Automatically generating high-quality mathematical problems that align with
educational objectives is a crucial task in NLP-based educational technology.
Traditional generation methods focus primarily on textual quality, but they
often overlook educational objectives. Moreover, these methods address only
single-dimensional, simple question generation, failing to meet complex,
multifaceted educational requirements. To address these challenges, we
constructed and annotated EduMath, a dataset of 16k mathematical questions with
multi-dimensional educational objectives. Based on this dataset, we developed
EQGEVAL, which incorporates three evaluation dimensions and is designed to
assess the ability of models to generate educational questions. Drawing
inspiration from teachers' problem design processes, we propose the Educational
Question Planning with self-Reflection (EQPR) method for educational
mathematical question generation, following a "plan-evaluate-optimize"
approach. Specifically, by combining planning algorithm based on Monte Carlo
Tree Search with the generative capabilities of Large Language Models, we
continuously optimize questions through iterative feedback. This
self-optimization mechanism ensures that the generated questions both fit the
educational context and strategically achieve specific basic educational
objectives. Through extensive experiments based on EQGEVAL, we have
demonstrated that EQPR achieves significant improvements in generating
questions that meet multi-dimensional educational objectives.