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Why Proof Planning for Maths Education and How?

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Mechanizing Mathematical Reasoning

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2605))

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Abstract

Artificial Intelligence techniques have massively been applied for Intelligent Tutor systems (ITS), e.g., user modeling, error diagnosis, user adaptation, knowledge representation, and dialog techniques. In this paper, I will argue in favor of the application of another AI-technique in ITS, namely of proof planning, a methodology from automated theorem proving.

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References

  1. Gutachten zur Vorbereitung des Programms Steigerung der Effizienz des mathematischen-naturwissenschaftlichen Unterrichts. Bund-Länder-Kommission, Materialien zur Bildungsplanung und zur Forschungsförderung (1997)

    Google Scholar 

  2. Aleven, V., Koedinger, K.R., Cross, K.: Tutoring answer explanation fosters learning with understanding. In: Lajoie, S.P., Vivet, M. (eds.) Artificial Intelligence in Education, pp. 199–206. IOS Press, Amsterdam (1999)

    Google Scholar 

  3. Bartle, R.G., Sherbert, D.R.: Introduction to Real Analysis. John Wiley& Sons, New York (1982)

    MATH  Google Scholar 

  4. Baumert, J., Lehmann, R., Lehrke, M., Schmitz, B., Clausen, M., Hosenfeld, I., Köller, O., Neubrand, J.: Mathematisch-naturwissenschaftlicher Unterricht im internationalen Vergleich. Leske und Budrich (1997)

    Google Scholar 

  5. Bledsoe, W.W., Boyer, R.S., Henneman, W.H.: Computer proofs of limit theorems. Artificial Intelligence 3(1), 27–60 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  6. Boero, P.: Argumentation and mathematical proof: A complex, productive, unavoidable relationship in mathematics and mathematics education. Proof Newsletter (1999)

    Google Scholar 

  7. Boero, P., Garutti, R., Mariotti, M.A.: Some dynamic mental processes underlying producing and proving conjectures. In: Proceedings of PME-XX, vol. 2, pp. 121–128 (1996)

    Google Scholar 

  8. Bundy, A., van Harmelen, F., Ireland, A., Smaill, A.: Extensions to the ripplingout tactic for guiding inductive proofs. In: Stickel, M.E. (ed.) CADE 1990. LNCS (LNAI), vol. 449. Springer, Heidelberg (1990)

    Google Scholar 

  9. Catrambone, R., Holyoak, K.J.: Learning subgoals and methods for solving probability problems. Memory and Cognition 18(6), 593–603 (1990)

    Article  Google Scholar 

  10. Dubinsky, E., Leron, U.: Learning Abstract Algebra with ISETL. Springer, Heidelberg (1993)

    Google Scholar 

  11. Chi, M.T.H., et al.: Self-explanation: How students study and use examples in learning to solve problems. Cognitive Science 15, 145–182 (1989)

    Article  Google Scholar 

  12. Ferguson, G., Allen, J., Miller, B.: Trains-95: Towards a mixed-initiative planning assistant. In: Drabble, B. (ed.) Third Conference on Artificial Intelligence Planning Systems (AIPS 1996), pp. 70–77 (1996)

    Google Scholar 

  13. Holland, G.: Geolog-Win. Dümmler (1996)

    Google Scholar 

  14. Hutter, D.: Guiding inductive proofs. In: Stickel, M.E. (ed.) CADE 1990. LNCS (LNAI), vol. 449. Springer, Heidelberg (1990)

    Google Scholar 

  15. Joolingen, W.R., Jong, T.: Design and implementation of simulation-based discovery environments: the SMISLE solution. Journal of Artificial Intelligence and Education 7, 253–277 (1996)

    Google Scholar 

  16. Lajoie, S., Derry, S. (eds.): Computers as Cognitive Tools. Erlbaum, Hillsdale (1993)

    Google Scholar 

  17. Leron, U.: Heuristic presentations: the role of structuring. For the Learning of Mathematics 5(3), 7–13 (1985)

    Google Scholar 

  18. Leron, U., Dubinsky, E.: An abstract algebra story. American Mathematical Monthly 102(3), 227–242 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  19. Lowe, H., Bundy, A., McLean, D.: The use of proof planning for co-operative theorem proving. Research Paper 745, Department of AI (1995)

    Google Scholar 

  20. Lowe, H., Duncan, D.: Xbarnacle: Making theorem provers more accessible. In: McCune, W. (ed.) CADE 1997. LNCS (LNAI), vol. 1249, pp. 404–408. Springer, Heidelberg (1997)

    Google Scholar 

  21. Melis, E.: AI-techniques in proof planning. In: European Conference on Artificial Intelligence, Brighton, pp. 494–498. Kluwer, Dordrecht (1998)

    Google Scholar 

  22. Melis, E.: The “limit” domain. In: Simmons, R., Veloso, M., Smith, S. (eds.) Proceedings of the Fourth International Conference on Artificial Intelligence in Planning Systems, pp. 199–206 (1998)

    Google Scholar 

  23. Melis, E., Glasmacher, C., Ullrich, C., Gerjets, P.: Automated proof planning for instructional design. In: Annual Conference of the Cognitive Science Society, pp. 633–638 (2001)

    Google Scholar 

  24. Melis, E., Leron, U.: A proof presentation suitable for teaching proofs. In: Lajoie, S.P., Vivet, M. (eds.) 9th International Conference on Artificial Intelligence in Education, Le Mans, pp. 483–490. IOS Press, Amsterdam (1999)

    Google Scholar 

  25. Melis, E., Richardson, J.: Separation of control and logic in rippling and unwraphyp (1998)

    Google Scholar 

  26. Newell, A.: The Heuristic of George Polya and its Relation to Artificial Intelligence. Technical Report CMU-CS-81-133, Carnegie-Mellon-University, Dept. of Computer Science, Pittsburgh, Pennsylvania, U.S.A (1981)

    Google Scholar 

  27. Piaget, J.: Equilibration of Cognitive Structures. Viking, New York (1977)

    Google Scholar 

  28. Polya, G.: How to Solve it. Princeton University Press, Princeton (1945)

    MATH  Google Scholar 

  29. Richter-Gebert, J., Kortenkamp, U.H.: The Interacitive Geometry Software Cinderella. Springer, Heidelberg (1999)

    Google Scholar 

  30. Schmidt, P.: Preparing oral examinations of mathematical domains with the help of a knowledge-based dialogue system. In: Proceedings of Ed-Media (2001)

    Google Scholar 

  31. Schoenfeld, A.H.: Mathematical Problem Solving. Academic Press, New York (1985)

    MATH  Google Scholar 

  32. Schoenfeld, A.H.: Learning to Think Mathematically: Problem Solving, Metacognition, and Sense Making in Mathematics, ch. 15. McMillan Publ.Company, New York (1992)

    Google Scholar 

  33. Simon, M.: Beyond inductive and deductive reasoning: The search for a sense of knowing. Educational Studies in Mathematics 30, 197–210 (1996)

    Article  Google Scholar 

  34. Suthers, D., Weiner, A., Connely, J., Paolucci, M.: Belvedere: Engaging students in critical discussion of science and public policy issues. In: 7th World Conference on Artificial Intelligence in Education, AIED 1995, pp. 266–273 (1995)

    Google Scholar 

  35. Veloso, M.M.: Towards mixed-initiative rationale-supported planning. In: Tate, A. (ed.) Advanced Planning Technology, pp. 277–282. AAAI Press, Menlo Park (1996)

    Google Scholar 

  36. Vygotsky, L.: Thought and Language. MIT press, Cambridge (1986) (originally published 1962)

    Google Scholar 

  37. White, B.Y., Frederiksen, J.R.: Inquiry, Modeling, and Metacognition: Making Science Accessible to all Students. Lawrence Erlbaum, Mahwah (1998)

    Google Scholar 

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Melis, E. (2005). Why Proof Planning for Maths Education and How?. In: Hutter, D., Stephan, W. (eds) Mechanizing Mathematical Reasoning. Lecture Notes in Computer Science(), vol 2605. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-32254-2_21

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  • DOI: https://doi.org/10.1007/978-3-540-32254-2_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25051-7

  • Online ISBN: 978-3-540-32254-2

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