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.

Large Language Models (LLMs) have achieved remarkable performance across a wide range of mathematical benchmarks. However, concerns remain as to whether these successes reflect genuine reasoning or superficial pattern recognition. Existing evaluation methods, which typically focus either on the final answer or on the intermediate reasoning steps, reduce mathematical reasoning to a shallow input–output mapping, overlooking its inherently multi-stage and multi-dimensional cognitive nature. Inspired by P’olya’s problem-solving theory, we propose SMART, a benchmark that decomposes mathematical problem-solving into four cognitive dimensions: **S**emantic Understanding, **M**athematical Reasoning, **A**rithmetic Computation, and **R**eflection Refinemen**T**, and introduces dimension-specific tasks to measure the corresponding cognitive processes of LLMs. We apply SMART to 22 state-of-the-art open- and closed-source LLMs and uncover substantial discrepancies in their capabilities across dimensions. Our findings reveal genuine weaknesses in current models and motivate a new metric, the All-Pass Score, designed to better capture true problem-solving capability.