common…
Qualitative relationships illustrate how changing one property (e.g., moving velocity) affects another (e.g., kinetic energy) and constitutes a considerable portion of textual knowledge. Current approaches use either semantic parsers to…
Models of physical systems are used to explain and predict experimental results and observations. The Modeling Framework for Experimental Physics describes the process by which physicists revise their models to account for the newly…
Biological infants are naturally curious and try to comprehend their physical surroundings by interacting, in myriad multisensory ways, with different objects - primarily macroscopic solid objects - around them. Through their various…
A common hope of many physics educators and researchers is that students leave the course with a stronger sense that physics is relevant to them than when they entered the course. Multiple survey measures have attempted to measure shifts in…
In their study of physics beyond the first year of University -- termed upper-division in the US, many of students' primary learning opportunities come from working long, complex back-of-the-book style problems, and from trying to develop…
We study how large language models (LLMs) ``think'' through their representation space. We propose a novel geometric framework that models an LLM's reasoning as flows -- embedding trajectories evolving where logic goes. We disentangle…
A goal of physics is to understand the greatest possible breadth of natural phenomena in terms of the most economical set of basic concepts. However, as the understanding of physics has developed historically, its pedagogy and language have…
Learning to create, use, and evaluate models is a central element of becoming a scientist. In physics, we often begin an analysis of a complex system with highly simplified or toy models. In introductory physics classes, we tend to use them…
Broad instructional methods like interactive engagement have been shown to be effective, but such general characterization provides little guidance on the details of how to structure the instructional materials. In this study, we seek…