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A Constructivist Model for Redesigning AI Tutors in Mathematics

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Part of the book series: NATO ASI Series ((NATO ASI F,volume 117))

Abstract

This chapter suggests a new approach to designing AI tutors that grew primarily out of results from a study that is reported in greater detail in a paper entitled The development of tutoring capabilities in middle school mathematics teachers (Lesh & Kelly, in press). That study focused on a ten-week project in which real human tutors provided the intelligence behind a computer-based tutoring system. Our goal was to investigate the understandings, assumptions, and procedures that were really used in tutoring by teachers who were at various levels of expertise — and to observe the evolution of these tutoring abilities over time, as tutoring effectiveness gradually improved.

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References

  • American Association for the Advancement of Sciences Project 2061 Science for all Americans. Washington, D.C.: AAAS,1989.

    Google Scholar 

  • American Association for the Advancement of Science. Project 2061 (1989). What Science is most worth knowingà Washington, D.C.

    Google Scholar 

  • Bunderson, V. A . (1983) The diagnosis and remediation of cognitive bugs in arithmetic.(with J.B. Olsen). Final Report, NSF Contract #SED 80-12500, WICAT Education Institute Technical Report, September.

    Google Scholar 

  • Carey, S. (1988). Reorganization of knowledge in the course of acquisition. In S.Strauss (Ed.), Ontogeny, Phylogeny, and historical development. Norwood, NJ:Ablex.

    Google Scholar 

  • Clement, J. (1982a). Students preconceptions in introductory mechanics. American Journal of Physics, 50, 66 – 71.

    Article  Google Scholar 

  • Collins, A.; Brown, J. S.; & Newman, S. E. (1990). cognitive apprenticeship: Teaching the craft of reading, writing, and mathematics. In L. B. Resnick (Ed.) Cognition and instruction: Issues and agendas, Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Cronbach, L. J., & Snow, R. E. (1977). Aptitudes and instructional methods. New York:Irvington.

    Google Scholar 

  • De Kleer, J. & Brown, J.S. (1980). Mental models of physical mechanisms and their acquisition. In J.R. Anderson (Ed.), Cognitive skills and their acquisition, (pp. 285– 309).Hillsdale,NJ:Erlbaum.

    Google Scholar 

  • Dienes, Z. (1960). Building up mathematics. London: Hutchinson Educational Ltd.

    Google Scholar 

  • diSessa, A. (1989) Knowledge in pieces. In G. Gorman & P Pufall (Eds) Constructivism in the Computer Age. Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • diSessa. S . (1987) Toward an epistemology of physics. Cognitive Science Technical Report. Berkeley, CA: Institute for Cognitive Science.

    Google Scholar 

  • Krutetskii, V.A . The psychology of mathematical abilities in school children. Chicago: University of Chicago Press, 1976.

    Google Scholar 

  • Lesh, R. & Kelly, A. (in press) The development of tutoring capabilities in middle school teachers. Journal for Research in Mathematics Education. Reston, VA: NCTM.

    Google Scholar 

  • Lesh, R., & Akerstrom, M. (1982). Applied problem solving: Priorities for mathematics education research. In F. Lester & J. Garofalo (Eds.), Mathematical Problem Solving: Issues in Research (pp. 117–129). Philadelphia: Franklin Institute Press.

    Google Scholar 

  • Lesh, R . (1985). Processes, skills and abilities needed to use mathematics in everyday situations. Education and Urban Society, 17 (4), 439–446.

    Article  Google Scholar 

  • Lesh, R . (1989). Computer-based assessment of higher-order understandings and processes in elementary mathematics. In J. Kulm (Ed.) Assessing Higher Order Thinking in Mathematics. AAAS: Washington, DC

    Google Scholar 

  • Lesh, R., Post, T. & Behr, M. (1989) Proportional reasoning. In M. Behr & J. Hiebert (Eds.) Number Concepts and Operations in the Middle Grades. Reston, VA: NCTM

    Google Scholar 

  • Lesh, R., Post, T., & Behr, M. (1987) Dienes revisited: Multiple embodiments in computer environments. In I. Wirszup & R. Streit (Eds.), Developments in School Mathematics Education Around the World. Reston, VA: NCTM.

    Google Scholar 

  • Lesh, R. & Zawojewski, J. (1987). Problem solving. In T. Post ( Ed. ), Teaching Mathematics in Grades K-8: Research-based Methods. Boston: Allyn & Bacon

    Google Scholar 

  • Lesh, R. (1990). Computer-based assessment of higher-order understandings and processes in elementary mathematics. In J. Kulm (Ed.) Assessing Higher Order Thinking in Mathematics. AAAS: Washington, DC

    Google Scholar 

  • Mathematical Sciences Education Board, National Research Council. Reshaping School Mathematics. Washington, D.C., National Academy Press, 1990 )

    Google Scholar 

  • McCloskey, M . (1983). Naive theories of motion. In D. Gentner & A. Stevens (Eds.)Mental models. Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • McCloskey, M . (1983) Intuitive Physics. Scientific American, 284, 222.

    Google Scholar 

  • Minstrell, J . (1982). Conceptual development research in the natural setting of a secondary school science classroom. In M. B. Rowe (Ed.) Education for the 80’s:Science. National Education Association.

    Google Scholar 

  • Naisbitt & Aburdene, 1990 National Council of Teachers of Mathematics’ Curriculum and Evaluation Standards for School Mathematics. Reston, VA: NCTM.

    Google Scholar 

  • National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM.

    Google Scholar 

  • Polya, G. (1957). How to solve it: A new aspect of mathematical method. (2nd. ed.).Princeton, NJ: Princeton University Press. (Original work published 1945 ).

    Google Scholar 

  • Polya, G . (1984). With, or without, motivation. In Gian-Carlos Rots (Ed.). George Polya:Collected papers, Vol. IV. (pp. 496-503).Cambridge, MA: MIT Press.

    Google Scholar 

  • Schwartz, J. L . (1989). Intellectual mirrors: A step in the direction of making schools knowledge-making places. Harvard Educational Review.

    Google Scholar 

  • Sleeman, D., Kelly, A. E, Martinak, R., Ward, R., & Moore, J. (1989). Studies of diagnosis and remediation with high school algebra students. Cognitive Science, 13 (4), 551–568.

    Article  Google Scholar 

  • Thompson, P. & Lesh, R. (in press) Quantitative Structures and Procedural Structures in Mathematical Problem Solving. In R. Lesh & S. Lamon. Assessing Deeper and Higher-Order Understandings in Elementary Mathematics. ETS Princeton, NJ.

    Google Scholar 

  • Thompson, P. W . (1989). Artificial intelligence, advanced technology, and learning and teaching algebra. In S. Wagner & C. Kieran (Ed.), Research issues in the learning and teaching of algebra, (pp. 135 – 161 ). Reston, VA: NCTM.

    Google Scholar 

  • Winograd, T., & Flores, F. (1985). Understanding computers and cognition: A new foundation for design. Norwood, NJ: Ablex.

    Google Scholar 

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© 1996 Springer-Verlag Berlin Heidelberg

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Lesh, R., Kelly, A.E. (1996). A Constructivist Model for Redesigning AI Tutors in Mathematics. In: Laborde, JM. (eds) Intelligent Learning Environments: The Case of Geometry. NATO ASI Series, vol 117. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60927-5_9

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  • DOI: https://doi.org/10.1007/978-3-642-60927-5_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-64608-9

  • Online ISBN: 978-3-642-60927-5

  • eBook Packages: Springer Book Archive

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