Mathematical problem transformation is a teaching-and-learning strategy that extends conceptual understanding and problem-solving ability by expressing the same concept across diverse situations. It has recently attracted attention in artificial intelligence as a tool for data augmentation, difficulty control, and model evaluation. However, existing approaches struggle to jointly represent and control how core mathematical elements—such as operational structure, quantitative relations, and conditions—are preserved or modified. This limitation is particularly evident in natural-language problems, where intertwined components make it difficult to perform targeted partial transformations or verify structural validity. To address these challenges, we propose the Symbolic Math Problem Representation Framework (SyMPRep), which represents the relationships among sentences, conditions, questions, quantities, units, and operations in a symbolic structure. It classifies free-form instructions into predefined categories and decomposes problems into constituent elements, enabling transformation over an explicit abstraction structure. This allows problem transformation to be treated as a controllable , traceable, and recoverable structural operation rather than surface rewriting. Experiments on GSM8K and Math500 show that SyMPRep achieves stable alignment and recoverability, and confirm that the main challenge lies in structural control rather than surface fluency. Ablation results highlight the importance of symbolic schema and show that different metrics capture distinct aspects of transformation quality. In downstream applications, answer-invariant transformations yield modest improvements on easier problems, while human evaluation indicates that the generated problems are coherent and suitable for educational use. These findings suggest that SyMPRep serves as a representation-driven interface for controllable structural transformation.
Namgoong et al. (Sun,) studied this question.