Related papers: Unpacking Students' Use of Mathematics in Upper-di…
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…
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.…
How students use mathematics in their physics classes has been studied extensively in the physics education literature. In addition to specific mathematical methods in specific physics contexts, possible effects of more general "cultural"…
At the University of Colorado Boulder, as part of our broader efforts to transform middle- and upper-division physics courses, we research students' difficulties with particular concepts, methods, and tools in classical mechanics,…
Symbolic equations are one of the many representations used in physics. Understanding these representations is important for students because they are how students access knowledge in physics. In this paper I build off of the work by Redish…
We describe the development of a junior-senior level course for Physics majors designed to teach Mathematica skills in support of their undergraduate coursework, but also to introduce students to modern research level results. Standard…
Physics makes powerful use of mathematics, yet the way this use is made is often poorly understood. Professionals closely integrate their mathematical symbology with physical meaning, resulting in a powerful and productive structure. But…
Separation of variables can be a powerful technique for solving many of the partial differential equations that arise in physics contexts. Upper-division physics students encounter this technique in multiple topical areas including…
High school science classrooms across the United States are answering calls to make computation a part of science learning. The problem is that there is little known about the barriers to learning that computation might bring to a science…
We investigate upper-division student difficulties with direct integration in multiple contexts involving the calculation of a potential from a continuous distribution (e.g., mass, charge, or current). Integration is a tool that has been…
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…
Computational physics is a key part of what it means to do physics in the twenty-first century. However, upper division computational physics remains a largely understudied area. We set out to understand the experiences of students in an…
The Dirac delta function is a standard mathematical tool that appears repeatedly in the undergraduate physics curriculum in multiple topical areas including electrostatics, and quantum mechanics. While Dirac delta functions are often…
University students taking introductory physics are generally successful executing mathematical procedures in context, but often struggle with the use of mathematical concepts for sense making. Physics instructors note that their students…
Learning advanced physics, in general, is challenging not only due to the increased mathematical sophistication but also because one must continue to build on all of the prior knowledge acquired at the introductory and intermediate levels.…
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…
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…
We demonstrate how students' use of modeling can be examined and assessed using student notebooks collected from an upper-division electronics lab course. The use of models is a ubiquitous practice in undergraduate physics education, but…
Symbolic calculators like Mathematica are becoming more commonplace among upper level physics students. The presence of such a powerful calculator can couple strongly to the type of mathematical reasoning students employ. It does not merely…
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…