Abstract
The feedback given by e-learning tools that support incrementally solving problems in mathematics, logic, physics, etc. is limited, or laborious to specify. In this paper we introduce a language for specifying strategies for solving exercises. This language makes it easier to automatically calculate feedback when users make erroneous steps in a calculation. Although we need the power of a full programming language to specify strategies, we carefully distinguish between context-free and non-context-free sublanguages of our strategy language. This separation is the key to automatically calculating all kinds of desirable feedback.
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Anderson, J.R.: Rules of the Mind. Lawrence Erlbaum Associates (1993)
Anderson, J.R., Corbett, A.T., Koedinger, K.R., Pelletier, R.: Cognitive tutors: lessons learned. The Journal of the Learning Sciences 4(2), 167–207 (1995)
Anderson, J.R., Skwarecki, E.: The automated tutoring of introductory computer programming. Communications of the ACM 29(9), 842–849 (1986)
Beeson, M.J.: Design principles of Mathpert: Software to support education in algebra and calculus. In: Kajler, N. (ed.) Computer-Human Interaction in Symbolic Computation, pp. 89–115. Springer, Heidelberg (1998)
Bouwers, E.: Improving automated feedback – a generic rule-feedback generator. Master’s thesis, Utrecht University, department of Information and Computing Sciences (2007)
Brown, J.S., Burton, R.R.: Diagnostic models for procedural bugs in basic mathematical skills. Cognitive Science 2, 155–192 (1978)
Brown, J.S., VanLehn, K.: Repair theory: A generative theory of bugs in procedural skills. Cognitive Science 4, 379–426 (1980)
Bundy, A.: The Computer Modelling of Mathematical Reasoning. Academic Press, London (1983)
Chaachoua, H., et al.: Aplusix, a learning environment for algebra, actual use and benefits. In: ICME 10: 10th International Congress on Mathematical Education (2004) (retrieved May 2008), http://www.itd.cnr.it/telma/papers.php
Cohen, A., Cuypers, H., Jibetean, D., Spanbroek, M.: Interactive learning and mathematical calculus. In: Mathematical Knowledge Management (2005)
Cohen, A., Cuypers, H., Barreiro, E.R., Sterk, H.: Interactive mathematical documents on the web. In: Algebra, Geometry and Software Systems, pp. 289–306. Springer, Heidelberg (2003)
Cunha, A., Visser, J.: Strongly typed rewriting for coupled software transformation. Electron. Notes Theor. Comput. Sci. 174(1), 17–34 (2007)
Erev, I., Luria, A., Erev, A.: On the effect of immediate feedback (2006), http://telem-pub.openu.ac.il/users/chais/2006/05/pdf/e-chais-erev.pdf
Goguadze, G., González Palomo, A., Melis, E.: Interactivity of exercises in ActiveMath. In: International Conference on Computers in Education, ICCE 2005 (2005)
Heeren, B., Jeuring, J., van Leeuwen, A., Gerdes, A.: Specifying strategies for exercises. Technical Report UU-CS-2008-001, Utrecht University (2008)
Hennecke, M.: Online Diagnose in intelligenten mathematischen Lehr-Lern-Systemen (in German). PhD thesis, Hildesheim University, Fortschritt-Berichte VDI Reihe 10, Informatik / Kommunikationstechnik; 605. Düsseldorf: VDI-Verlag (1999)
Hinze, R., Jeuring, J., Löh, A.: Comparing approaches to generic programming in Haskell. In: Backhouse, R., Gibbons, J., Hinze, R., Jeuring, J. (eds.) SSDGP 2006. LNCS, vol. 4719, pp. 72–149. Springer, Heidelberg (2007)
Horacek, H., Wolska, M.: Handling errors in mathematical formulas. In: Ikeda, M., Ashley, K.D., Chan, T.-W. (eds.) ITS 2006. LNCS, vol. 4053, pp. 339–348. Springer, Heidelberg (2006)
Hudak, P.: Building domain-specific embedded languages. ACM Computing Surveys 28A(4) (December 1996)
Hutton, G.: Higher-order Functions for Parsing. Journal of Functional Programming 2(3), 323–343 (1992)
Issakova, M.: Solving of linear equations, linear inequalities and systems of linear equations in interactive learning environment. PhD thesis, University of Tartu (2007)
Lämmel, R., Jones, S.P.: Scrap your boilerplate: a practical approach to generic programming. ACM SIGPLAN Notices 38(3), 26–37 (2003); TLDI 2003
R. Lämmel, E. Visser, J. Visser.: The Essence of Strategic Programming. In: Draft, p. 18 , October15 (2002), http://www.cwi.nl/~ralf
Lodder, J., Jeuring, J., Passier, H.: An interactive tool for manipulating logical formulae. In: Manzano, M., Pérez Lancho, B., Gil, A. (eds.) Proceedings of the Second International Congress on Tools for Teaching Logic (2006)
Passier, H., Jeuring, J.: Feedback in an interactive equation solver. In: Seppälä, M., Xambo, S., Caprotti, O. (eds.) Proceedings of the Web Advanced Learning Conference and Exhibition, WebALT 2006, pp. 53–68. Oy WebALT (2006)
Paulson, L.C.: ML for the Working Programmer., 2nd edn. Cambridge University Press, Cambridge (1996)
Jones, S.P., et al.: Haskell 98, Language and Libraries. The Revised Report. Cambridge University Press, Cambridge (2003); A special issue of the Journal of Functional Programming, http://www.haskell.org/
Plasmeijer, R., Achten, P., Koopman, P.: iTasks: executable specifications of interactive work flow systems for the web. In: ICFP 2007, New York, NY, USA, pp. 141–152 (2007)
Sweller, J., van Merriënboer, J.J.G., Paas, F.: Cognitive architecture and instructional design. Educational Psychology Review 10, 251–295 (1998)
Swierstra, S.D., Duponcheel, L.: Deterministic, error-correcting combinator parsers. In: Launchbury, J., Sheard, T., Meijer, E. (eds.) AFP 1996. LNCS, vol. 1129, pp. 184–207. Springer, Heidelberg (1996)
VanLehn, K.: Mind Bugs – The Origins of Procedural Misconceptions. MIT Press, Cambridge (1990)
Visser, E., Benaissa, Z., Tolmach, A.: Building program optimizers with rewriting strategies. In: ICFP 1998, pp. 13–26 (1998)
Zinn, C.: Supporting tutorial feedback to student help requests and errors in symbolic differentiation. In: Ikeda, M., Ashley, K.D., Chan, T.-W. (eds.) ITS 2006. LNCS, vol. 4053, pp. 349–359. Springer, Heidelberg (2006)
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Heeren, B., Jeuring, J., van Leeuwen, A., Gerdes, A. (2008). Specifying Strategies for Exercises. In: Autexier, S., Campbell, J., Rubio, J., Sorge, V., Suzuki, M., Wiedijk, F. (eds) Intelligent Computer Mathematics. CICM 2008. Lecture Notes in Computer Science(), vol 5144. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85110-3_36
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DOI: https://doi.org/10.1007/978-3-540-85110-3_36
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