Imagine trying to teach a brilliant but easily distracted student a complex math problem. That’s the challenge with Large Language Models (LLMs). They're great at many things, including math, but their massive size makes them computationally expensive and difficult to deploy widely. This new research explores how to "distill" the mathematical reasoning abilities of these giant LLMs into smaller, more efficient models, called SLMs, which are easier to run on everyday devices. The problem? SLMs often stumble on tricky problems, not because they can't calculate, but because they misinterpret the question's meaning (semantic errors) or miss crucial steps. The researchers propose a clever two-step solution called "Key-Point-Driven Mathematical Reasoning Distillation" (KPDD). First, KPDD trains one SLM to identify the core question and relevant information, much like a student underlining the essential parts of a word problem. Second, another SLM, guided by these highlighted key points, solves the problem step-by-step. The researchers tested two versions: KPDD-CoT, generating human-readable explanations (Chain-of-Thought), and KPDD-PoT, generating Python programs (Program-of-Thought). Both showed improvement, but KPDD-PoT, with its precise instructions, proved especially powerful, significantly reducing errors and even reaching state-of-the-art accuracy on certain math datasets. This innovative method is a significant step toward making AI-powered math tutors, automated problem solvers, and educational tools more accessible. However, further research is needed to understand how the distillation process could be further improved and applied to other types of reasoning tasks.