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.

Large language models (LLMs) have demonstrated exceptional performance across a wide range of natural language tasks. However, selecting the optimal LLM to respond to a user query often necessitates a delicate balance between performance and cost. While powerful models deliver better results, they come at a high cost, whereas smaller models are more cost-effective but less capable. To address this trade-off, we propose IRT-Router, a multi-LLM routing framework that efficiently routes user queries to the most suitable LLM. Inspired by Item Response Theory (IRT), a psychological measurement methodology, IRT-Router explicitly models the relationship between LLM capabilities and user query attributes. This not only enables accurate prediction of response performance but also provides interpretable insights, such as LLM abilities and query difficulty. Additionally, we design an online query warm-up technique based on semantic similarity, further enhancing the online generalization capability of IRT-Router. Extensive experiments on 20 LLMs and 12 datasets demonstrate that IRT-Router outperforms most baseline methods in terms of effectiveness and interpretability. Its superior performance in cold-start scenarios further confirms the reliability and practicality of IRT-Router in real-world applications. Code is available at https://github.com/Mercidaiha/IRT-Router.

As intelligent education evolves, it will provide students with multiple personalized learning services based on their individual abilities. Computerized adaptive testing (CAT) is designed to accurately measure a student’s ability using the least questions, providing an efficient and personalized testing method. However, existing methods mainly focus on minimizing the number of questions required to assess ability, often lacking clear and reliable explanations for the question selection process. Educators and students can hardly trust and accept CAT systems without an understanding of the rationale behind the question selection process. To address this issue, we introduce LLM-Agent-Based CAT (LACAT), a novel agent powered by large language models to enhance CAT with human-like interpretability and explanation capabilities. LACAT consists of three key modules: the Summarizer, which generates interpretable student profiles; the Reasoner, which personalizes questions and provides human-readable explanations; and the Critic, which learns from past choices to optimize future question selection. We conducted extensive experiments on three real-world educational datasets. The results demonstrate that LACAT can perform comparably or superior to traditional CAT methods in accuracy and significantly improve the transparency and acceptability of the testing process. Human evaluations further confirm that LACAT can generate high-quality, understandable explanations, thereby enhancing student trust and satisfaction.