Abstract
The translation of word problems into equations is one of the major difficulties for students regarding problem solving. This paper describes both a domain-specific knowledge representation and an inference engine based on hypergraphs that permits intelligent student supervision of this stage of the solving process. The framework presented makes it possible to simultaneously: a) represent all potential algebraic solutions to a given word problem; b) keep track of the student’s actions; c) provide automatic remediation; and d) determine the current state of the resolution process univocally. Starting from these ideas, we have designed an intelligent tutoring system (ITS). An experimental evaluation supports the use of this ITS in practice.
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Filloy, E., Rojano, T., Puig, L.: Educational Algebra. A Theoretical and Empirical Approach. Springer, New York (2008)
Croteau, E.A., Heffernan, N.T., Koedinger, K.R.: Why are Algebra Word Problems Difficult? Using Tutorial Log Files and the Power Law of Learning to Select the Best Fitting Cognitive Model. In: Lester, J.C., Vicari, R.M., Paraguaçu, F. (eds.) ITS 2004. LNCS, vol. 3220, pp. 240–250. Springer, Heidelberg (2004)
Chang, K.E., Sung, Y.T., Lin, S.F.: Computer-assisted learning for mathematical problem solving. Computers & Education 46(2), 140–151 (2006)
Heffernan, N.T., Koedinger, K.R.: Intelligent Tutoring Systems are Missing the Tutor: Building a More Strategic Dialog-Based Tutor. In: Rose, C.P., Freedman, R. (eds.) Building Dialogue Systems for Tutorial Applications, Papers of the 2000 AAAI Fall Symposium, pp. 14–19. AAAI Press, Menlo Park (2000)
Koedinger, K.R., Anderson, J.R.: Illustrating Principled Design: The Early Evolution of a Cognitive Tutor for Algebra Symbolization. Interactive Learning Environments 5(1), 161–179 (1998)
Fridman, L.M.: Los grafos trinomiales como metalenguaje de los problemas. Matemáticas. Revista del Departamento de Matemáticas de la Universidad de Sonora 17-18, 51–59 (1990)
Do, N., Pham, T.-L.: Knowledge representation and algorithms for automatic solving integral problems. In: Proc. 6th Int. Computer Science & Education (ICCSE), pp. 730–735 (2011)
Mitrovic, A., Martin, B., Suraweera, P.: Intelligent tutors for all: the constraint based approach. IEEE Intelligent Systems 22(4), 38–45 (2007)
Anderson, J.R., Bothell, D., Byrne, M.D., Douglass, S., Lebiere, C., Qin, Y.: An integrated theory of the mind. Psychological Review 111(4), 1036–1060 (2004)
VanLehn, K.: The behavior of tutoring systems. International Journal of Artificial Intelligence in Education 16(3), 227–265 (2006)
Arevalillo-Herráez, M., Arnau, D., González-Calero, J.A., Ayesh, A.: Domain specific knowledge Representation for an Intelligent Tutoring System to Teach Algebraic Reasoning. In: Cerri, S.A., Clancey, W.J., Papadourakis, G., Panourgia, K. (eds.) ITS 2012. LNCS, vol. 7315, pp. 630–631. Springer, Heidelberg (2012)
Arnau, D., Arevalillo-Herráez, M., Puig, L., González-Calero, J.A.: Fundamentals of the design and the operation of an intelligent tutoring system for the learning of the arithmetical and algebraic way of solving word problems. Computers & Education 63, 119–130 (2013)
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Arevalillo-Herráez, M., Arnau, D. (2013). A Hypergraph Based Framework for Intelligent Tutoring of Algebraic Reasoning. In: Lane, H.C., Yacef, K., Mostow, J., Pavlik, P. (eds) Artificial Intelligence in Education. AIED 2013. Lecture Notes in Computer Science(), vol 7926. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39112-5_52
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DOI: https://doi.org/10.1007/978-3-642-39112-5_52
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