Failures are Treasures: Constructing a Pedagogical Bridge for Agentic Strategy Distillation

While Large Language Models (LLMs) excel in reasoning tasks, small language models (SLMs) remain fragile, often collapsing after encountering errors. Traditional knowledge distillation focuses on imitating successful trajectories, while existing "learning from mistakes" methods treat errors as auxiliary signals rather than states requiring recoverable policies, leaving the dynamics of failure and recovery in agent settings largely unexplored. Inspired by Donald Schön's theory of reflective practice, we propose P-BRIDGE (Pedagogical Bridge for Reflective Insight and Distillation of Guiding Errors). P-BRIDGE combines reflectionin-action with reflection-on-action, enabling agents to diagnose and correct critical errors during execution while abstracting transferable strategies from contrastive student-teacher trajectories. Experiments across eight benchmarks in controlled environments demonstrate that P-BRIDGE significantly elevates SLM performance-e.g., raising the 2WikiMultiHopQA accuracy of a 0.6B model from 6.2% to 34.2%.