Optimizing Mathematical Problem-Solving Reasoning Chains and Personalized Explanations Using Large Language Models: A Study in Applied Mathematics Education

Abstract

This study investigates the optimization of mathematical problem-solving through Large Language Models (LLMs), focusing on developing enhanced reasoning chains and personalized explanations in applied mathematics education. The research implements a novel framework integrating LLM-based reasoning chain generation with adaptive personalization algorithms, demonstrating significant improvements in student learning outcomes. Through a comprehensive experimental evaluation involving 2,854 students across different proficiency levels, the system achieved a 98.7% accuracy rate in mathematical problem-solving and a 92.3% user satisfaction rate. Implementing personalized explanation systems resulted in a 27.8% improvement in student comprehension and a 31.5% increase in engagement rates. Performance analysis revealed robust scalability, maintaining response times below 312ms under peak loads of 850 requests per second. The findings demonstrate the effectiveness of LLM-based approaches in enhancing mathematics education through automated reasoning chain generation and personalized instruction. The research contributes to advancing AI-assisted educational technologies and provides valuable insights for developing intelligent tutoring systems in STEM education.