Knowledge Tracing (KT) is a critical component in online learning, but traditional approaches face limitations in interpretability and cross-domain adaptability. This paper introduces Language Model-based Code Knowledge Tracing (CodeLKT), an innovative application of Language model-based Knowledge Tracing (LKT) to programming education. CodeLKT leverages pre-trained language models to process learning data, demonstrating superior performance over existing KT and Code KT models. We explore Domain Adaptive Pre-Training (DAPT) and Task Adaptive Pre-Training (TAPT), showing enhanced performance in the coding domain and investigating cross-domain transfer between mathematics and coding. Additionally, we present an theoretically-informed integrated system combining CodeLKT with large language models to generate personalized, in-depth feedback to support students' programming learning. This work advances the field of Code Knowledge Tracing by expanding the knowledge base with language model-based approach and offering practical implications for programming education through data-informed feedback.
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