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Teaching is inherently complex and decomposing teaching into core practices is a productive way to help preservice mathematics teachers (PSMTs) learn high-quality mathematics instruction. Generative artificial intelligence (GenAI) tools mark a new era in leveraging AI-based approaches to support teaching. However, limited research exists on using GenAI to support the learning of teaching practices and there is little guidance for teacher educators on integrating GenAI into teacher preparation programs. This paper introduces the GenAI Simulation (GenSim) Model, which embeds GenAI technologies into mathematics education courses to help PSMTs learn and enact high-leverage core teaching practices. The GenSim application proposes a practice-based learning environment where PSMTs engage in a structured four-phase cycle to develop core teaching practices with AI integration.