MENON: automating a Socratic teaching model for mathematical proofs

Adaptive teaching strategies that take the needs of different learners into account are a prerequisite for successful intelligent tutoring systems. They should ideally incorporate elements of all facets of teaching that together are responsible for learning. One such facet is natural language tutorial dialogue, which is crucial to the application of teaching strategies by human teachers. Although there is an increasing amount of research on teaching strategies and on tutorial dialogues, an analysis of the multiple facets of feedback in the context of a tutorial dialogue remains to be investigated. State-of-the-art approaches do not do justice to either of these aspects. Commonly, intelligent tutoring systems concentrate on cognitive and domain-specific content and resort to precompiled feedback. This feedback is either derived from learning theories, or is dictated by human tutors. The feedback is then associated with pre-defined input for specific tasks, and is presented to the student as canned or templatebased natural-language output in fixed sequences. As a result, adaptivity and non-cognitive aspects of feedback are sacrificed for precision of cognitive and domain-specific content designed for individual tasks. Moreover, these menubased variants of dialogue management do not preserve the characteristics of natural-language dialogue that make it effective, such as dialogical and rhetorical structure, expressive power, and mixed initiative of the collocutors. This thesis presents techniques to automatically integrate different aspects of teaching in a unified natural-language output. The automatic production and natural-language generation of feedback enables its personalisation both at the pedagogical and at the natural-language dialogue level. As a result, feedback can be tailored to the needs of the individual students and the discourse context. Our approach moves away from resource-intensive pre-compiled feedback and towards producing adaptive feedback for arbitrary tasks. As a consequence, the number of tasks with pedagogical feedback that can be offered to the student increases, and with it the opportunity for practice. We propose a method for automating adaptive feedback and implement the tutorial manager Menon as a proof-of-concept for the domain of set theory proofs. More specifically, we define a pedagogical model that abides by schema theory and cognitive load theory, and by the synergistic approach to learning. We implement this model in a Socratic teaching strategy whose basic units of feedback are dialogue moves. We use empirical educational data from two domains: an existing corpus on electricity and electronics, and a corpus which we collected