, Volume 42, Issue 6, pp 621–633 | Cite as

Overcoming intuitive interference in mathematics: insights from behavioral, brain imaging and intervention studies

  • Ruth Stavy
  • Reuven BabaiEmail author
Original Article


It is well known that many students encounter difficulties when solving problems in mathematics. Research indicates that some of these difficulties may stem from intuitive interference with formal/logical reasoning. Our research aims at deepening the understanding of these difficulties and their underlying reasoning mechanisms to help students overcome them. For this purpose we carried out behavioral, brain imaging and intervention studies focusing on a previously demonstrated obstacle in mathematics education. The literature reports that many students believe that shapes with a larger area must have a larger perimeter. We measured the accuracy of responses, reaction time, and neural correlates (by fMRI) while participants compared the perimeters of geometrical shapes in two conditions: (1) congruent, in which correct response was in line with intuitive reasoning (larger arealarger perimeter) and (2) incongruent, in which the correct answer was counterintuitive. In the incongruent condition, accuracy dropped and reaction time for correct responses was longer than in the congruent condition. The congruent condition activated bilateral parietal brain areas, known to be involved in the comparison of quantities, while correctly answering the incongruent condition activated bilateral prefrontal areas known for their executive control over other brain regions. The intervention, during which students’ attention was drawn to the relevant variable, increased accuracy in the incongruent condition, while reaction times increased in both congruent and incongruent conditions. The findings of the three studies point to the importance of control mechanisms in overcoming intuitive interference in mathematics. Overall, it appears that adding a cognitive neuroscience perspective to mathematics education research can contribute to a better understanding of students’ difficulties and reasoning processes. Such information is important for educational research and practice.


Brain imaging Control mechanisms Intuitive interference Intuitive reasoning Geometry 


  1. Aron, A. R., Robbins, T. W., & Poldrack, R. A. (2004). Inhibition and the right inferior frontal cortex. Trends in Cognitive Sciences, 8, 170–177.CrossRefGoogle Scholar
  2. Babai, R. (2010). Piagetian cognitive level and the tendency to use intuitive rules when solving comparison tasks. International Journal of Science and Mathematics Education, 8, 203–221.CrossRefGoogle Scholar
  3. Babai, R., & Amsterdamer, A. (2008). The persistence of solid and liquid naive conceptions: A reaction time study. Journal of Science Education and Technology, 17, 553–559.CrossRefGoogle Scholar
  4. Babai, R., Brecher, T., Stavy, R., & Tirosh, D. (2006a). Intuitive interference in probabilistic reasoning. International Journal of Science and Mathematics Education, 4, 627–639.CrossRefGoogle Scholar
  5. Babai, R., Levyadun, T., Stavy, R., & Tirosh, D. (2006b). Intuitive rules in science and mathematics: A reaction time study. International Journal of Mathematical Education in Science and Technology, 37, 913–924.CrossRefGoogle Scholar
  6. Babai, R., Sekal, R., & Stavy, R. (2010a). Persistence of the intuitive conception of living things in adolescence. Journal of Science Education and Technology, 19, 20–26.CrossRefGoogle Scholar
  7. Babai, R., Zilber, H., Stavy, R., & Tirosh, D. (2010b). The effect of intervention on accuracy of students’ responses and reaction times to geometry problems. International Journal of Science and Mathematics Education, 8, 185–201.CrossRefGoogle Scholar
  8. Deliyianni, E., Michael, E., & Pitta-Pantazi, D. (2006). The effect of different teaching tools in overcoming the impact of the intuitive rules. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings 30th conference of the international group for the psychology of mathematics education (Vol. 2, pp. 409–416). Prague: PME.Google Scholar
  9. 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, 92–103.CrossRefGoogle Scholar
  10. Dempster, F. N., & Corkill, A. J. (1999). Interference and inhibition in cognition and behavior: Unifying themes for educational psychology. Educational Psychology Review, 11, 1–88.CrossRefGoogle Scholar
  11. Denes, G., & Pizzamiglio, L. (1999). Handbook of clinical and experimental neuropsychology (pp. 28–30). Hove, UK: Psychology Press.Google Scholar
  12. Faw, B. (2003). Pre-frontal executive committee for perception, working memory, attention, long-term memory, motion control, and thinking: A tutorial review. Consciousness and Cognition, 12, 83–139.CrossRefGoogle Scholar
  13. Fias, W., Lammertyn, J., Reynvoet, B., Dupont, P., & Orban, G. A. (2003). Parietal representation of symbolic and nonsymbolic magnitude. Journal of Cognitive Neuroscience, 15, 47–56.CrossRefGoogle Scholar
  14. Gillard, E., Van Dooren, W., Schaeken, W., & Verschaffel, L. (2009). Dual-processes in the psychology of mathematics education and cognitive psychology. Human Development, 52, 95–108.CrossRefGoogle Scholar
  15. Goel, V., Makale, M., & Grafman, J. (2004). The hippocampal system mediates logical reasoning about familiar spatial environments. Journal of Cognitive Neuroscience, 16, 654–664.CrossRefGoogle Scholar
  16. Henik, A., & Tzelgov, J. (1982). Is three greater than five: The relation between physical and semantic size in comparison tasks. Memory and Cognition, 10, 389–395.CrossRefGoogle Scholar
  17. Hoffer, A. R., & Hoffer, S. A. K. (1992). Geometry and visual thinking. In R. Post (Ed.), Teaching mathematics in grades K-8: Research-based methods (2nd ed.). Boston: Allyn and Bacon.Google Scholar
  18. Houde, O., & Guichart, E. (2001). Negative priming effect after inhibition of number/length interference in a Piaget-like task. Developmental Science, 4, 119–123.CrossRefGoogle Scholar
  19. Houde, O., Zago, L., Mellet, E., Moutier, S., Pineau, A., Mazoyer, B., et al. (2000). Shifting from the perceptual brain to the logical brain: The neural impact of cognitive inhibition training. Journal of Cognitive Neuroscience, 12, 721–728.CrossRefGoogle Scholar
  20. Konishi, S., Nakajima, K., Uchida, I., Kikyo, H., Kameyama, M., & Miyashita, Y. (1999). Common inhibitory mechanism in human inferior prefrontal cortex revealed by event-related functional MRI. Brain, 122, 981–991.CrossRefGoogle Scholar
  21. Lavie, N. (2005). Distracted and confused?: Selective attention under load. Trends in Cognitive Sciences, 9, 75–82.CrossRefGoogle Scholar
  22. Lavie, N., Hirst, A., de Fockert, J. W., & Viding, E. (2004). Load theory of selective attention and cognitive control. Journal of Experimental Psychology: General, 133, 339–354.CrossRefGoogle Scholar
  23. Moutier, S., Angeard, N., & Houde, O. (2002). Deductive reasoning and matching-bias inhibition training: Evidence from a debiasing paradigm. Thinking and Reasoning, 8, 205–224.CrossRefGoogle Scholar
  24. Moutier, S., & Houde, O. (2003). Judgement under uncertainty and conjunction fallacy inhibition training. Thinking and Reasoning, 9, 185–201.CrossRefGoogle Scholar
  25. Pinel, P., Piazza, M., Le Bihan, D., & Dehaene, S. (2004). Distributed and overlapping cerebral representations of number, size, and luminance during comparative judgments. Neuron, 41, 983–993.CrossRefGoogle Scholar
  26. Rogers, R. D., Owen, A. M., Middleton, H. C., Williams, E. J., Pickard, J. D., Sahakian, B. J., et al. (1999). Choosing between small, likely rewards and large, unlikely rewards activates inferior and orbital prefrontal cortex. The Journal of Neuroscience, 20, 9029–9038.Google Scholar
  27. Schoenfeld, A. H. (1985). Mathematical problem solving. New York: Academic Press.Google Scholar
  28. Shultz, T., Dover, A., & Amsel, E. (1979). The logical and empirical bases of conservation judgments. Cognition, 7, 99–123.CrossRefGoogle Scholar
  29. Stavy, R., & Babai, R. (2008). Complexity of shapes and quantitative reasoning in geometry. Mind, Brain, and Education, 2, 170–176.CrossRefGoogle Scholar
  30. Stavy, R., Babai, R., Tsamir, P., Tirosh, D., Lin, F., & McRobbie, C. (2006a). Are intuitive rules universal? International Journal of Science and Mathematics Education, 4, 417–436.CrossRefGoogle Scholar
  31. Stavy, R., Goel, V., Critchley, H., & Dolan, R. (2006b). Intuitive interference in quantitative reasoning. Brain Research, 1073–1074, 383–388.CrossRefGoogle Scholar
  32. 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.CrossRefGoogle Scholar
  33. Stavy, R., & Tirosh, D. (2000). How students (mis-)understand science and mathematics. New York: Teachers College Press.Google Scholar
  34. Stroop, R. J. (1935). Studies of interference in serial verbal reactions. Journal of Experimental Psychology, 18, 643–662.CrossRefGoogle Scholar
  35. Tang, J., Critchley, H. D., Glaser, D. E., Dolan, R. J., & Butterworth, B. (2006). Imaging informational conflict: A functional magnetic resonance imaging study of numerical Stroop. Journal of Cognitive Neuroscience, 18, 2049–2062.CrossRefGoogle Scholar
  36. Tirosh, D., & Stavy, R. (1999). Intuitive rules and comparison tasks. Mathematical Thinking and Learning, 1, 179–194.CrossRefGoogle Scholar
  37. Walter, N. (1970). A common misconception about area. Arithmetic Teacher, 17, 286–289.Google Scholar
  38. Woodward, E., & Byrd, F. (1983). Area: Included topic, neglected concept. School Science and Mathematics, 83, 343–347.CrossRefGoogle Scholar
  39. 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

© FIZ Karlsruhe 2010

Authors and Affiliations

  1. 1.Department of Science Education, The Constantiner School of EducationTel Aviv UniversityTel AvivIsrael

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