The role of conceptual problem solving in learning physics: A study in a general relativity university course

Effective physics learning, especially in complex topics, requires balancing mathematical formalism with conceptual understanding. Conceptual problem-solving involves connecting math to physical reality, and using an epistemological framework like problem framing helps students justify their mathematical decisions. This approach deepens students' understanding by linking theory to practice and enhancing their reasoning skills. This study explores the effectiveness of conceptual problem-solving in learning complex topics like general relativity (GR) through a pedagogical framework that emphasizes the integration of qualitative and quantitative reasoning. We present a case study conducted at the University of Cagliari in 2021 and 2022, examining how students construct problem frames and how this influences their conceptual understanding of GR. Findings indicate that students who effectively integrate conceptual reasoning with mathematical formalism demonstrate a deeper grasp of physical principles and enhanced problem-solving capabilities. The research underscores the importance of symbol sense and the iterative nature of problem framing, suggesting that an integrated approach—combining visual, symbolic, and natural language representations—can improve students’ conceptual engagement. Furthermore, the methodology offers instructors valuable insights into students’ thinking processes, supporting more effective and targeted feedback.