Providing mathematical proofs to resolve conceptual difficulties is common practice in Physics teaching, especially by instructors following traditional lecture methods. We problematise the inefficacy of this instructional move by using episodes from a high school Physics classroom discussion about the working of a mercury barometer. It consists of a student experiencing difficulty understanding that the mercury column height remains unchanged irrespective of change in cross-sectional area of the barometer tube. This student maintained that a larger cross-sectional area would hold a greater volume of mercury. As a result, he maintained that the mercury column height couldn't be equal for two cases having varying cross-sectional areas. The instructors' response to this conceptual difficulty was to mathematically derive that the heights are equal. Analysis of the associated discourse revealed that the student’s difficulties remained unresolved despite the proof presented to him. We discuss the plausible reasons and instructional implications for the same. 

Universal Design for Learning (UDL) is a framework that supports instructors in designing inclusive learning environments that anticipate and plan for variations in students’ needs, abilities, and interests. UDL-aligned instructional design may reduce the need for accommodations for some students with disabilities. In this study, we explore postsecondary physics instructors’ approaches to adapting their teaching and learning environment while engaged in a year-long UDL learning community. Revealed causal mapping (RCM) is an analytic technique that uncovers experts’ mental maps about their subject domain. We employ RCM to value instructors’ knowledge and experiences and identify motivations and goals of the learning community members as they select, implement, and reflect on UDL-aligned modifications to their instruction.

Many elementary quantum mechanics textbooks are full of paradoxes. Nevertheless, the advanced quantum theory, quantum electrodynamics, is free from paradoxes. We show that the origin of paradoxes in elementary quantum mechanics textbooks is the concept of material point, a geometrical point r(t) with a fixed mass m. It does not exist in reality as it implies an infinite density. The Lagrangean-Hamiltonian mechanics of general coordinates q_n and general momenta p_n, is equally unrealistic. In quantum electrodynamics, there are no material points, there are only continuous fields. Upon interacting with other fields, mass, energy, and electrical charge are quantized. In the 1920s, several formulations of quantum mechanics were built upon the unrealistic Lagrangean-Hamiltonian mechanics of material points. By eliminating the concept of material points and starting from the all-field view of quantum electrodynamics, elementary quantum mechanics becomes free from paradoxes.

We outline the design and development of an interactive system - and associated teaching narrative - to learn the derivation of  variation of atmospheric pressure with height - the barometric formula. Our approach rethinks derivation - as a process of loading real-world phenomena into mathematical symbols. The resulting equation is considered a ’prediction machine’, as it enacts behavior of the starting phenomenon, which the derivation process loads into mathematical symbols. To understand the nature of learning based on this system, we invited two participants with minimal physics background to interact with it. Analysis of their interview data revealed indicative evidence of participants considering the system - and the narrative - as an improvement over their prior derivation learning experiences, based on traditional lecture format. However, the interviews did not provide any significant input on ways to redesign the system. We briefly discuss the implications and plausible reasons for these results.