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…

This study examines the feasibility and potential advantages of using large language models, in particular GPT-4o, to perform partial credit grading of large numbers of student written responses to introductory level physics problems. Students were instructed to write down verbal explanations of their reasoning process when solving one conceptual…

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 a typical first physics class, homework consists of problems in which numerical values for physical quantities are given and the desired answer is a number with appropriate units. In contrast, most calculations in upper-division undergraduate physics are entirely symbolic. Despite the need to learn symbolic manipulation, students are often…

Nowadays, physics learning in the classroom should no longer only focus on achieving academics. It must prepare students to face challenges in the future. One of the abilities that are important for learners is problem solving, and the problem-solving ability that is becoming increasingly important in today's digital era is computational thinking…

This paper presents research activity on computer-based mathematics learning to study the effectiveness of open-source teaching computer platforms (Canvas) in computer-assisted instruction. We designed a set of multiple-choice online quizzes as a dynamical flow-chart of possible paths to follow while solving a difficult math problem on…

We report an educational tool for the upper level undergraduate quantum chemistry or quantum physics course that uses a symbolic approach via the PySyComp Python library. The tool covers both time-independent and time-dependent quantum chemistry, with the latter rarely considered in the foundations course due to topic complexity. We use quantized…

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…

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…

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…

Identifying students' difficulties in understanding Gauss's and Ampere's laws is important for developing educational strategies that promote an expertlike understanding of the field concept and Maxwell's equations of electromagnetic phenomena. This study aims to analyze and compare students' understanding of symmetry when applying Gauss's and…

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…

In quantum mechanics courses, students are often asked to solve bound and scattering state problems. The use of an ordinary differential equation is a standard technique to solve these questions. Here, we investigated students' problem-solving processes for two typical problems of a single particle in one spatial dimension: a bound state problem…

An important step in learning to use math in science is learning to see symbolic equations not just as calculational tools, but as ways of expressing fundamental relationships among physical quantities, of coding conceptual information, and of organizing physics knowledge structures. In this paper, I propose "anchor equations" as a…

An onto-semiotic analysis of the mathematical connections established by one in-service mathematics teachers and university students when solving a problem about launching a projectile using the derivative was carried out. Theoretically, this research was based on the articulation between the Extended Theory of Mathematical Connections and the…