Linguistic Processing in a Mathematics Tutoring System: Cooperative Input Interpretation and Dialogue Modelling

Formal domains, such as mathematics, require exact language to communicate the intended content. Special symbolic notations are used to express the semantics precisely, compactly, and unambiguously. Mathematical textbooks offer plenty of examples of concise, accurate presentations. This effective communication is enabled by interleaved use of formulas and natural language. Since natural language interaction has been shown to be an important factor in the efficiency of human tutoring [29], it would be desirable to enhance interaction with Intelligent Tutoring Systems for mathematics by allowing elements of mixed language combining the exactness of formal expressions with natural language flexibility.

[1]  Johanna D. Moore,et al.  Robustness versus Fidelity in Natural Language Understanding , 2004 .

[2]  Christoph Benzmüller,et al.  Assertion-level Proof Representation with Under-Specification , 2004, Electron. Notes Theor. Comput. Sci..

[3]  Johanna D. Moore What Makes Human Explanations Effective , 1993 .

[4]  Magdalena Wolska,et al.  Towards Modelling and Using Common Ground in Tutorial Dialogue , 2007 .

[5]  Kurt VanLehn,et al.  Modeling Students' Reasoning About Qualitative Physics: Heuristics for Abductive Proof Search , 2004, Intelligent Tutoring Systems.

[6]  Arthur C. Graesser,et al.  When Are Tutorial Dialogues More Effective Than Reading? , 2007, Cogn. Sci..

[7]  Magdalena Wolska,et al.  Fault-Tolerant Context-Based Interpretation of Mathematical Formulas , 2005, IJCAI.

[8]  Christoph Benzmüller,et al.  Assertion Application in Theorem Proving and Proof Planning , 2003, IJCAI.

[9]  David Traum,et al.  Computational Models of Grounding in Collaborative Systems , 1999 .

[10]  Herbert H. Clark,et al.  Contributing to Discourse , 1989, Cogn. Sci..

[11]  D. C. Merrill,et al.  Tutoring: Guided Learning by Doing , 1995 .

[12]  C. Stasz,et al.  Tutoring Techniques in Algebra , 1990 .

[13]  Arthur C. Graesser,et al.  Using Latent Semantic Analysis to Evaluate the Contributions of Students in AutoTutor , 2000, Interact. Learn. Environ..

[14]  Claus Zinn,et al.  Computational Framework For Understanding Mathematical Discourse , 2003, Log. J. IGPL.

[15]  Marilyn A. Walker,et al.  Informational redundancy and resource bounds in dialogue , 1993 .

[16]  Kenneth R. Koedinger,et al.  Towards Understanding Geometry Explanations , 2000 .

[17]  Ronnie W. Smith,et al.  Current and New Directions in Discourse and Dialogue , 2004 .

[18]  Michael J. Baker,et al.  The role of grounding in collaborative learning tasks , 1999 .

[19]  Kai Pata,et al.  Collaborative scaffolding in synchronous environment: congruity and antagonism of tutor/student facilitation acts , 2005, CSCL.

[20]  Petr Sgall,et al.  The Meaning Of The Sentence In Its Semantic And Pragmatic Aspects , 1986 .

[21]  Christoph Benzmüller,et al.  An Agent-Based Architecture for Dialogue Systems , 2006, Ershov Memorial Conference.

[22]  Magdalena Wolska,et al.  Modeling anaphora in informal mathematical dialogue , 2006 .

[23]  Magdalena Wolska,et al.  Interpreting semi-formal utterances in dialogs about mathematical proofs , 2006, Data Knowl. Eng..

[24]  Ivana Kruijff-Korbayová,et al.  A corpus of tutorial dialogs on theorem proving; the influence of the presentation of the study-material , 2006, LREC.

[25]  Neil T. Heffernan,et al.  An Intelligent Tutoring System Incorporating a Model of an Experienced Human Tutor , 2002, Intelligent Tutoring Systems.

[26]  Oliver Lemon,et al.  DIPPER: Description and Formalisation of an Information-State Update Dialogue System Architecture , 2003, SIGDIAL Workshop.

[27]  Michael Glass Processing Language Input in the CIRCSIM-Tutor Intelligent Tutoring System , 2000 .

[28]  Ivana Kruijff-Korbayová,et al.  An Annotated Corpus of Tutorial Dialogs on Mathematical Theorem Proving , 2004, LREC.

[29]  Joseph P. Magliano,et al.  Collaborative dialogue patterns in naturalistic one-to-one tutoring , 1995 .

[30]  Jörg H. Siekmann,et al.  A Wizard of Oz Experiment for Tutorial Dialogues in Mathematics , 2003 .

[31]  Neil T. Heffernan,et al.  Intelligent Tutoring Systems are Missing the Tutor: Building a More Strategic Dialog-Based Tutor , 2000 .

[32]  Helmut Horacek,et al.  Building Hint Specifications in an NL Tutorial System for Mathematics , 2004, FLAIRS.

[33]  Ivana Kruijff-Korbayová,et al.  Analysis of Mixed Natural and Symbolic Input in Mathematical Dialogs , 2004, ACL.

[34]  David Traum,et al.  The Information State Approach to Dialogue Management , 2003 .

[35]  Claus Zinn,et al.  Using dialogue to learn math in the LeActiveMath project , 2006 .

[36]  Jörg H. Siekmann,et al.  Natural Language Dialog with a Tutor System for Mathematical Proofs , 2005, Cognitive Systems.

[37]  Claus Zinn,et al.  The BE&E Tutorial Learning Environment (BEETLE) , 2000 .