论文标题
在辅导系统中提供提示，下一步和反馈以进行结构归纳
Providing Hints, Next Steps and Feedback in a Tutoring System for Structural Induction
论文作者
论文摘要
结构诱导是一种证明技术，可广泛用于证明有关离散结构的陈述。学生发现很难构建归纳证明，并且在学习构建此类证明时，收到反馈很重要。在本文中，我们讨论了辅导系统（Logind）的设计，该系统通过提供提示，下一步和反馈来帮助学生构建逐步归纳证明的学生。据我们所知，这是使用该功能的第一个结构性诱导的辅导系统。我们解释了如何使用策略来为有限的问题构建证据。该策略也可以用于完成部分学生解决方案，因此可以提供提示或下一步。我们使用约束来提供反馈。与一小群学生进行的试点评估表明，在几乎所有情况下，登录确实可以给出提示和下一步。
Structural induction is a proof technique that is widely used to prove statements about discrete structures. Students find it hard to construct inductive proofs, and when learning to construct such proofs, receiving feedback is important. In this paper we discuss the design of a tutoring system, LogInd, that helps students with constructing stepwise inductive proofs by providing hints, next steps and feedback. As far as we know, this is the first tutoring system for structural induction with this functionality. We explain how we use a strategy to construct proofs for a restricted class of problems. This strategy can also be used to complete partial student solutions, and hence to provide hints or next steps. We use constraints to provide feedback. A pilot evaluation with a small group of students shows that LogInd indeed can give hints and next steps in almost all cases.
