Why proof planning for maths education and how?

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2605 LNAI, Issue , 2005, Pages 364-378

  Melis, Erica ^a  

^a GERMAN RESEARCH CENTER FOR ARTIFICIAL INTELLIGENCE DFKI   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 36849047274     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-32254-2_21     Document Type: Article

References (37)

1. Gutachten zur Vorbereitung des Programms "Steigerung der Effizienz des mathematischen-naturwissenschaftlichen Unterrichts. Bund-Länder- Kommission, 1997. Materialien zur Bildungsplanung und zur Forschungsfö rderung.
2. V. Aleven, K.R. Koedinger, and K. Cross. Tutoring answer explanation fosters learning with understanding. In S.P. Lajoie and M. Vivet, editors, Artificial Intelligence in Education, pages 199-206. IOS Press, 1999.
3. R.G. Bartle and D.R. Sherbert. Introduction to Real Analysis. John Wiley & Sons, New York, 1982.
4. J. Baumert, R. Lehmann, M. Lehrke, B. Schmitz, M. Clausen, I. Hosenfeld, O. Köller, and J. Neubrand. Mathematisch-naturwissenschaftlicher Unterricht im internationalen Vergleich. Leske und Budrich, 1997.
5. WW. Bledsoe, R.S. Boyer, and W.H. Henneman. Computer proofs of limit theorems. Artificial Intelligence, 3(1):27-60, 1972.
6. P. Boero. Argumentation and mathematical proof: A complex, productive, unavoidable relationship in mathematics and mathematics education. Proof Newsletter, 1999.
7. P. Boero, R. Garutti, and M.A. Mariotti. Some dynamic mental processes underlying producing and proving conjectures. In Proceedings of PME-XX, volume 2, pages 121-128, 1996.
8. A. Bundy, F. van Harmelen, A. Ireland, and A. Smaill. Extensions to the rippling-out tactic for guiding inductive proofs. In M.E. Stickel, editor, Proceedings of the 10th International Conference on Automated Deduction, volume 449 of Lecture Notes in Artificial Intelligence. Springer, 1990.
9. R. Catrambone and K.J. Holyoak. Learning subgoals and methods for solving probability problems. Memory and Cognition, 18(6):593-603, 1990.
10. E. Dubinsky and U. Leron. Learning Abstract Algebra with ISETL. Springer-Verlag, 1993.
11. M.T.H. Chi et al. Self-explanation: How students study and use examples in learning to solve problems. Cognitive Science, 15:145-182, 1989.
12. G. Ferguson, J. Allen, and B. Miller. Trains-95: Towards a mixed-initiative planning assistant. In B. Drabble, editor, Third Conference on Artificial Intelligence Planning Systems (AIPS-96), pages 70-77, 1996.
13. G. Holland. Geolog-Win. Dümmler, 1996.
14. D. Hutter. Guiding inductive proofs. In M.E. Stickel, editor, Proceedings of 10th International Conference on Automated Deduction, volume 449 of Lecture Notes in Artificial Intelligence. Springer, 1990.
15. W:R: Joolingen and T. Jong. Design and implementation of simulation-based discovery environments: the SMISLE solution. Journal of ARtificial Intelligence and Education, 7:253-277, 1996.
16. S. Lajoie and S. Derry, editors. Computers as Cognitive Tools. Erlbaum, Hillsdale, NJ, 1993.
17. U. Leron. Heuristic presentations: the role of structuring. For the Learning of Mathematics, 5(3):7-13, 1985.
18. U. Leron and E. Dubinsky. An abstract algebra story. American Mathematical Monthly, 102(3):227-242, March 1995.
19. H. Lowe, A. Bundy, and D. McLean. The use of proof planning for co-operative theorem proving. Research Paper 745, Department of AI, 1995.
20. H. Lowe and D. Duncan. Xbarnacle: Making theorem provers more accessible. In W. McCune, editor, Proceedings of the Fourteenth Conference on Automated Deduction (CADE-I4), volume 1249 of Lecture Notes in Artificial Intelligence, pages 404-408. Springer, 1997.
21. E. Melis. Al-techniques in proof planning. In European Conference on Artificial Intelligence, pages 494-498, Brighton, 1998. Kluwer.
22. E. Melis. The "limit" domain. In R. Simmons, M. Veloso, and S. Smith, editors, Proceedings of the Fourth International Conference on Artificial Intelligence in Planning Systems, pages 199-206, 1998.
23. E. Melis, Ch. Glasmacher, C. Ullrich, and P. Gerjets. Automated proof planning for instructional design. In Annual Conference of the Cognitive Science Society, pages 633-638, 2001.
24. E. Melis and U. Leron. A proof presentation suitable for teaching proofs. In S.P. Lajoie and M. Vivet, editors, 9th International Conference on Artificial Intelligence in Education, pages 483-490, Le Mans, 1999. IOS Press.
25. Erica Melis and Julian Richardson. Separation of control and logic in rippling and unwraphyp, 1998.
26. A. Newell. 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.
27. J. Piaget. Equilibration of Cognitive Structures. Viking, New York, 1977.
28. G. Polya. How to Solve it. Princeton University Press, Princeton, 1945.
29. J. Richter-Gebert and U.H. Kortenkamp. The Interacitive Geometry Software Cinderella. Springer-Verlag, 1999.
30. P. Schmidt. Preparing oral examinations of mathematical domains with the help of a knowledge-based dialogue system. In Proceedings of Ed-Media, 2001.
31. A.H. Schoenfeld. Mathematical Problem Solving. Academic Press, New York, 1985.
32. A.H. Schoenfeld. Learning to Think Mathematically: Problem Solving, Metacognition, and Sense Making in Mathematics, chapter 15. McMillan Publ.Company, New York, 1992.
33. M. Simon. Beyond inductive and deductive reasoning: The search for a sense of knowing. Educational Studies in Mathematics, 30:197-210, 1996.
34. D. Suthers, A. Weiner, J. Connely, and M. Paolucci. Belvedere: Engaging students in critical discussion of science and public policy issues. In 7th World Conference on Artificial Intelligence in Education, AIED-95, pages 266-273, 1995.
35. Manuela M. Veloso. Towards mixed-initiative rationale-supported planning. In A. Tate, editor, Advanced Planning Technology, pages 277-282. AAAI Press, May 1996.
36. L. Vygotsky. Thought and Language. MIT press, Cambridge, MA, 1986. originally published 1962.
37. B.Y. White and J.R. Frederiksen. Inquiry, Modeling, and Metacognition: Making Science Accessible to all Students. Lawrence Erlbaum, 1998.