Skeleton-based reasoning prompting is a promising training-free approach for structuring LLM reasoning, but prior work largely assumes an English-centric setting. We propose the Language-Aware Skeleton Exploration Framework (LASEF) to study skeleton-language choice in multilingual mathematical reasoning. Across math benchmarks, model scales, and languages, we show that English skeletons yield a small positive tendency on average, most visible for smaller models and low-resource languages. However, few language-level gains remain significant after correction, and English is not universally optimal. Combining greedy decoding, multi-rollout evaluation, translation ablation, and cross-benchmark validation, we further find three patterns of skeleton-language effects: directionally consistent, evaluation- and benchmark-dependent, and asymmetric negative. These effects cannot be fully explained by generation quality alone. Overall, skeleton language is a context-dependent design variable that requires multi-level exploration. All resources are released at https://github.com/lhsstn/LASEF.

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