Examining AI interaction profiles in generative AI supported fraction division problem posing

Introduction Generative artificial intelligence (GenAI) offers new opportunities for mathematical problem posing, yet its relationship with the conceptual quality of posed problems and learners’ interaction profiles remains insufficiently understood. This study examines pre-service mathematics teachers’ fraction-division problem posing with and without GenAI support. Methods Using a mixed-methods descriptive–relational design, 57 pre-service mathematics teachers first posed a fraction-division word problem independently and then posed or revised a second problem with Google Gemini support. Problems were assessed using a rubric addressing general-mathematical quality and content-specific meanings of fraction division. Qualitative analysis of AI interactions identified three profiles: AI-Reliant, AI-Collaborative, and AI-Assistant. Quantitative analyses compared scores across phases and gains across profiles, incorporating robustness checks, multiple-comparison correction, effect sizes, and confidence intervals. Results AI-supported problems received significantly higher scores for contextual richness, language clarity, and content-specific meaning use; these differences remained significant after Holm correction. Problem type and solvability did not differ significantly. All participants retained the fraction-division meaning used in their independently posed problem, with changes consisting solely of added meanings, most often measurement division. Although AI-Assistant participants showed descriptively greater gains, differences across profiles were not statistically significant. Discussion The findings are consistent with refinement of representational and communicative features and more explicit articulation of existing fraction-division meanings, rather than correction of foundational mathematical understanding. The fixed-order design requires interpreting phase differences as associations rather than causal effects of GenAI. Small, unequal profile groups and wide confidence intervals also preclude interpreting nonsignificant differences as evidence of profile equivalence.