STEP: From Local Teacher Scaffolds to Student-Owned Reasoning in Small Language Models

Improving the reasoning abilities of small language models requires successful reasoning experience that can be converted into independent problem-solving ability. Teacher distillation provides correct solutions, but teacher-generated reasoning paths are not always suitable for the student to learn from. Self-training on the student’s own successful traces, in contrast, rarely provides successful experience beyond the student’s current ability. We therefore ask how a small reasoning model can learn to reason beyond its current limits from self-generated experience with the help of temporary external scaffolds. Inspired by instructional scaffolding, we propose STEP (Scaffolded Training through Experience Production), in which a teacher provides a local scaffold at the reasoning obstacle exposed by a student’s failed attempt, allowing the student to complete the remaining reasoning and produce a verified successful trace. During training, STEP includes the scaffold explicitly in the input and concentrates supervision on the scaffold and the student continuation that follows it, turning assisted experience into a learning resource. We evaluate STEP after removing the scaffold. Across two student sizes, two teacher models, and five mathematical reasoning benchmarks, STEP raises the scaffold-free MATH500 mean@4 of Qwen2.5-3B-Instruct from 57.15% to 62.05% in the Qwen3-235B teacher setting, exceeding P-ALIGN by 4.80 percentage points. These results suggest that local teacher scaffolds can turn successful experience that the student could not otherwise generate independently into stronger independent reasoning ability.