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 instructional materials. In this study, we seek instructional specificity by comparing two ways of using an analogy to learn a target physical principle:…

Superposition gives rise to the probabilistic nature of quantum mechanics and is therefore one of the concepts at the heart of quantum mechanics. Although we have found that many students can successfully use the idea of superposition to calculate the probabilities of different measurement outcomes, they are often unable to identify the…

It is known that experts identify or perceive meaningful patterns in visual stimuli related to their domain of expertise. This study explores the speed with which experts and novices detect changes in physics diagrams. Since change detection depends on where individuals direct their attention, differences in the speed with which experts and…

It is well known that introductory physics students often have alternative conceptions that are inconsistent with established physical principles and concepts. Invoking alternative conceptions in the quantitative problem-solving process can derail the entire process. In order to help students solve quantitative problems involving strong…

Problem solving is a critical element of learning physics. However, traditional instruction often emphasizes the quantitative aspects of problem solving such as equations and mathematical procedures rather than qualitative analysis for selecting appropriate concepts and principles. This study describes the development and evaluation of an…

We present a study of active learning pedagogies in an upper-division physics course. This work was guided by the principle of deliberate practice for the development of expertise, and this principle was used in the design of the materials and the orchestration of the classroom activities of the students. We present our process for efficiently…

The formalism of quantum mechanics includes a rich collection of representations for describing quantum systems, including functions, graphs, matrices, histograms of probabilities, and Dirac notation. The varied features of these representations affect how computations are performed. For example, identifying probabilities of measurement outcomes…

Energy measurements play a fundamental role in the theory of quantum mechanics, yet there is evidence that the underlying concepts are difficult for many students, even after all undergraduate instruction. We present results from an investigation into student ability to determine the possible energies that can be measured for a given wave function…

The time evolution of quantum states is arguably one of the more difficult ideas in quantum mechanics. In this article, we report on results from an investigation of student understanding of this topic after lecture instruction. We demonstrate specific problems that students have in applying time dependence to quantum systems and in recognizing…

Students learning to separate variables in order to solve a differential equation have multiple ways of correctly doing so. The procedures involved in "separation" include "division" or "multiplication" after properly "grouping" terms in an equation, "moving" terms (again, at times grouped) from…

The use of validated conceptual assessments alongside conventional course exams to measure student learning in introductory courses has become standard practice in many physics departments. These assessments provide a more standard measure of certain learning goals, allowing for comparisons of student learning across instructors, semesters,…

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. In addition, learning quantum mechanics can be especially challenging because the paradigms of classical…

As part of an ongoing project to examine student learning in upper-division courses in thermal and statistical physics, we have examined student reasoning about entropy and the second law of thermodynamics. We have examined reasoning in terms of heat transfer, entropy maximization, and statistical treatments of multiplicity and probability. In…

As part of a longitudinal study into identity development in upper-level physics students, we used a phenomenographic research method to examine students' perceptions of what it means to be a physicist. Analysis revealed six different categories of perception of what it means to be a physicist. We found the following themes: research and its…

Instructors and researchers think "thinking like a physicist" is important for students' professional development. However, precise definitions and observational markers remain elusive. We reinterpret popular beliefs inventories in physics to indicate what physicists think thinking like a physicist entails. Through discourse analysis of…