Intuitive Interference in Probabilistic Reasoning

  • Reuven Babai
  • Tali Brecher
  • Ruth Stavy
  • Dina Tirosh
Article

Abstract

One theoretical framework which addresses students’ conceptions and reasoning processes in mathematics and science education is the intuitive rules theory. According to this theory, students’ reasoning is affected by intuitive rules when they solve a wide variety of conceptually non-related mathematical and scientific tasks that share some common external features. In this paper, we explore the cognitive processes related to the intuitive rule more Amore B and discuss issues related to overcoming its interference. We focused on the context of probability using a computerized “Probability Reasoning – Reaction Time Test.” We compared the accuracy and reaction times of responses that are in line with this intuitive rule to those that are counter-intuitive among high-school students. We also studied the effect of the level of mathematics instruction on participants’ responses. The results indicate that correct responses in line with the intuitive rule are more accurate and shorter than correct, counter-intuitive ones. Regarding the level of mathematics instruction, the only significant difference was in the percentage of correct responses to the counter-intuitive condition. Students with a high level of mathematics instruction had significantly more correct responses. These findings could contribute to designing innovative ways of assisting students in overcoming the interference of the intuitive rules.

Key Words

intuition intuitive interference intuitive rules mathematics education probability reaction time science education 

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References

  1. Andersson, B. (1986). The experiential gestalt of causation: A common core to pupils’ preconceptions in science. European Journal of Science Education, 2, 155–171.Google Scholar
  2. Babai, R. & Alon, T. (2004). Intuitive thinking, cognitive level or grade level: What predicts students’ incorrect responses in science and mathematics? Paper presented at the National Association of Research in Science Teaching (NARST) Annual Conference. Vancouver, Canada.Google Scholar
  3. Babai, R., Levyadun, T., Stavy, R. & Tirosh, D. (in press). Intuitive rules in science and mathematics: A reaction time study. International Journal of Mathematical Education in Science and Technology.Google Scholar
  4. Confrey, J. (1990). A review of the research on student conceptions in mathematics, science and programming. Review of Research in Education, 16, 3–56.CrossRefGoogle Scholar
  5. Dehaene, S. (1997). The number sense: How the mind creates mathematics. New York: Oxford University Press.Google Scholar
  6. diSessa, A.A. (1983). Phenomenology and the evaluation of intuition. In D. Gentner & A.L. Stevens (Eds.), Mental models (pp. 15–33). Hillsdale, New Jersey: Lawrence Erlbaum.Google Scholar
  7. Driver, R. (1994). Making a sense of secondary science. London: Routledge.Google Scholar
  8. Falk, R., Falk, R. & Levin, I. (1980). A potential for learning probability in young children. Educational Studies in Mathematics, 11, 181–204.CrossRefGoogle Scholar
  9. Fischbein, E. (1987). Intuition in science and mathematics. Dordrecht, The Netherlands: Reidel.Google Scholar
  10. Fischbein, E. (1999). Intuitions and schemata in mathematical reasoning. Educational Studies in Mathematics, 38, 11–50.CrossRefGoogle Scholar
  11. Greca, I.M. & Moreira, M.A. (2000). Mental models, conceptual models, and modeling. International Journal of Science Education, 22, 1–11.CrossRefGoogle Scholar
  12. Green, D.R. (1983). A survey of probabilistic concepts in 3000 students aged 11–16 years. In D.R. Grey et al. (Eds.), Proceedings of the First International Conference on Teaching Statistics (pp. 766–783). Sheffield, England: Teaching Statistics Trust.Google Scholar
  13. Gutierrez, R. & Ogborn, J. (1992). A causal framework for analysing alternative conceptions. International Journal of Science Education, 14, 201–220.Google Scholar
  14. Kahneman, D. & Tversky, A. (2000). Choices, values and frames. New York: Cambridge University Press and the Russell Sage Foundation.Google Scholar
  15. Perkins, D.N. & Simmons, R. (1988). Patterns of misunderstanding: An integrative model for science, math, and programming. Review of Educational Research, 58, 303–326.CrossRefGoogle Scholar
  16. Shaughnessy, J.M. (1992). Research in probability and statistics: Reflections and directions. In D.A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 465–494). New York: Macmillan Publishing.Google Scholar
  17. Spieler, D. (2000). Encyclopedia of Psychology, 7, 12–14.Google Scholar
  18. Stavy, R. & Tirosh, D. (1996). Intuitive rules in science and mathematics: The case of ‘more of A–more of B.’ International Journal of Science Education, 18, 653–667.Google Scholar
  19. Stavy, R. & Tirosh, D. (2000). How students (mis-)understand science and mathematics: Intuitive rules. New York: Teachers College Press.Google Scholar
  20. Stavy, R., Babai, R., Tsamir, P., Tirosh, D., Lin, F.L. & McRobbie, C. (in press). Are intuitive rules universal? International Journal of Science and Mathematics Education.Google Scholar
  21. Tirosh, D. & Stavy, R. (1999). Intuitive rules: A way to explain and predict students’ reasoning. Educational Studies in Mathematics, 38, 51–66.CrossRefGoogle Scholar
  22. Tsamir, P., Tirosh, D. & Stavy, R. (1997). Intuitive rules and comparison tasks: The grasp of vertical angles. In G.A. Makrides (Ed.), Proceedings of the First Mediterranean Conference: Mathematics Education and Applications. Nicosia, Cyprus: Cyprus Pedagogical Institute and Cyprus Mathematical Society.Google Scholar
  23. Viennot, L. (1985). Analyzing students’ reasoning: Tendencies in interpretation. American Journal of Physics, 53, 432–436.CrossRefGoogle Scholar
  24. Vosniadou, S. & Ioannides, C. (1998). From conceptual development to science education: A psychological point of view. International Journal of Science Education, 20, 1213–1230.Google Scholar
  25. Vosniadou, S., Ioannides, C., Dimitrakopoulou, A. & Papademetriou, E. (2001). Designing learning environments to promote conceptual change in science. Learning and Instruction, 11, 381–420.CrossRefGoogle Scholar
  26. Wandersee, J.H., Mintzes, J.J. & Novak, J.D. (1994). Research on alternative conceptions in science. In D.L. Gabel (Ed.), Handbook of research on science teaching and learning (pp. 177–210). New York: Macmillan.Google Scholar
  27. Zazkis, R. (1999). Intuitive rules in number theory: Example of ‘the more of A, the more of B’ rule implementation. Educational Studies in Mathematics, 40, 197–209.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Reuven Babai
    • 1
  • Tali Brecher
    • 1
  • Ruth Stavy
    • 1
  • Dina Tirosh
    • 1
  1. 1.Department of Science Education, The Jaime and Joan Constantiner School of EducationTel Aviv UniversityTel AvivIsrael

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