Intelligent tutoring systems can support students in solving multi-step tasks by providing a hint regarding what to do next. However, engineering such next-step hints manually or using an expert model becomes infeasible if the space of possible states is too large. Therefore, several approaches have emerged to infer next-step hints automatically, relying on past student's data. Such hints typically have the form of an edit which could have been performed by capable students in the given situation, based on what past capable students have done. In this contribution we provide a mathematical framework to analyze edit-based hint policies and, based on this theory, propose a novel hint policy to provide edit hints for learning tasks with a vast state space and sparse student data. We call this technique the continuous hint factory because it embeds student data in a continuous space, in which the most likely edit can be inferred in a probabilistic sense, similar to the hint factory. In our experimental evaluation we demonstrate that the continuous hint factory can predict what capable students would do in solving a multi-step programming task and that hints provided by the continuous hint factory match to some extent the edit hints that human tutors would have given in the same situation.
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