Generative AI in Mathematics Teacher Education: Designing Simulated Students to Generate Approximations to Practice Around Equal-Sign Misconceptions

This paper reports the design and refinement of a generative-AI simulation for mathematics teacher education centred on equal-sign misconceptions. We developed three custom chatbots that simulate middle-school students (11–12 years old) who exhibit distinct operational interpretations of “=” across three research-based tasks: 8 + 4 = + 5, a chained equality (4 + 5 = 9 + 3 = 12), and 37 + 54 = + 55. Each simulated student was paired with a short video depicting the student’s incorrect reasoning and was engineered through persona prompting to sustain “student-like” dialogue (brief initial justifications, resistance to immediate correction, inconsistent improvement, and spontaneous doubts) to preserve teachers’ opportunities to elicit, interpret, and respond to student thinking. In parallel, we designed a mentor chatbot that provides structured formative feedback (strengths, areas for improvement, suggestions) anchored in equal-sign instruction and responsive teaching. We describe iterative development and cross-linguistic adaptation that addressed common failure modes of GenAI-based simulations, such as overly articulate student responses and generic feedback. The paper contributes a practical design account of how prompt constraints, role separation, and task-misconception alignment can make GenAI-based simulations more stable and instructionally useful as approximations to practice.