Computational Blueprints: Generating Isomorphic Mathematics Problems with Large Language Models

TL;DR

This paper introduces a new task called Isomorphic Math Problem Generation (IMPG) and presents the CBIT framework, which uses large language models to generate structurally consistent math problems efficiently, improving correctness and reducing costs.

Contribution

The paper defines IMPG, a novel task for generating structurally similar math problems, and proposes CBIT, a framework that leverages meta-level generation and templates for high-quality problem creation.

Findings

CBIT achieves high mathematical correctness and structural consistency.

CBIT reduces generation costs compared to previous methods.

Problems generated by CBIT have 17.8% fewer errors than expert-authored items.

Abstract

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.