Computational Blueprints: Generating Isomorphic Mathematics Problems with Large Language Models
This work addresses the demand for scalable, personalized practice problems in mathematics education, representing an incremental advance by applying LLMs to a specific educational task.
The paper tackled the need for personalized mathematics education by introducing the Isomorphic Math Problem Generation (IMPG) task to create structurally consistent practice problems, and developed the CBIT framework using LLMs, which reduced error rates by 17.8% compared to expert-authored items and was deployed to 6,732 learners with 186,870 interactions.
Personalized mathematics education is growing rapidly, creating a strong demand for large sets of similar practice problems. Yet existing studies on mathematics problem generation have focused on data augmentation for training neural language models rather than on direct educational deployment. To bridge this gap, we define a new task, Isomorphic Math Problem Generation (IMPG), designed to produce structurally consistent variants of source problems. Subsequently, we explored LLM-based frameworks for automatic IMPG through successive refinements, and established Computational Blueprints for Isomorphic Twins (CBIT). With meta-level generation and template-based selective variation, CBIT achieves high mathematical correctness and structural consistency while reducing the cost of generation. Empirical results across refinements demonstrate that CBIT is superior on generation accuracy and cost-effectiveness at scale. Most importantly, CBIT-generated problems exhibited an error rate 17.8% lower than expert-authored items, with deployment to 6,732 learners on a commercial education platform yielding 186,870 interactions.