Related papers: How students blend conceptual and formal mathemati…
Equations are about more than computing physical quantities or constructing formal models; they are also about understanding. The conceptual systems physicists use to think about nature are made from many different resources, formal and…
Effective physics learning, especially in complex topics, requires balancing mathematical formalism with conceptual understanding. Conceptual problem-solving involves connecting math to physical reality, and using an epistemological…
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.…
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…
Pre-college mathematics modeling instruction often frames mathematics as being separated from reasoning about the real world -- and commonly treats reasoning mathematically and reasoning about the real-world context as separate stages of a…
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…
What kind of problem-solving instruction can help students apply what they have learned to solve the new and unfamiliar problems they will encounter in the future? We propose that mathematical sensemaking, the practice of seeking coherence…
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…
In recent years there has been growing evidence that even after teaching designed to address the learning difficulties dictated by literature, many physics learners fail to create the proper reasoning chains that connect the fundamental…
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…
Mathematical reasoning flexibility across physics contexts is a desirable learning outcome of introductory physics, where the math world and physical world meet. Physics Quantitative Literacy (PQL) is a set of interconnected skills and…
Expressing physics problems in the form of a mathematical model is one of the most important stages in the problem-solving process. Particularly in algebraic symbolization, understanding the meanings of signs and being able to manipulate…
Developing expert-like problem-solving skills is a central goal of undergraduate physics education. In this study, we investigate the impact of teaching explicit problem-solving frameworks, combined with deliberate practice, on students'…
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…
A primary goal of physics is to create mathematical models that allow both predictions and explanations of physical phenomena. We weave maths extensively into our physics instruction beginning in high school, and the level and complexity of…
Researchers in physics education have advocated both for including modeling in science classrooms as well as promoting student engagement with sensemaking. These two processes facilitate the generation of new knowledge by connecting to…
One finding of cognitive research is that people do not automatically acquire usable knowledge by spending lots of time on task. Because students' knowledge hierarchy is more fragmented, "knowledge chunks" are smaller than those of experts.…
Relating two quantities to describe a physical system or process is at the heart of "doing physics" for novices and experts alike. In this paper, we explore the ways in which experts use covariational reasoning when solving introductory…
Students must learn effective problem solving strategies in order to develop expertise in physics. Effective problem solving strategies include a conceptual analysis of the problem followed by planning of the solution, and then…
Mathematics is an essential element of physics problem solving, but experts often fail to appreciate exactly how they use it. Math may be the language of science, but math-in-physics is a distinct dialect of that language. Physicists tend…