Understanding the strategies that make expert-led explanations effective is a core challenge in didactics and a key goal for explainable AI. To study this computationally, we introduce ReWIRED, a large corpus of explanatory dialogues annotated by education experts with fine-grained, span-level teaching acts across five levels of explainee knowledge. We use this resource to assess the capabilities of modern language models, finding that while few-shot LLMs struggle to label these acts, fine-tuning is a highly effective methodology. Moving beyond structural annotation, we propose and validate a suite of didactic quality metrics. We demonstrate that a prompt-based evaluation using an LLM as a judge'' is required to capture how the functional quality of an explanation aligns with the learner's expertise -- a nuance missed by simpler static metrics. Together, our dataset, modeling insights, and evaluation framework provide a comprehensive methodology to bridge pedagogical principles with computational discourse analysis.