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.

Knowledge Tracing (KT) is a crucial research task for dynamically monitoring students' knowledge states, particularly in online education systems. Recently, knowledge tracing has gained significant attention and in-depth research. Most existing methods rely on students' response data for question understanding and modeling, which helps better updating students' knowledge states. Meanwhile, question ID is utilized to indicate and represent questions. However, this presents a challenge when transitioning to new, cold-start questions that few students has answered before. Also, prior work has overlooked the semantic modeling of questions, which could better assist in modeling the transfer of students' knowledge states. In this paper, we explore leveraging the power of Large Language Models (LLMs) to help understand questions for knowledge tracing, which benefits mitigating cold-start and sparse problems and modeling the transfer of students' knowledge states in a sophisticated manner. Specifically, we first design an attribute estimation module to estimate the attribute of the questions (e.g., difficulty, ability requirements, expected response time) by prompting Large Language Models. Subsequently, we have developed a question embedding module that incorporates graph attention network to effectively utilizing these attributes. Extensive experiments on various datasets demonstrate that our model outperforms existing state-of-the-art models and effectively addresses the problems of cold-start and sparsity. In addition, due to the estimation of multiple attributes of the questions, our model exhibits superior interpretability.