MENON [Elektronische Ressource] : automating a Socratic teaching model for mathematical proofs / Dimitra Tsovaltzi
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MENON [Elektronische Ressource] : automating a Socratic teaching model for mathematical proofs / Dimitra Tsovaltzi

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Published 01 January 2010
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Automating a Socratic Teaching Model
for Mathematical Proofs
Dimitra Tsovaltzi
Saarbru¨cken, 2010
Dissertation zur Erlangung des Grades des Doktors der
Ingenieurwissenschaften der Naturwissenschaftlich-Technischen
Fakult¨aten der Universit¨at des Saarlandesii
Dekan Prof. Dr. Joachim Weickert, Universita¨t des Saarlandes,
Vorsitzender Prof. Dr. Raimund Seidel, Universita¨t des Saarlandes,
Gutachter Prof. Dr. Jo¨rg Siekmann, Universita¨t des Saarlandes,
Prof. Dr. Roland Bru¨nken, Universita¨t des Saarlandes,
Dr. Bruce M. McLaren, Carnegie Mellon University, Pitts-
Dr. Colin Matheson, the University of Edinburgh, Edinburgh
Beisitzer Priv.-Doz. Dr. Helmut Horacek
Kolloquium 11. Ma¨rz 2010iiiv
“And it won’t be as a result of any teaching that he’ll have become knowledge-
able: he’ll just have been asked questions, and he’ll recover the knowledge by
himself, from within himself.”
I would like to thank from the heart my advisor Prof. Dr. Jo¨rg Siekmann
who gaveme the opportunity to do this researchand supported me throughout
the years towards its completion, both intellectually and morally. From the
beginning of my PhD research and until now, I have always admired his sharp
scientific grasp, as well as his open mind and his readiness to endorse the inter-
ests of other people. I am indebted to the members of my PhD committee Dr.
Bruce M. McLaren and Dr. Colin Matheson for their meticulous and insightful
feedbackonthe PhDthat wasbeyondmyexpectations. Bothofthem, eachone
in his own way, have been a source of inspiration and motivation to continue in
the demanding arena of scientific research. I would also like to sincerely thank
Prof. Dr. Roland Bru¨nken who generously agreed to be a member of my PhD
committee. I look up to his research in educational psychology.
I havehad the luckto workin two researchgroupsduring my PhDresearch.
I have felt at home and have thoroughly enjoyed working in both of them.
In particular, I would like to thank the Omega group for their willingness to
provide help whenever I needed it, and the ActiveMath group for giving me
a future perspective that motivated me to carry the PhD through. I would
especially like to express my gratitude to Dr. Armin Fiedler who believed in
me, invited me to the Omega group and helped me in my very first steps as
an independent researcher. I have learned a lot from him, from his intellectual
clarity and scientific integrity. Special thanks also to Dr. Chad Brown and
Dr. Helmut Horacek who sacrificed their precious time to review this work and
provide acute and critical comments.
I cannot be grateful enough to my mother, my sisters and their families in
Greece who have never seized to support me and wholeheartedly embrace my
successes and failures, my happy and sad moments.
My husband, Florian, and my daughter, Sophia, have had to tolerate me, or
my necessary absence in the past years. I thank them for all their patience, for
accepting my aspirations and for their love that drives me at difficult times.viiiix
Brief Abstract
This thesis presents an approach to adaptive pedagogical feedback for arbi-
trary domains as an alternative to resource-intensive pre-compiled feedback,
which represents the state-of-the-art in intelligent tutoring systems today. A
consequence of automatic adaptive feedback is that the number of tasks with
pedagogical feedback that can be offered to the student increases, and with
it the opportunity for practice. We focus on automating different aspects of
teaching that together are primarily responsible for learning and can be inte-
grated in a unified natural-language output. The automatic production and
natural-language generation of feedback enables its personalisation both at the
pedagogical and the natural-language dialogue level. We propose a method
for automating the production of domain-independent adaptive feedback. The
proof-of-concept implementation of the tutorial manager Menon is carried out
for the domain of set-theory proofs.
More specifically, we define a pedagogical model that abides by schema and
cognitive load theory, and by the synergistic approach to learning. We imple-
ment this model in a Socratic teaching strategy whose basic units of feedback
aredialoguemoves. We useempirical data from two domainsto derivea taxon-
omy of tutorial-dialogue moves, and define the most central and sophisticated
move hint. The formalisation of the cognitive content of hints is inspired by
schema theory and is facilitated by a domain ontology.x