Reasoning distillation is widely used to transfer the reasoning capabilities of large language models to smaller students through teacher-generated supervision. In the black-box setting, however, teachers may expose only final answers and brief solutions, leaving intermediate calculations and validity conditions unavailable and thus limiting the reasoning supervision available for distillation. We propose Stepwise Querying, which elicits step-specific explanations without requiring access to the teacher's internal chain-of-thought (CoT) traces. Independent queries to the same teacher request intermediate derivations, validity checks, and corrections for individual steps, the assembled solutions are then used for standard supervised fine-tuning. Across two teachers, two students, and four mathematics and code benchmarks, our method achieves the highest score in 14 of 16 comparisons with three baselines. We further introduce Stepwise Explanation Information Gain (SEIG), a diagnostic based on the log-ratio of a frozen student's probabilities of correct step completion under stepwise and global explanations. Analyses on GSM8K show that incorrect-answer trajectories can remain useful when they preserve valid intermediate reasoning, while further decomposition yields limited additional gains.

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