[This paper is part of the Focused Collection on Upper Division Physics Courses.] 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 for a state described in Dirac notation may involve identifying expansion coefficients by inspection, but if the state is described as a function, identifying those expansion coefficients often involves performing integrals. In this study, we focus on three notational systems: Dirac notation, algebraic wavefunction notation, and matrix notation. These quantum notations must include information about basis states and their associated complex probability amplitudes. In this theory paper, we identify four structural features of quantum notations, which we term individuation, degree of externalization, compactness, and symbolic support for computational rules. We illustrate how student reasoning interacts with these structural features with episodes from interviews with advanced undergraduate physics majors reasoning about a superposition state of an infinite square well system. We find evidence of the students coordinating different notations through the use of Dirac notation, using an expression in Dirac notation to guide their work in another notation. These uses are supported by the high degree of individuation, compactness, and symbolic support for computation and the moderate degree of externalization provided by Dirac notation.

Students in introductory physics courses are likely to have views about physics that differ from those of experts. However, students who continue to study physics eventually become experts themselves. Presumably these students either possess or develop more expertlike views. To investigate this process, the views of introductory physics students majoring in physics are compared with the views of introductory physics students majoring in engineering. In addition, the views of physics majors are assessed at various stages of degree progress. The Colorado learning attitudes about science survey is used to evaluate students’ views about physics, and students’ overall survey scores and responses to individual survey items are analyzed. Beginning physics majors are significantly more expertlike than nonmajors in introductory physics courses, and this high level of sophistication is consistent for most of undergraduate study

Representations in physics possess both physical and conceptual aspects that are fundamentally intertwined and can interact to support or hinder sense making and computation. We use distributed cognition and the theory of conceptual blending with material anchors to interpret the roles of conceptual and material features of representations in students' use of representations for computation. We focus on the vector-arrows representation of electric fields and describe this representation as a conceptual blend of electric field concepts, physical space, and the material features of the representation (i.e., the physical writing and the surface upon which it is drawn). In this representation, spatial extent (e.g., distance on paper) is used to represent both distances in coordinate space and magnitudes of electric field vectors. In conceptual blending theory, this conflation is described as a clash between the input spaces in the blend. We explore the benefits and drawbacks of this clash, as well as other features of this representation. This analysis is illustrated with examples from clinical problem-solving interviews with upper-division physics majors. We see that while these intermediate physics students make a variety of errors using this representation, they also use the geometric features of the representation to add electric field contributions and to organize the problem situation productively.

In upper division electricity and magnetism, the manipulation and interpretation of vector functions is pervasive and a significant challenge to students. At CSU San Marcos, using in-class activities adapted from the Oregon State University Paradigms in Physics Curriculum, students' difficulties with vector functions become evident in two types of in-class activities: sketching vector functions and relating vector and scalar functions (e.g., electric field and electric potential). For many students, the cause of these difficulties is a failure to fully distinguish between the components of a vector function and its coordinate variables. To address this difficulty, we implement an additional inclass activity requiring students to translate between graphical and algebraic representations of vector functions. We present our experience with these issues, how to address them, and how in-class activities can provide evidence of student thinking that facilitates curricular refinement.

Background Adoption and use of effective, research-based instructional strategies (RBISs) for STEM education is less widespread than hoped. To promote further use of RBISs, the propagation paradigm suggests that developers work with potential adopters during the development process, and provide ongoing support after adoption. This article investigates the impact of a faculty online learning community (FOLC) as a professional development mechanism for supporting faculty adopting a research-based curriculum. A FOLC uses video conference technology and online platforms to connect geographically dispersed faculty with similar backgrounds (e.g., physics faculty) and supports their teaching development. In the context of a specific FOLC, this article seeks to determine the outcomes the FOLC achieves, and how. Results Analysis of a FOLC meeting identified opportunities for rich, complex social interaction centered on the research-based curriculum. By functioning as a sounding board for ideas, a space to share experiences, a source of affective support, and a venue for troubleshooting, the FOLC mediates the achievement of a range of outcomes related to implementation of the curriculum. Survey results indicate that members feel a sense of community in the FOLC and that it provides encouragement through teaching challenges. Further results indicate participants’ increased confidence in using the curriculum; familiarity with the curriculum structure and content; increased knowledge of pedagogical techniques; reflection on teaching practices in the curriculum; and use of pedagogical techniques aligned with the curriculum’s core principles. Emerging evidence supports more distal outcomes, including student learning, persistence in using the curriculum, reflection in teaching practice across courses taught, and use of research-based pedagogy in other courses. Conclusions The propagation paradigm emphasizes the need for ongoing support for adopters of RBISs. The FOLC model provides participating faculty with ongoing support through participation in a community and is an effective support mechanism for adopters of a research-based curriculum. In this study, FOLC members are increasing their knowledge and use of pedagogical techniques in the curriculum-specific course and beyond. This is facilitated by the opportunities in the FOLC for troubleshooting, idea sharing, and receiving encouragement through challenges. This model has the potential to support adopters of additional educational innovations.