A self-distillation approach for enhancing intelligence tutoring system math solving based on large language models

Intelligent tutoring systems have demonstrated strong capabilities in supporting students' learning, particularly in solving predefined problems. However, they have a key limitation: intelligent tutoring systems are designed to solve only the problems specifically programmed into the system. This paper introduces a novel approach that integrates large pre-trained models into local intelligent tutoring systems to address this challenge. Specifically, we propose a method where a local large pre-trained model generates high-accuracy logical reasoning through the chain of thought and enhanced computational capabilities via the program of thought. By combining these two outputs, we generate high-quality synthetic data to train the local model, improving its ability to solve a broader range of mathematical problems, including those it has not previously encountered. Experimental results demonstrate that our approach significantly enhances both reasoning precision and computational efficiency, ultimately improving the overall performance of local intelligent tutoring systems in supporting students with mathematical problem-solving.