Abstract
Intelligent tutors that emulate one-on-one tutoring with a human have been shown to effectively support student learning, but these systems are often challenging to build. Most methods for implementing tutors focus on generating intelligent explanations, rather than generating practice problems and problem progressions. In this work, we explore the possibility of using a single model of a learning domain to support the generation of both practice problems and intelligent explanations. In the domain of algebra, we show how problem generation can be supported by modeling if-then production rules in the logic programming language answer set programming. We also show how this model can be authored such that explanations can be generated directly from the rules, facilitating both worked examples and real-time feedback during independent problem-solving. We evaluate this approach through a proof-of-concept implementation and two formative user studies, showing that our generated content is of appropriate quality. We believe this approach to modeling learning domains has many exciting advantages.
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Ahmed, U.Z., Gulwani, S., Karkare, A.: Automatically generating problems and solutions for natural deduction. In: Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence, IJCAI 2013, pp. 1968–1975. AAAI Press (2013). http://dl.acm.org/citation.cfm?id=2540128.2540411
Andersen, E., Gulwani, S., Popović, Z.: A trace-based framework for analyzing and synthesizing educational progressions. In: Proceedings of the SIGCHI Conference on Human Factors in Computing Systems, CHI 2013, pp. 773–782. ACM, New York (2013). https://doi.org/10.1145/2470654.2470764
Anderson, J.R., Corbett, A.T., Koedinger, K.R., Pelletier, R.: Cognitive tutors: lessons learned. J. Learn. Sci. 4(2), 167–207 (1995)
Anderson, J.R., Pelletier, R.: A development system for model-tracing tutors. In: Proceedings of the International Conference of the Learning Sciences, pp. 1–8 (1991)
Butler, E., Andersen, E., Smith, A.M., Gulwani, S., Popovic, Z.: Automatic game progression design through analysis of solution features (2015)
Corbett, A., Koedinger, K.R., Anderson, J.R.: Intelligent tutoring systems. In: Helander, M., Landauer, T.K., Prahu, P. (eds.) Handbook of Human-Computer Interaction, 2nd edn, pp. 849–874. Elsevier Science, Amsterdam (1997)
van Gog, T., Paas, F., van Merriënboer, J.J.: Process-oriented worked examples: improving transfer performance through enhanced understanding. Instr. Sci. 32(1–2), 83–98 (2004). https://doi.org/10.1023/B:TRUC.0000021810.70784.b0
Heffernan, N.T., Heffernan, C.L.: The assistments ecosystem: building a platform that brings scientists and teachers together for minimally invasive research on human learning and teaching. Int. J. Artif. Intell. Educ. 24(4), 470–497 (2014). https://doi.org/10.1007/s40593-014-0024-x
Koedinger, K.R., Aleven, V., Heffernan, N., McLaren, B., Hockenberry, M.: Opening the door to non-programmers: authoring intelligent tutor behavior by demonstration. In: Lester, J.C., Vicari, R.M., Paraguaçu, F. (eds.) ITS 2004. LNCS, vol. 3220, pp. 162–174. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30139-4_16
Koedinger, K.R., Anderson, J.R., Hadley, W.H., Mark, M.A.: Intelligent tutoring goes to school in the big city. Int. J. Artif. Intell. Educ. 8, 30–43 (1997)
Koedinger, K.R., Brunskill, E., de Baker, R.S.J., McLaughlin, E.A., Stamper, J.C.: New potentials for data-driven intelligent tutoring system development and optimization. AI Mag. 34(3), 27–41 (2013)
Koedinger, K.R., Heffernan, N.: Toward a rapid development environment for cognitive tutors. In: Proceedigns of the International Conference on Artificial Intelligence in Education, pp. 455–457. IOS Press (2003)
Martin, B., Mitrovic, A.: Automatic problem generation in constraint-based tutors. In: Cerri, S.A., Gouardères, G., Paraguaçu, F. (eds.) ITS 2002. LNCS, vol. 2363, pp. 388–398. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-47987-2_42
Martin, B.I.: Intelligent tutoring systems: the practical implementation of constraint-based modelling. Ph.D. thesis, University of Canterbury (2001)
McLaren, B.M., Lim, S.J., Koedinger, K.R.: When and how often should worked examples be given to students? New results and a summary of the current state of research. In: Love, B.C., McRae, K., Sloutsky, V.M. (eds.) Cognitive Science Society, pp. 2176–2181. Cognitive Science Society, Austin (2008)
Mitrovic, A.: Fifteen years of constraint-based tutors: what we have achieved and where we are going. User Model. User-Adapt. Interact. 22(1–2), 39–72 (2012). https://doi.org/10.1007/s11257-011-9105-9
Mitrovic, A., Koedinger, K.R., Martin, B.: A comparative analysis of cognitive tutoring and constraint-based modeling. In: Brusilovsky, P., Corbett, A., de Rosis, F. (eds.) UM 2003. LNCS (LNAI), vol. 2702, pp. 313–322. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-44963-9_42
Ohlsson, S.: Constraint-based student modeling. In: Greer, J.E., McCalla, G.I. (eds.) Student Modelling: The Key to Individualized Knowledge-Based Instruction, vol. 125, pp. 167–189. Springer, Heidelberg (1994). https://doi.org/10.1007/978-3-662-03037-0_7
Polozov, O., O’Rourke, E., Smith, A., Zettlemoyer, L., Gulwani, S., Popović, Z.: Personalized mathematical word problem generation. In: Proceedings of the 24th International Joint Conference on Artificial Intelligence, IJCAI (2015)
Renkl, A.: Learning from worked-out examples: a study on individual differences. Cogn. Sci. 21(1), 1–29 (1997)
Renkl, A., Atkinson, R.K., Große, C.S.: How fading worked solution steps works - a cognitive load perspective. Instr. Sci. 32(1–2), 59–82 (2004). https://doi.org/10.1023/B:TRUC.0000021815.74806.f6
Renkl, A., Atkinson, R.K., Maier, U.H., Staley, R.: From example study to problem solving: smooth transitions help learning. J. Exp. Educ. 70(4), 293–315 (2002). http://www.jstor.org/stable/20152687
Sadigh, D., Seshia, S.A., Gupta, M.: Automating exercise generation: a step towards meeting the MOOC challenge for embedded systems. In: Proceedings of the Workshop on Embedded and Cyber-Physical Systems Education, WESE 2012, pp. 2:1–2:8. ACM, New York (2013). https://doi.org/10.1145/2530544.2530546
Salden, R.J.C.M., Aleven, V.A.W.M.M., Renkl, A., Schwonke, R.: Worked examples and tutored problem solving: redundant or synergistic forms of support? Top. Cogn. Sci. 1(1), 203–213 (2008). https://doi.org/10.1111/j.1756-8765.2008.01011.x
Shanahan, M.: The event calculus explained. In: Wooldridge, M.J., Veloso, M. (eds.) Artificial Intelligence Today. LNCS (LNAI), vol. 1600, pp. 409–430. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48317-9_17
Singh, R., Gulwani, S., Rajamani, S.: Automatically generating algebra problems. In: Proceedings of the Twenty-Sixth AAAI Conference on Artificial Intelligence (2012)
Smith, A., Butler, E., Popović, Z.: Quantifying over play: constraining undesirable solutions in puzzle design. In: Proceedings of the 8th International Conference on the Foundations of Digital Games (2013)
Smith, A.M., Andersen, E., Mateas, M., Popović, Z.: A case study of expressively constrainable level design automation tools for a puzzle game. In: FDG 2012: Proceedings of the Seventh International Conference on the Foundations of Digital Games. ACM, New York (2012)
VanLehn, K.: The behavior of tutoring systems. Int. J. Artif. Intell. Educ. 16, 227–265 (2006)
Vanlehn, K., et al.: The Andes physics tutoring system: five years of evaluations. In: In Proceedings of the 12th International Conference on Artificial Intelligence in Education, pp. 678–685. IOS Press (2005)
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O’Rourke, E., Butler, E., Díaz Tolentino, A., Popović, Z. (2019). Automatic Generation of Problems and Explanations for an Intelligent Algebra Tutor. In: Isotani, S., Millán, E., Ogan, A., Hastings, P., McLaren, B., Luckin, R. (eds) Artificial Intelligence in Education. AIED 2019. Lecture Notes in Computer Science(), vol 11625. Springer, Cham. https://doi.org/10.1007/978-3-030-23204-7_32
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