Large Language Models (LLMs) excel at complex tasks, including reasoning, but their massive size makes them impractical for everyday devices. Researchers are exploring how to distill this intelligence into smaller, more efficient models, a process known as knowledge distillation. But simply transferring raw knowledge isn't enough. A new study has found a clever way to boost the math skills of these smaller AIs by using a feedback-driven approach. Imagine a teacher adapting their lessons based on a student's strengths and weaknesses. This research does something similar. By identifying which math problems a small AI model solves easily and which ones it struggles with, researchers can tailor the training process. For easy problems, the AI is challenged with more complex variations, pushing its abilities further. For difficult problems, similar problems are generated, reinforcing the core concepts. This targeted training method, called Feedback-Driven Distillation (FDD), allows the smaller models to learn more efficiently. The results are impressive. Small language models trained with FDD achieve state-of-the-art performance on math reasoning tasks, rivaling even some larger, open-source models. This approach not only improves their ability to solve problems within the training data but also enhances their ability to generalize to new, unseen math problems. This breakthrough has significant implications for the future of AI. By making powerful reasoning abilities accessible to smaller models, we can integrate advanced AI capabilities into a wider range of applications, from smartphones and personal assistants to embedded systems in various devices. While promising, challenges remain. The process still relies on larger models to generate training data, which can be computationally expensive. Future research will focus on streamlining this process and exploring new ways to further enhance the reasoning abilities of smaller, more efficient AI models, making them truly powerful thinkers in a compact package.