Dialogs about problem solving in mathematics are characterized by a mixture of telegraphic natural language text and embedded formal expressions. Behaving adequately in such an environment is extremely important for tutorial systems, as follows from Moore’s empirical findings which show that flexible natural language dialog is needed to support active learning [9]. However, most state-of-the-art tutorial systems are only able to process limited forms of dialogs, either menu-based or requiring exact wordings [10,2,6].
Motivated by the lack of empirical data, we have collected a corpus of dialogs with a simulated tutoring system for teaching proofs in naive set theory, to identify genre-specific variants of linguistic phenomena which impose specific requirements on natural language dialog management. This work is embedded in a project whose goal is to develop a mathematical tutoring system with flexible natural language dialog. The outline of this paper is as follows. We first present the aims of our project. Next, we describe an experiment in which we collected a corpus of natural language tutorial dialogs. We follow with an analysis of the phenomena observed. Finally, we discuss challenges for natural language dialog management.
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