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Technology, Knowledge and Learning

, Volume 20, Issue 3, pp 317–337 | Cite as

Cognitive Demand of Model Tracing Tutor Tasks: Conceptualizing and Predicting How Deeply Students Engage

  • Aaron M. Kessler
  • Mary Kay Stein
  • Christian D. Schunn
Work-in-Progress
First Online:

Abstract

Model tracing tutors represent a technology designed to mimic key elements of one-on-one human tutoring. We examine the situations in which such supportive computer technologies may devolve into mindless student work with little conceptual understanding or student development. To analyze the support of student intellectual work in the model tracing tutor case, we adapt a cognitive demand framework that has been previously applied with success to teacher-guided mathematics classrooms. This framework is then tested against think-aloud data from students using a model tracing tutor designed to teach proportional reasoning skills in the context of robotics movement planning problems. Individual tutor tasks are coded for designed level of cognitive demand and compared to students’ enacted level of cognitive demand. In general, designed levels predicted how students enacted the tasks. However, just as in classrooms, student enactment was often at lower levels of demand than designed. Several contextual design features were associated with this decline. Implications for intelligent tutoring system design and research are discussed.

Keywords

Model tracing tutor Cognitive demand framework Student task engagement 
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References

  1. Alibali, M. W., & Nathan, M. J. (2012). Embodiment in mathematics teaching and learning: Evidence from learners’ and teachers’ gestures. Journal of the Learning Sciences, 21(2), 247–286.CrossRefGoogle Scholar
  2. Anderson, J. R. (1996). ACT: A simple theory of complex cognition. American Psychologist, 51(4), 355–365.CrossRefGoogle Scholar
  3. Baumert, J., Kunter, M., Blum, W., Voss, T., Jordan, A., Klusmann, U., et al. (2010). Teachers’ mathematical knowledge, cognitive activation in the classroom, and student progress. American Educational Research Journal, 47(1), 133–180.CrossRefGoogle Scholar
  4. Boaler, J., & Brodie, K. (2004). The importance of depth and breadth in the analysis of teaching: A framework for analyzing teacher questions. In Proceedings of the 26th meeting of the North American chapter of the international group for the psychology of mathematics education. Toronto, Ontario, Canada.Google Scholar
  5. Boaler, J., & Staples, M. (2008). Creating mathematical futures through an equitable teaching approach: The case of Railside School. The Teachers College Record, 110(3), 608–645.Google Scholar
  6. Bosch, M., Chevallard, Y., & Gascón, J. (2006). Science or magic? The use of models and theories in didactics of mathematics. In M. Bosch (Eds.), Proceedings of the fourth congress of the European Society for research in mathematics education (pp. 1254–1263). Barcelona.Google Scholar
  7. Boston, M. D., & Smith, M. S. (2009). Transforming secondary mathematics teaching: Increasing the cognitive demands of instructional tasks used in teachers’ classrooms. Journal for Research in Mathematics Education, 40(2),119–156.Google Scholar
  8. Brophy, J. (2000). Teaching. Brussels: International Academy of Education.Google Scholar
  9. Carmel, E., Crawford, S., & Chen, H. (1992). Browsing in hypertext: A cognitive study. IEEE Transactions on Systems, Man, and Cybernetics, 22, 865–884.CrossRefGoogle Scholar
  10. Doyle, W. (1983). Academic work. Review of Educational Research, 53, 159–199.CrossRefGoogle Scholar
  11. Ericsson, K. A., & Simon, H. A. (1993). Protocol analysis: Verbal reports as data (revised ed.). Cambridge, MA: MIT Press.Google Scholar
  12. Grouws, D., Smith, M. S., & Sztajn, P. (2004). The preparation an detaching practices of U.S. mathematics teachers: 1990–2000 mathematics assessments of the National Assessment of Educational Progress; Results and interpretations (pp. 221–269). Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  13. Harel, G., Behr, M., Lesh, R., & Post, T. (1994). Invariance of ratio: The case of children’s anticipatory scheme for constancy of taste. Journal for Research in Mathematics Education, 25, 324–345.CrossRefGoogle Scholar
  14. Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 524–549.Google Scholar
  15. Hiebert, J. (Ed.). (2013). Conceptual and procedural knowledge: The case of mathematics. London: Routledge.Google Scholar
  16. Hiebert, J., & Carpenter, T. (1992). Learning and teaching with understanding. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 65–97). New York: Macmillan.Google Scholar
  17. Hiebert, J., & Grouws, D. (2007). The effects of classroom mathematics teaching on students’ learning. In F. Lester (Ed.), Handbook of research on mathematics teaching and learning (pp. 371–404). Charlotte, NC: Information Age.Google Scholar
  18. Hiebert, J., & Wearne, D. (1993). Instructional tasks, classroom discourse, and students’ learning in second-grade arithmetic. American Educational Research Journal, 30(2), 393–425.CrossRefGoogle Scholar
  19. Huntley, M. A., Rasmussen, R. S., Villarubi, J., Sangtong, J., & Fey, J. T. (2000). Effects of standards-based mathematics education: A study of the Core-plus mathematics project algebra and functions strand. Journal for Research in Mathematics Education, 31(3), 328–361.CrossRefGoogle Scholar
  20. Jang, J., & Schunn, C. D. (2014). A framework for unpacking cognitive benefits of distributed complex visual displays. Journal of Experimental Psychology Applied 20(3), 260–269.Google Scholar
  21. Jang, J., Schunn, C.D., & Nokes, T. J. (2011). Spatially distributed instructions improve learning outcomes and efficiency. Journal of Educational Psychology, 103(1), 60–72.Google Scholar
  22. Kessler, A., Boston, M., & Stein, M. K. (2014). Conceptualizing Teacher’s Practices in Supporting Students’ Mathematical Learning in Computer-Directed Learning Environments. Report published in the proceedings of the 11th International Conference of the Learning Sciences, Boulder, CO.Google Scholar
  23. Koedinger, K., & Corbett, A. (2006). Cognitive tutors: Technology bringing learning science to the classroom. In K. Sawyer (Ed.), The Cambridge handbook of the learning sciences. Cambridge, MA: Cambridge University Press.Google Scholar
  24. Lamon, S. J. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. Second Handbook of Research on Mathematics Teaching and Learning, 1, 629–667.Google Scholar
  25. Liu, A., & Schunn, C. D. (2014). Applying math onto mechanism: Investigating the relationship between mechanistic and mathematical understanding. Paper presented at the 36th annual meeting of the cognitive science society. Quebec City, Canada.Google Scholar
  26. Lobato, J., Ellis, A. B., Charles, R., & Zbiek, R. (2010). Developing essential understanding of ratios, proportions & proportional reasoning: Grades 6–8. Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  27. Ma, W., Adesope, O. O., Nesbit, J. C., & Liu, Q. (2014). Intelligent tutoring systems and learning outcomes: A meta-analysis. Journal of Educational Psychology, 106(4), 901–918.CrossRefGoogle Scholar
  28. Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis. Thousand Oaks, CA: Sage.Google Scholar
  29. National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  30. National Research Council. (2004). On evaluating curricular effectiveness: Judging the quality of K-12 mathematics evaluations (Committee for a Review of the Evaluation Data on the Effectiveness of NSF-Supported and Commercially Generated Mathematics Curriculum Materials). Washington, DC: The National Academies Press.Google Scholar
  31. O’Connor, M. C. (2001). Can any fraction be turned into a decimal? A case study of a mathematical group discussion. Educational Studies in Mathematics, 46, 143–185.CrossRefGoogle Scholar
  32. Paas, F. G. W. C., Renkl, A., & Sweller, J. (2004). Cognitive load theory: Instructional implications of the interaction between information structures and cognitive architecture. Instructional Science, 32, 1–8.CrossRefGoogle Scholar
  33. Ritter, S., Anderson, J. R., Keodinger, K. R., & Corbett, A. (2007). Cognitive tutor: Applied research in mathematics education. Psychonomic Bulletin & Review, 14(2), 249–255.CrossRefGoogle Scholar
  34. Rittle-Johnson, B., & Alibali, M. W. (1999). Conceptual and procedural knowledge of mathematics: Does one lead to the other? Journal of Educational Psychology, 91(1), 175.CrossRefGoogle Scholar
  35. Rittle-Johnson, B., Siegler, R. S., & Alibali, M. W. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology, 93(2), 346.CrossRefGoogle Scholar
  36. Seidel, T., & Shavelson, R. (2007). Teaching effectiveness research in the past decade: The role of theory and research design in disentangling meta-analysis results. Review of Educational Research, 77(4), 454–499.CrossRefGoogle Scholar
  37. Senk, S. L., & Thompspn, D. R. (Eds.). (2003). Standards-based school mathematics curricula: What are they? What do students learn?. Mahwah, NJ: Erlbaum.Google Scholar
  38. Silk, E. M., Higashi, R., & Schunn, C. D. (2011). Resources for robot competition success: Assessing math use in grade-school-level engineering design. In American Society for Engineering Education. American Society for Engineering Education.Google Scholar
  39. Silk, E. M., & Schunn, C. D. (2011). Calculational versus mechanistic mathematics in propelling the development of physical knowledge. Paper presented at the 41st annual meeting of The Jean Piaget Society, Berkeley, CA.Google Scholar
  40. Smith, M. S. (2000). Balancing old and new: An experienced middle school teacher’s learning in the context of mathematics instructional reform. The Elementary School Journal, 100(4), 351–375.Google Scholar
  41. Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33(2), 455–488.CrossRefGoogle Scholar
  42. Stein, M. K., & Lane, S. (1996). Instructional tasks and the development of student capacity to think and reason: An analysis of the relationship between teaching and learning in a reform mathematics project. Educational Research and Evaluation, 2(1), 50–80.Google Scholar
  43. Stein, M. K., & Kaufman, J. H. (2010). Selecting and supporting the use of mathematics curricula at scale. American Educational Research Journal, 47(3), 663–693.Google Scholar
  44. Stein, M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A. (2009). Implementing standards-based mathematics instruction: A casebook for professional development. New York, NY: Teachers College Press, Columbia University.Google Scholar
  45. Stigler, J. W., & Hiebert, J. (2004). Improving mathematics teaching. Educational Leadership, 61(5), 12–17.Google Scholar
  46. Tarr, J. E., Reys, R. E., Reys, B. J., Chávez, Ó., Shih, J., & Osterlind, S. J. (2008). The impact of middle-grades mathematics curricula and the classroom learning environment on student achievement. Journal for Research in Mathematics Education, 39, 247–280.Google Scholar
  47. Thompson, P. W., & Saldanha, L. (2003). Fractions and multiplicative reasoning. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A research companion to principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  48. van Merrienboer, J. J. G., & Sweller, J. (2005). Cognitive load theory and complex learning: Recent developments and future directions. Educational Psychology Review, 17(2), 147–177.CrossRefGoogle Scholar
  49. VanLehn, K. (2011). The relative effectiveness of human tutoring, intelligent tutoring systems, and other tutoring systems. Educational Psychologist, 46, 197–221.CrossRefGoogle Scholar
  50. VanLehn, K., Freedman, R., Jordan, P., Murray, C., Osan, R., Ringenberg, M., et al. (2000). Fading and deepening: The next steps for Andes and other model-tracing tutors. In G. Guathier, C. Frasson, & K. VanLehn (Eds.), Intelligent tutoring systems (pp. 474–483). Berlin: Springer.CrossRefGoogle Scholar
  51. VanLehn, K., Lynch, C., Schulze, K., Shapiro, J. A., Shelby, R., Taylor, L., et al. (2005). The Andes physics tutoring system: Lessons learned. International Journal of Artificial Intelligence in Education, 15(3), 147–204.Google Scholar
  52. Venezky, R. (1992). Textbooks in school and society. In P. Jackson. (Ed.), Handbook of research on curriculum (pp. 436–462). New York: Macmillan.Google Scholar
  53. Weaver, R., & Junker, B. W. (2004). Model specification for cognitive assessment of proportional reasoning (No. 777). Department of Statistics Technical Report.Google Scholar
  54. Wilson, M., & Lloyd, G. (2000). The challenge to share mathematical authority with students: High school teachers’ experiences reforming classroom roles and activities through curriculum implementation. Journal of Curriculum and Supervision, 15, 146–169.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Aaron M. Kessler
    • 1
  • Mary Kay Stein
    • 1
  • Christian D. Schunn
    • 1
  1. 1.University of PittsburghPittsburghUSA

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