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Tutorial dialogs on mathematical proofs
 In Proceedings of the IJCAI Workshop on Knowledge Representation
, 2003
"... The representation of knowledge for a mathematical proof assistant is generally used exclusively for the purpose of proving theorems. Aiming at a broader scope, we examine the use of mathematical knowledge in a mathematical tutoring system with flexible natural language dialog. Based on an analysis ..."
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Cited by 21 (17 self)
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The representation of knowledge for a mathematical proof assistant is generally used exclusively for the purpose of proving theorems. Aiming at a broader scope, we examine the use of mathematical knowledge in a mathematical tutoring system with flexible natural language dialog. Based on an analysis of a corpus of dialogs we collected with a simulated tutoring system for teaching proofs in naive set theory, we identify several interesting problems which lead to requirements for mathematical knowledge representation. This includes resolving reference between natural language expressions and mathematical formulas, determining the semantic role of mathematical formulas in context, and determining the contribution of inference steps specified by the user. 1
Assertionlevel proof representation with underspecification
, 2003
"... We propose a proof representation format for humanoriented proofs at the assertion level with underspecification. This work aims at providing a possible solution to challenging phenomena worked out in empirical studies in the DIALOG project at Saarland University. A particular challenge in this pro ..."
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Cited by 16 (7 self)
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We propose a proof representation format for humanoriented proofs at the assertion level with underspecification. This work aims at providing a possible solution to challenging phenomena worked out in empirical studies in the DIALOG project at Saarland University. A particular challenge in this project is to bridge the gap between the humanoriented proof representation format with underspecification used in the proof manager of the tutorial dialogue system and the calculus and machineoriented representation format of the domain reasoner.
2003b. A WizardofOz experiment for tutorial dialogues in mathematics
 In AIED03 Supplementary Proc., Advanced Technologies for Mathematics Education
"... Abstract. In this paper we report on a WizardofOz (WOz) experiment which ..."
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Cited by 14 (13 self)
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Abstract. In this paper we report on a WizardofOz (WOz) experiment which
An approach to facilitating reflection in a mathematics tutoring system
 In Proceedings of AIED Workshop on Learner Modelling for Reflection
, 2003
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Enhancement and use of a mathematical ontology in a tutorial dialogue system
 In Proceedings of the IJCAI Workshop on Knowledge and Reasoning in Practical Dialogue Systems
, 2003
"... Despite empirical evidence that natural language dialog capabilities are necessary for the success of tutorial sessions, only few stateoftheart tutoring systems use naturallanguage style interaction. Since domain knowledge, tutoring and pedagogical knowledge, and dialog management are tightly in ..."
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Cited by 7 (4 self)
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Despite empirical evidence that natural language dialog capabilities are necessary for the success of tutorial sessions, only few stateoftheart tutoring systems use naturallanguage style interaction. Since domain knowledge, tutoring and pedagogical knowledge, and dialog management are tightly intertwined, the modeling and integration of proper natural language dialog capabilities in a tutoring system turns out to be barely manageable. In the DIALOG project, we aim at a mathematical tutoring dialog system that employs an elaborate natural language dialog component. To tutor naive set theory, we use a formally encoded mathematical theory including definitions and theorems along with their proofs. In this paper we present how we enhance this ontology by making relations explicit and we show how these relations can be used by the socratic tutoring strategy, which we employ, in planning the next system utterance. The decisive characteristic of the socratic strategy is the use of hints in order to achieve selfexplanation. 1
Discourse phenomena in tutorial dialogs on mathematical proofs
 In In Proceedings of AI in Education (AIED 2003) Workshop on Tutorial Dialogue Systems: With a View Towards the Classroom
, 2003
"... 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 flexibl ..."
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Cited by 5 (4 self)
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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 [3]. Motivated by the lack of empirical data for such
An Agentbased Platform for Dialogue Management
 Proceedings of the Tenth ESSLLI Student Session
, 2005
"... Abstract. In this paper we propose a platform for developing dialogue management applications supporting the information state update approach which uses agentbased techniques and a hierarchical blackboard architecture to provide concurrency, runtime
exibility and the inclusion of heuristic cont ..."
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Cited by 1 (1 self)
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Abstract. In this paper we propose a platform for developing dialogue management applications supporting the information state update approach which uses agentbased techniques and a hierarchical blackboard architecture to provide concurrency, runtime
exibility and the inclusion of heuristic control. 1
Towards a Principled Approach to Tutoring Mathematical Proofs
"... Studies comparing human and computerbased tutoring have identified natural language communication about the tutorial goal as a major source for the increased learning success in human tutoring. However, due to the inherent difficulty of natural language processing in nontightly restricted tasks, ..."
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Studies comparing human and computerbased tutoring have identified natural language communication about the tutorial goal as a major source for the increased learning success in human tutoring. However, due to the inherent difficulty of natural language processing in nontightly restricted tasks, which tutoring is even in simple domains, only few stateoftheart systems use naturallanguage style interaction. Addressing tutoring in a principled way, we are developing a system that teaches proving skills in mathematics, by incrementally enhancing a testable Wizardof Oz environment with tutoring components, existing domain reasoning systems and natural language processing components. The first component integrated is an elaborate hinting algorithm. Experiments carried out recently provided valuable insights in relevant phenomena and demands for tutorial and taskspecific enhancements of available mathematical reasoning and natural language processing components.