Enrico Fermi is remembered for his many contributions to theoretical and experimental physics, but from an educational point of view he also popularized the use of the kind of questions we now call "Fermi problems" (or "Fermi questions"). Fermi problems (FPs) are back-of-envelope problems that arose from the need to make order…

To make sense of our interconnected and algorithm driven world, students increasingly need proficiency with computational thinking (CT), systems thinking (ST), and computational modeling. One aspect of computational modeling that can support students with CT, ST, and modeling is testing and debugging. Testing and debugging enables students to…

The pretrained large language models have been widely tested for their performance on some challenging tasks including arithmetic, commonsense, and symbolic reasoning. Recently how to combine LLMs with prompting techniques has attracted lots of researchers to propose their models to automatically solve math word problems. However, most research…

In this article we show that the electrostatic field intensity of a uniformly charged straight line equals that of the corresponding arc of a circle charged with the same linear density. This new method greatly simplifies the calculation of the electrostatic field of a system consisting of uniformly charged straight lines.

In the context of quantum mechanics, students are often asked to use delta functions to solve problems. Here, we investigate three typical problem-solving processes using delta functions: a delta function potential well problem, a position space delta function problem, and a momentum space delta function problem. We studied students'solutions in…

Commonly used methods to simulate the oxidation-reduction (redox) titration curves include the three-step method and the rigorous method. The simple three-step method simulates the redox titration curve with the assumption that the reaction is complete, which is widely used in undergraduate quantitative analysis courses. For the rigorous…

A well known physics problem is to calculate the friction forces required to support a ladder against a wall. A more tractable problem is to calculate the friction forces needed to support an inclined beam on a ball or a cylinder. In the latter case there are three rather than two points of sliding support. Measurements and calculations are…

The use of approximations in solving problems in sciences can be vital for students. Order of magnitude estimation also helps with physical understanding of the quantities involved in a calculation. For example, in the first exam in a first-year class in chemistry the student must find the mass in grams of an atom; a couple of students will…

Back-of-the-envelope (BOTE) calculations require the use of estimations and approximations. They are used by expert physicists to simplify complex problems to obtain quick and approximate solutions. Though BOTE calculations are routine for experts in physics, they are not well defined in academic literature. In this study we interviewed 9…

The purpose of this study was to quantitatively assess the integration of computational thinking with learning about biological evolution. Specifically, we investigated the effectiveness of a framework from a recently developed learning progression that emphasises the complex nature of teaching both computational thinking and biological evolution.…

Teaching quantum physics (QP) to high school (HS) students is gaining momentum, necessitating the exploration of various effective methods. Specifically, the research on quantitative teaching methods is still in its early stages. Understanding the power of Dirac notation (DN) in teaching is crucial for grasping the complexities of QP, as it…

The purpose of this study was to evaluate the implementation and impact of the Pack program. The Pack was developed by the New York Hall of Science (NYSCI) and includes a digital game and set of curricular and professional development resources that aim to support computational thinking teaching and learning in middle school science and computer…

Symmetry and invariance play a fundamental role in modern physics and related disciplines, and students entering a STEM field need practice with symmetry-based arguments as part of the preparation for their future careers. We refer to symmetry based solutions as those that either make use of the existing geometric symmetry in a problem to simplify…

An undergraduate-level Computational Chemistry project was incorporated initially into a Physical Chemistry course and then into the laboratory curriculum in the subsequent application. Before the introduction of the project, the lectures covered quantum chemistry, spectroscopy, and kinetics while simultaneously including computational chemistry…

Student performance on open-response calculations involving acid and base solutions before and after instruction in general chemistry and analytical chemistry courses was compared with the output from the artificial intelligence chatbot ChatGPT. Applying a theoretical model of expertise for problem solving that includes problem conceptualization,…