Recent advances in large language models (LLMs) have led to the development of AI-powered tutoring systems that provide interactive support via dialogue. To enable these tutoring systems to provide personalized support, it is essential to assess student performance at each turn, motivating knowledge tracing (KT) in dialogue settings. However, existing dialogue-based KT approaches often ignore question difficulty and rely on opaque LLM latent representations, hindering accurate and interpretable prediction. In this work, we propose an interpretable difficulty-aware conversational KT framework that leverages LLMs to explicitly model student knowledge state and the difficulty of tutor-posed tasks at each dialogue turn. The framework incorporates the original question and the next tutor-posed task to estimate the student’s knowledge state and the difficulty of the upcoming turn. It further integrates Item Response Theory to map LLM outputs into student ability and question difficulty parameters, enabling interpretable prediction of student performance grounded in cognitive theories of learning. We evaluate the framework on two tutor-student dialogue datasets. Quantitative and qualitative results show that our framework outperforms existing KT baselines, meanwhile generating interpretable outputs consistent with cognitive theory. Our code and data are available at https://github.com/umass-ml4ed/Difficulty-Aware-DialogKT.