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Human communication often involves information gaps between the interlocutors. For example, in an educational dialogue a student often provides an answer that is incomplete, and there is a gap between this answer and the perfect one expected by the teacher. Successful dialogue then hinges on the teacher asking about this gap in an effective manner, thus creating a rich and interactive educational experience. We focus on the problem of generating such gap-focused questions (GFQs) automatically. We define the task, highlight key desired aspects of a good GFQ, and propose a model that satisfies these. Finally, we provide an evaluation by human annotators of our generated questions compared against human generated ones, demonstrating competitive performance.