The use of large language models to solve mathematical modeling problems: preservice mathematics teachers’ use practices, perceived affordances and challenges, and trustworthiness judgments of AI-generated outputs

Abstract Mathematical modeling is a core component of mathematics education, enabling learners to connect mathematical ideas with real-world phenomena. Yet, it remains challenging for preservice teachers (PSTs), who must develop their own modeling competence while preparing to guide future students in reasoning about authentic situations. Large language models (LLMs) offer promising, though underexplored, potential to scaffold these complex learning processes by providing real-time explanations, supporting reasoning, and assisting with problem solving. This study examines how PSTs engage with LLMs while solving modeling problems, focusing on the perceived affordances, challenges, and trustworthiness of these tools, an essential aspect for developing critical and pedagogically responsible AI use in modeling. The study involved 150 PSTs enrolled in a master’s-level mathematics course at a German university who worked collaboratively on three authentic modeling tasks. Multiple data sources were analyzed, including worksheets documenting LLM-user interactions, open-ended survey responses, and semi-structured interviews. The findings revealed that LLMs were predominantly used during the mathematization and understanding/simplifying phases of modeling, supporting assumption-making, formula retrieval, and the development of mathematical models and solution strategies. While participants valued LLMs’ efficiency and support, they raised concerns about inaccuracies, overreliance, and limited usefulness for reflective phases of modeling, such as validation. These results highlight the potentials and constraints of LLMs in modeling and call for pedagogical frameworks to cultivate critical AI literacy, epistemic awareness, and responsible use of LLMs in teacher education.