Giving feedback to students is not just about marking their answers as correct or incorrect, but also finding mistakes in their thought process that led them to that incorrect answer. In this paper, we introduce a machine learning technique for mistake captioning, a task that attempts to identify mistakes and provide feedback meant to help learners correct these mistakes. We do this by training a sequence-to-sequence network to generate this feedback based on domain experts. To evaluate this system, we explore how it can be used on a Linguistics assignment studying Grimm's Law. We show that our approach generates feedback that outperforms a baseline on a set of automated NLP metrics. In addition, we perform a series of case studies in which we examine successful and unsuccessful system outputs.