Abstract
This article describes an intelligent, model-tracing system for tutoring expansion and factoring of algebraic expressions. The system is implemented as a set of procedures in a Maple document that tutor a breadth of 18 top-level mathematical skills (algebraic operations). Twelve (12) skills for expansion (monomial multiplication, monomial division and power of monomial, monomial-polynomial and polynomial-polynomial multiplication, parentheses elimination, collection of like terms, identities square of sum and difference, product of sum by difference, cube of sum and difference) and six (6) skills for factoring (common factor, identities square of sum and difference, product of sum by difference, quadratic form by sum and product, quadratic form by roots). These skills are further decomposed in simpler ones giving a deep domain expertise model of 68 primitive skills. The tutor has two novel features: (a) it exhibits intelligent task recognition by identifying all skills present in any expression through intelligent parsing, and (b) for each identified skill, the tutor traces all the sub-skills, a feature called deep model tracing. Furthermore, based on these features, the tutor achieves broad knowledge monitoring by recording student performance for all skills present in any expression.
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References
Aleven, V., McLaren, B.M., Sewall, J., Koedinger, K.R.: The cognitive tutor authoring tools (CTAT): preliminary evaluation of efficiency gains. In: Ikeda, M., Ashley, K.D., Chan, T.-W. (eds.) ITS 2006. LNCS, vol. 4053, pp. 61–70. Springer, Heidelberg (2006). https://doi.org/10.1007/11774303_7
Aleven, V., McLaren, B.M., Sewall, J.: Scaling up programming by demonstration for intelligent tutoring systems development: an open-access web site for middle school mathematics learning. IEEE Trans. Learn. Technol. 2(2), 64–78 (2009)
Anderson, J.R., Corbett, A.T., Koedinger, K.R., Pelletier, R.: Cognitive tutors: lessons learned. J. Learn. Sci. 4(2), 167–207 (1995)
Bloom, B.S.: The 2 sigma problem: the search of methods for group instruction as effective as one-to- one tutoring. Educ. Res. 13(6), 4–16 (1984)
Corbett, A.: Cognitive computer tutors: solving the two-sigma problem. In: Bauer, M., Gmytrasiewicz, P.J., Vassileva, J. (eds.) UM 2001. LNCS (LNAI), vol. 2109, pp. 137–147. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44566-8_14
Dicheva, D., Mizoguchi, R., Greer, J. (eds.): Semantic Web Technologies for e-Learning, The Future of Learning, vol. 4. IOS Press, Amsterdam (2009)
Koedinger, K., Corbett, A.: Cognitive tutors: technology bringing learning science to the classroom. In: Sawyer, K. (ed.) The Cambridge Handbook of the Learning Sciences, pp. 61–78. University Press, Cambridge (2006)
Mizoguchi, R., Bourdeau, J.: Using ontological engineering to overcome common AI-ED problems. Int. J. Artif. Intell. Educ. 11(2), 107–121 (2000)
Mizoguchi, R., Hayasi, Y., Bourdeau, J.: Inside a theory-aware authoring system. In: Dicheva, D., Mizoguchi, R., Greer, J. (eds.) Semantic Web Technologies for e-Learning: The Future of Learning, vol. 4, pp. 59–76. IOS Press, Amsterdam (2009)
Murray, T.: Principles for pedagogy-oriented knowledge based tutor authoring systems. In: Murray, T., Ainsworth, S., Blessing, S. (eds.) Authoring Tools for Advanced Technology Learning Environments, pp. 439–466. Kluwer Academic Publishers, Netherlands (2003)
Sklavakis, D.: Implementing problem solving methods in CYC. MSc dissertation, Department of Artificial Intelligence, University of Edinburgh (1998)
Sklavakis, D., Refanidis, I.: An individualized web-based algebra tutor based on dynamic deep model tracing. In: Darzentas, J., Vouros, G.A., Vosinakis, S., Arnellos, A. (eds.) SETN 2008. LNCS (LNAI), vol. 5138, pp. 389–394. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-87881-0_38
Sklavakis, D., Refanidis, I.: The MATHESIS algebra tutor: web-based expert tutoring via deep model tracing. Interactive Event. Proceedings of the 14th International Conference on Artificial Intelligence in Education (AIED 2009), p. 795. IOS Press, Amsterdam (2009)
Sklavakis, D., Refanidis, I.: Ontology-based authoring of intelligent model-tracing math tutors. In: Dicheva, D., Dochev, D. (eds.) AIMSA 2010. LNCS (LNAI), vol. 6304, pp. 201–210. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15431-7_21
Sklavakis, D., Refanidis, I.: MATHESIS: an intelligent web-based algebra tutoring school. Int. J. Artif. Intell. Educ. 22(2), 191–218 (2013)
Sklavakis, D., Refanidis, I.: The MATHESIS meta-knowledge engineering framework: ontology-driven development of intelligent tutoring systems. Appl. Ontol. 9(3–4), 237–265 (2014)
VanLehn, K.: The behavior of tutoring systems. Int. J. Artif. Intell. Educ. 16(3), 227–265 (2006)
VanLehn, K., Lynch, C., Schulze, K., Shapiro, J., Shelby, R.: The andes physics tutoring system: lessons learned. Int. J. Artif. Intell. Educ. 15(3), 147–204 (2005)
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Sklavakis, D. (2020). Transforming Maple into an Intelligent Model-Tracing Math Tutor. In: Gerhard, J., Kotsireas, I. (eds) Maple in Mathematics Education and Research. MC 2019. Communications in Computer and Information Science, vol 1125. Springer, Cham. https://doi.org/10.1007/978-3-030-41258-6_22
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