Effective teacher training requires exposure to a wide array of student behaviors and learning challenges. This paper introduces MisstepMath (MisstepMath Dataset: https://huggingface.co/datasets/LLMEducation/MisstepMath ), a novel semi-synthetic dataset comprising 12,000 categorized student mistakes paired with instructional teacher responses. Designed to enhance AI-driven teacher training, MisstepMath spans mathematics topics and sub-topics from Kindergarten through Grade 8, systematically categorizing errors into conceptual misunderstandings, procedural mistakes, learning disabilities, and language-related difficulties. Developed in three phases—expert brainstorming and categorization, AI-assisted data generation, and expert review and refinement—MisstepMath ensures diverse and contextually rich student simulations. This approach combines human expertise with AI generation to improve coverage of rare errors, reduce bias, and maintain pedagogical quality. The primary goal of MisstepMath is to support the development of AI models capable of generating diverse student interactions, therefore enabling teachers to practice addressing varied learning challenges. It can be used for fine-tuning conversational AI models to produce contextually relevant student responses, as a knowledge base in Retrieval-Augmented Generation (RAG) systems to improve AI-driven educational tools, or as a benchmark for evaluating AI-driven teacher models. By capturing a broad spectrum of student difficulties and instructional strategies, MisstepMath aims to enhance the adaptability and effectiveness of AI models in education, benefiting teacher training programs, intelligent tutoring systems, and adaptive learning platforms.