Large language models (LLMs) are considered a crucial technology for advancing intelligent education since they exhibit the potential for an in-depth understanding of teaching scenarios and providing students with personalized guidance. Nonetheless, current LLM-based application in personalized teaching predominantly follows a "Question-Answering" paradigm, where students are passively provided with answers and explanations. In this paper, we propose SocraticLM, which achieves a Socratic "Thought-Provoking" teaching paradigm that fulfills the role of a real classroom teacher in actively engaging students in the thought process required for genuine problem-solving mastery. To build SocraticLM, we first propose a novel "Dean-Teacher-Student" multi-agent pipeline to construct a new dataset, SocraTeach, which contains 35 K meticulously crafted Socratic-style multi-round (equivalent to 208 K single-round) teaching dialogues grounded in fundamental mathematical problems. Our dataset simulates authentic teaching scenarios, interacting with six representative types of simulated students with different cognitive states, and strengthening four crucial teaching abilities.