Large Language Models (LLMs) have taken the AI world by storm, but they're not without their limitations. One challenge is efficiently transferring the knowledge of massive, resource-intensive LLMs to smaller, more deployable models. Traditionally, this 'knowledge distillation' process has focused on mimicking the teacher model's direct outputs. But what if we could unlock even greater potential by changing *how* we prompt the teacher during this transfer? New research explores innovative 'response-priming' prompting strategies that significantly boost student model performance. Imagine a teacher LLM not just giving answers, but explaining its reasoning process step-by-step. This research does just that, testing different prompts to guide the teacher's responses. The results are striking, with some prompting methods leading to a 55% performance increase on complex mathematical reasoning tasks compared to standard distillation. One particularly effective technique involves telling the teacher LLM it's training a smaller model—almost like giving it a sense of purpose! This 'Ground Truth' prompting encourages the teacher to provide clearer, more digestible explanations, leading to remarkable improvements in the student's reasoning abilities. This research delves into *why* these prompting strategies work so well, examining the inner workings of the student models. It turns out that effective prompting leads to more structured and contextually aware attention patterns within the model, ultimately improving its understanding and problem-solving skills. While this study focuses on mathematical reasoning, the implications are far-reaching. These prompting techniques could revolutionize how we train and deploy smaller, more efficient LLMs across various domains, paving the way for more accessible and powerful AI in the future. However, further research is needed to explore the generalizability of these techniques across different LLMs and tasks. This study raises intriguing questions about the role of prompting in AI learning and opens up exciting new avenues for improving LLM performance. It's a fascinating glimpse into the future of AI education—where smarter prompting leads to smarter AI.