EduAgentQG: Multi-agent personalized mathematics question generation with explicit diversity and objective-aware evaluation

In intelligent education, personalized mathematics question generation aims to produce mathematics questions that satisfy educational requirements while supporting adaptive assessment and learning. Existing LLM-based single-agent and multi-agent methods improve generation flexibility, but they still tend to rely on aggregated feedback or model randomness, making it difficult to jointly ensure dimension-wise objective alignment and controllable diversity. To address these challenges, we propose EduAgentQG, a multi-agent collaborative framework for personalized mathematics question generation with explicit diversity and objective-aware evaluation. EduAgentQG organizes question generation as a closed-loop process of planning, writing, evaluation, refinement, and checking: structured generation plans and multiple generation directions guide candidate generation, while fine-grained evaluation verifies logical correctness, solvability, and objective alignment in knowledge concepts, difficulty, grade level, and core competencies. We first construct a mathematics question generation benchmark containing 10,273 questions across Grades 1–9, covering 634 knowledge concepts, 16 core competencies, and three difficulty levels; for evaluation, it is organized into two subsets: MathChoice, with 489 educational objectives for multiple-choice question generation, and MathBlank, with 500 educational objectives for fill-in-the-blank question generation. Experiments using Gemini-2.5-Flash, GPT-4o-mini, and Qwen2.5-72B-Instruct show that EduAgentQG consistently outperforms COT, COTN[jls-end-space/], ReAct, and EQPR in diversity, Objective Consistency, and Win Rate. On Gemini-2.5-Flash, EduAgentQG improves Win Rate by 3.90 and 4.75 percentage points on MathChoice and MathBlank, respectively, over the strongest baseline, demonstrating its ability to generate diverse, solvable, and educationally aligned personalized mathematics questions with stronger controllability.