From Objectives to Questions: A Planning-based Framework for Educational Mathematical Question Generation

TL;DR

This paper introduces a novel planning-based framework for generating educational mathematical questions that align with multi-dimensional objectives, utilizing a new dataset and self-reflective optimization to improve quality and relevance.

Contribution

It presents EduMath dataset, EQGEVAL evaluation, and EQPR method combining planning, self-reflection, and large language models for improved educational question generation.

Findings

EQPR outperforms baseline models in aligning questions with educational objectives.

The EduMath dataset enables multi-dimensional evaluation of question quality.

Self-optimization improves question relevance and educational fit.

Abstract

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.