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This study explores the potential of phonological reasoning within text-based large language models (LLMs). Utilizing the PhonologyBench benchmark, we assess tasks like rhyme word generation, g2p conversion, and syllable counting. Our evaluations across 12 LLMs reveal that while few-shot learning offers inconsistent gains, the introduction of a novel Pedagogically-motivated Participatory Chain-of-Thought (P-CoT) prompt, which is anchored in educational theories like scaffolding and discovery learning, consistently enhances performance. This method leverages structured guidance to activate latent phonological abilities, achieving up to 52% improvement and even surpassing human baselines in certain tasks. Future work could aim to optimize P-CoT prompts for specific models or explore their application across different linguistic domains.