Equipping Large Language Models (LLMs) with pedagogical tutoring capabilities holds significant promise for education. Existing approaches simulate tutor behaviors or preferences and use them to prompt or fine-tune LLMs for dialogue tutoring. However, such methods often fail to sustain high-quality pedagogical conversations that provide explicit stepwise scaffolding and adapt to learners’ evolving cognitive states. To address this, we propose ScaffoldLM, a planning-guided tutoring framework with an assessment-driven memory for multi-turn math dialogue tutoring. ScaffoldLM first generates a stepwise pedagogical plan from solution steps, which serves as a stable backbone for explicit scaffolding. During tutoring, the tutoring memory is updated by an assessment-driven control loop that infers the learner’s cognitive state, evaluates whether the current step target is met, and adaptively selects tutoring actions. The plan, step-level progress, inferred learner states, and dialogue history are maintained in memory to support coherent multi-turn guidance. Experiments on multi-turn math tutoring benchmarks demonstrate that ScaffoldLM substantially improves pedagogical tutoring quality over strong baselines. Code is publicly available at https://github.com/BNU-ERC-ITEA/ScaffoldLM.