Knowledge distillation improves a student model's reasoning ability through supervision from a teacher. On-policy self-distillation (OPSD) uses the same model as both teacher and student under different contexts: the student generates reasoning trajectories from the question alone, while the teacher additionally receives a complete worked example and provides token-level supervision along those trajectories. Because the problem statement is shared, its content and ordering shape both student generation and teacher feedback. Preserving its semantic structure therefore seems natural, but does it always improve learning? We introduce Shuffled OPSD, which shuffles the words of the shared problem statement while keeping the teacher-only worked example intact. Across three mathematical reasoning benchmarks and three Qwen3 model scales, the method improves mean accuracy over both an intact-target control and Standard OPSD under matched training configurations. The largest gain over Standard OPSD is 3.52 percentage points on Qwen3-1.7B. Further controls show that preserving larger word blocks offers no advantage over word-level shuffling at the evaluated scales, whereas shuffling the teacher-only worked example reduces accuracy at every scale. Cross-problem mixing and target-removal experiments further distinguish the roles of problem content, word order, and teacher context. These results show that disrupting the shared problem statement can improve learning, while disrupting the teacher-only reference hurts performance. They challenge semantic coherence as a universally beneficial principle for OPSD and motivate closer study of how input structure shapes student generation and teacher supervision.

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