Engagement and motivation are crucial for second-language acquisition, yet maintaining learner interest in educational conversations remains a challenge. While prior research has explored what makes educational texts interesting, still little is known about the linguistic features that drive engagement in conversations. To address this gap, we introduce IntrEx, the first large-scale dataset annotated for interestingness and expected interestingness in teacher-student interactions. Built upon the Teacher-Student Chatroom Corpus (TSCC), IntrEx extends prior work by incorporating sequence-level annotations, allowing for the study of engagement beyond isolated turns to capture how interest evolves over extended dialogues. We employ a rigorous annotation process with over 100 second-language learners, using a comparison-based rating approach inspired by reinforcement learning from human feedback (RLHF) to improve agreement. We analyze how linguistic and cognitive factors, such as concreteness, comprehensibility, readability, and uptake, influence engagement in educational dialogues. Finally, we investigate whether large language models (LLMs) can predict human interestingness judgments. We find that carefully fine-tuned LLMs (7B-8B parameters) on interesting ratings outperform larger proprietary models like GPT-4o, demonstrating the potential for specialised datasets to model engagement in educational settings.