This study aims to give chemistry students a deeper understanding of electron shielding and quantum transitions by interpreting the characteristic X-ray lines. There is a popular misunderstanding among learners and even teachers in which an outer-shell electron fills a vacancy in the inner shell, releasing some of its energy as an X-ray photon.…

Analysing graphs, formulating covariational relationships, and hypothesizing systems' behaviour have emerged as frequent objectives of contemporary research in physics education. As such, these studies aim to help students achieve these objectives. While a consensus has been reached on the cognitive benefits of emphasizing the structural domain of…

This paper was first motivated by the following question: "A pair of twins, R and S, each gives the "same" hard push on a block. R's block is on a rougher floor than S's. Who does more work?" It is shown that S will do more work on his block if there is no constraint on the distance over which the force is applied. On the other hand, if the…

Nearly 50 years ago, Henry Bent published his groundbreaking article in this "Journal" introducing the "global" formulation of thermodynamics. In the following years, the global formulation was elaborated by Bent and by one of the present authors. The global formulation of the first law focuses on conservation of energy and the recognition that…

The Lorentz velocity addition formula for one-dimensional motion presents a number of problems for beginning students of special relativity. In this paper we suggest a simple rewrite of the formula that is easier for students to memorize and manipulate, and furthermore is more intuitive in understanding the correction necessary when adding…

Benjamin Banneker, a self-taught mathematician, surveyor and astronomer published annual almanacs containing his astronomical observations and predictions. Banneker who also used logarithms to apply the Law of Sines believed that the method used to solve a mathematical problem depends on the tools available.