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Using the Intuitive Rules Theory as a Basis for Educating Teachers

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Making Sense of Mathematics Teacher Education

Abstract

In this chapter we illustrate how the explanatory and predictive power of the Intuitive Rules Theory can be used to plan instructional sequences that help students overcome the negative effects of intuitive rules on their work in mathematics and science. We then describe a research-based seminar we developed for raising mathematics and science teachers’ awareness of the role of intuitive rules in students’ thinking and to encourage them to take this knowledge into consideration when planning instruction. Finally, we discuss some initial impressions regarding the impact of the seminar on teachers’ actual teaching.

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References

  • Carey, S. (1992). The origin and evaluation of everyday concepts. In R.N. Giere (Ed.), Minnesota Studies in the Philosophy of Science, 15 (pp. 89–128). Minneapolis: University of Minnesota Press.

    Google Scholar 

  • Champagne, A.B., Klopfer, L.E., & Anderson, J.H. (1979). Factors influencing the learning of classical mechanics. (Research report). Pittsburgh: LRDC, University of Pittsburgh.

    Google Scholar 

  • Clement, J. (1993). Using bridging analogies and anchoring intuitions to deal with students’ preconceptions in physics. Journal of Research in Science Teaching, 30, 1241–1257.

    Article  Google Scholar 

  • Cooney, T. (1999). Conceptualizing teachers’ ways of thinking. Educational Studies in Mathematics, 38, 163–187.

    Article  Google Scholar 

  • Dembo, Y., Levin, I., & Siegler, R. S. (1997). A comparison of the geometric reasoning of students attending Israeli ultraorthodox and mainstream schools. Developmental Psychology, 33(1), 92–103.

    Article  Google Scholar 

  • Driver, R. (1994). Making a sense of secondary science. London: Routledge.

    Google Scholar 

  • Egozi, R. (1993). Subdivision processes in science and mathematics. Unpublished master’s thesis(in Hebrew), Tel-Aviv University, Israel.

    Google Scholar 

  • Fennema, E., Carpenter, T. P., Franke, M., L. Levi, L., Jacobs, V. R., & Empson, S. B. (1996). A longitudinal study of learning to use children’s thinking in mathematics instruction. Journal for Research in Mathematics Education, 27, 403–434.

    Article  Google Scholar 

  • Fischbein, E. (1987). Intuition in science and mathematics: An educational approach. Dordrecht, Netherlands: Reidel.

    Google Scholar 

  • Fischbein, E., Tirosh, P. & Hess, P. (1979). The intuition of infinity. Educational Studies in Mathematics, 12, 491–512.

    Article  Google Scholar 

  • Gunstone, R.F., & White, R.T. (1981). Understanding of gravity. Science Education, 65, 291–299.

    Article  Google Scholar 

  • Myers, S. (1998). Effects of conceptual conflict on using the intuitive rule “More A-more B” in 8th grade students. Unpublished master’s thesis (in Hebrew), Tel-Aviv University, Israel.

    Google Scholar 

  • Nunez R. (1991). A 3-dimension conceptual space of transformations for the study of the intuition of infinity in plane geometry. Proceedings of the Fifteen Conference for the Psychology of Mathematics Education (Vol. 3, pp. 362–368). Assisi, Italy.

    Google Scholar 

  • Pfundt, H. (1981). Pre-instructional conception about substances and transformation of substances. In W. Jung, H. Pfundt, & C. V. Rhonock (Eds.), Problems concerning students’ representation of physics and chemistry knowledge (pp. 320–341). Ludwigsburg: Frankfurt University.

    Google Scholar 

  • Piaget, J. (1980). Experiments in contradiction. Chicago: University of Chicago Press.

    Google Scholar 

  • Ronen, I. (2000). The intuitive rule “Same A — Same B ”: The case of overgeneralization of the conservation scheme. Unpublished doctoral dissertation (in Hebrew), Tel-Aviv University, Israel.

    Google Scholar 

  • Schifter, D. (1998). Learning mathematics for teaching: From a teachers’ seminar to the classroom. Journal of Mathematics Teacher Education, 1, 55–87.

    Article  Google Scholar 

  • Segal, N. (2000). Exploring the role of cognitive conflict in conservation task: The case of “same A — same B”. Unpublished master’s thesis (in Hebrew), Tel-Aviv University, Israel.

    Google Scholar 

  • Sowder, J., Armstrong, B., Lamon, S., Simon, M., Sowder, L., & Thompson, A. (1998). Educating Teachers to Teach Multiplicative Structures in the Middle Grades. Journal of Mathematics Teacher Education, 1(2), 127–155.

    Article  Google Scholar 

  • Stavy, R., & Berkovitz, B. (1980). Cognitive conflict as a basis for teaching quantitative aspects of the concept of temperature. Science Education, 64, 679–692.

    Article  Google Scholar 

  • Stavy, R., & Tirosh, D. (1996). Intuitive rules in mathematics and science: The case of “The more of A the more of B”. International Journal of Science Education, 18(6), 653–667.

    Article  Google Scholar 

  • Stavy, R., & Tirosh, D. (2000). How students (mis-)understand science and mathematics: Intuitive rules. New York: Teachers College Press.

    Google Scholar 

  • Stern, E., & Mevarech, Z.R. (1991). When familiar context does not facilitate mathematical understanding. Unpublished manuscript. Max Planck Institute, Germany.

    Google Scholar 

  • Tall, D. O. (1981). Intuition of infinity. Mathematics in School, 10(3), 30–33.

    Google Scholar 

  • Tirosh, D. (1991). The role of students’ intuitions of infinity in teaching the Cantorian theory. In D. Tall (Ed.), Advanced mathematical thinking (pp. 199–214). Dordrecht, Holland: Kluwer Academic.

    Google Scholar 

  • Tirosh, D., & Stavy, R. (1996). Intuitive rules in science and mathematics: The case of “Everything can be divided by two.” International Journal of Science Education, 18(6), 669–683.

    Article  Google Scholar 

  • Tirosh, D., & Stavy, R. (1999). Intuitive rules: A way to explain and predict students’ reasoning. Educational Studies in Mathematics, 38, 51–66.

    Article  Google Scholar 

  • Tirosh, D., Stavy, R., & Aboulafia, M. (1998). Is it possible to confine the application of the intuitive rule: Subdivision process can always be repeated? International Journal of Mathematics Education in Science and Technology, 29(6), 813–825.

    Article  Google Scholar 

  • Tirosh, D., Stavy, R., & Cohen, S. (1998). Cognitive conflict and intuitive rules. International Journal of Science Education, 20(10), 1257–1269.

    Article  Google Scholar 

  • Tirosh, D., & Tsamir, P. (1996). The role of representations in students’ intuitive thinking about infinity. International Journal of Mathematics Education in Science and Technology, 27(1), 33–40.

    Article  Google Scholar 

  • Tsamir, P., Tirosh, D., & Stavy, R. (1997). Intuitive rules and comparison tasks: The grasp of vertical angles. Proceedings of the First Mediterranean Conference: Mathematics, Education and Applications (pp. 298–304). Nicosia, Cyprus.

    Google Scholar 

  • Van den Heuvel-Panhuizen, M. (1994). Improvement of (didactic) assessment by improvements of problems: An attempt with respect to percentages. Educational Studies in Mathematics, 27, 341–372.

    Article  Google Scholar 

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© 2001 Springer Science+Business Media Dordrecht

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Tirosh, D., Stavy, R., Tsamir, P. (2001). Using the Intuitive Rules Theory as a Basis for Educating Teachers. In: Lin, FL., Cooney, T.J. (eds) Making Sense of Mathematics Teacher Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0828-0_4

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  • DOI: https://doi.org/10.1007/978-94-010-0828-0_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-6986-8

  • Online ISBN: 978-94-010-0828-0

  • eBook Packages: Springer Book Archive

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