Abstract
Symbolization is the ability to translate a real world situation into the language of algebra. We believe that symbolization is the single most important skill students learn in high school algebra. We present research on what makes this skill difficult and report the discovery of a “hidden” skill in symbolization. Contrary to past research that has emphasized that symbolization is difficult due to both comprehension difficulties and the abstract nature of variables, we found that symbolization is difficult because it is the articulation in the “foreign” language of “algebra”. We also present Ms. Lindquist, an Intelligent Tutoring System (ITS) designed to carry on a tutorial dialog about symbolization. Ms. Lindquist has a separate tutorial model encoding pedagogical content knowledge in the form of different tutorial strategies, which were partially developed by observing an experienced human tutor. We discuss aspects of this human tutor’s method that can be modeled well by Ms. Lindquist. Finally, we present an early formative showing that students can learn from the dialogs Ms. Lindquist is able to engage student in. Ms. Lindquist has tutored over 600 students at www.AlgebraTutor.org.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Anderson, J. R. (1993). Rules of the Mind. Hillsdale, NJ: Erlbaum.
Anderson, J. R., Boyle, D. F., & Reiser, B. J. (1985). Intelligent tutoring systems. Science, 228, 456–462.
Anderson, J. R., Corbett, A. T., Koedinger, K. R., & Pelletier, R. (1995) Cognitive tutors: lessons learned. The Journal of the Learning Sciences, 4(2), 167–207.
Anderson, J. R. & Pelletier, R. (1991) A developmental system for model-tracing tutors. In Lawrence Birnbaum (Eds.) The International Conference on the Learning Sciences. Association for the Advancement of Computing in Education. Charlottesville, Virginia (pp. 1–8).
Clancey, W. J., (1982) Tutoring rules for guiding a case method dialog. In D. Sleeman & J. S. Brown (Eds.) Intelligent Tutoring Systems London: Academic Press. (pp. 201–226.)
Corbett, A. T., and Anderson, J. R., (1995) Knowledge decomposition and subgoal reification in the ACT programming tutor. in Proceedings of Artificial Intelligence in Education (pp. 469–476)
Conati, C., Larkin, J. and VanLehn, K. (1997) A computer framework to support self-explanation. In: du Bolay, B. and Mizoguchi, R.(Eds.) Proceedings of AI-ED 97 World Conference on Artificial Intelligence in Education. Vol. 39, pp. 279–276, Amsterdam: IO Press.
Freedman, R. (2000) Using a reactive planner as the basis for a dialogue agent. In Proceedings of the Thirteenth Florida Artificial Intelligence Research Symposium (FLAIRS’ 00), Orlando.
Gluck, K. (1999). Eye movements and algebra tutoring. Doctoral dissertation. Psychology Department, Carnegie Melon University.
Graesser, A.C., Wiemer-Hastings, P., Wiemer-Hastings, K., Harter, D., Person, N., & the TRG (in press). Using latent semantic analysis to evaluate the contributions of students in AutoTutor. Interactive Learning Environments.
Heffernan, N. T. (2001). Intelligent Tutoring Systems have Forgotten the Tutor: Adding a Cognitive Model of an Experienced Human Tutor. Dissertation. Carnegie Mellon University, Computer Science Department. http://gs260.sp.cs.cmu.edu/diss
Heffernan, N. T., & Koedinger, K. R.(1997) The composition effect in symbolizing: the role of symbol production versus text comprehension. Proceeding of the Nineteenth Annual Conference of the Cognitive Science Society 307–312. Hillsdale, NJ: Erlbaum.
Heffernan, N. T., & Koedinger, K. R. (1998) A developmental model for algebra symbolization: The results of a difficulty factors assessment. In Proceedings of the Twentieth Annual Conference of the Cognitive Science Society, (pp. 484–489). Hillsdale, NJ: Erlbaum.
Koedinger, K. R., Anderson, J.R., Hadley, W.H., & Mark, M. A. (1997). Intelligent tutoring goes to school in the big city. International Journal of Artificial Intelligence in Education, 8, 30–43.
Koedinger, K. R., & Anderson, J. R. (1998). Illustrating principled design: The early evolution of a cognitive tutor for algebra symbolization. In Interactive Learning Environments, 5, 161–180.
Koedinger, K. R. & Nathan, M. J. (submitted to). The real story behind story problems: Effects of representations on quantitative reasoning. Submitted to Cognitive Psychology.
McArthur, D., Stasz, C., & Zmuidzinas, M. (1990) Tutoring techniques in algebra. Cognition and Instruction. 7 (pp. 197–244.)
Moore, J. D. (1996) Discourse generation for instructional applications: Making computer-based tutors more like humans. Journal of Artificial Intelligence in Education, 7(2), 118–124
Schoenfeld, A., Gamoran, M., Kessel, C., Leonard, M., Or-Bach, R., & Arcavi, A. (1992) Toward a comprehensive model of human tutoring in complex subject matter domains. Journal of Mathematical Behavior, 11, 293–319
Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15, 4–14.
VanLehn, K, Anderson, J., Ashley, K., Chi. M., Corbett, A., Koedinger, K., Lesgold, A., Levin, L., Moore, M., and Pollack, M., NSF Grant 9720359. CIRCLE: Center for Interdisciplinary Research on Constructive Learning Environments. NSF Learning and Intelligent Systems Center. January, 1998 to January, 2003.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Heffernan, N.T., Koedinger, K.R. (2002). An Intelligent Tutoring System Incorporating a Model of an Experienced Human Tutor. In: Cerri, S.A., Gouardères, G., Paraguaçu, F. (eds) Intelligent Tutoring Systems. ITS 2002. Lecture Notes in Computer Science, vol 2363. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47987-2_61
Download citation
DOI: https://doi.org/10.1007/3-540-47987-2_61
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43750-5
Online ISBN: 978-3-540-47987-1
eBook Packages: Springer Book Archive