Mathematical structures in quantum physics education for high school students: Unveiling the power of Dirac notation for conceptual and problem-solving proficiency

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 provides a concise and powerful symbolic framework that facilitates both conceptual and computational understanding. This study investigates the proficiency of HS students in interpreting, producing, and manipulating DN within QP. Utilizing qualitative content analysis of student responses to various tasks, quizzes, and final tests, the study aims to uncover the sensemaking opportunities DN provides and the difficulties students encounter. The findings indicate that DN facilitates both conceptual understanding and quantitative problem solving in QP by enabling students to interpret and produce representations of quantum states. The results highlight the importance of extensive practice and well-structured teaching sequences in developing DN proficiency, reinforcing the role of DN as an effective tool for teaching QP at the HS level. The study contributes to the ongoing discourse on integrating mathematical modeling in physics education, emphasizing the potential of DN in enhancing students' grasp of QP concepts and their application in problem solving.