Psychonomic Bulletin & Review

, Volume 15, Issue 6, pp 1174–1178 | Cite as

The use of heuristics in intuitive mathematical judgment

  • Rolf Reber
  • Morten Brun
  • Karoline Mitterndorfer
Brief Reports


Anecdotal evidence points to the use of beauty as an indication of truth in mathematical problem solving. In the two experiments of the present study, we examined the use of heuristics and tested the assumption that participants use symmetry as a cue for correctness in an arithmetic verification task. We manipulated the symmetry of sets of dot pattern addition equations. Speeded decisions about the correctness of these equations led to higher endorsements for both correct and incorrect equations when the addend and sum dot patterns were symmetrical. Therefore, this effect is not due to the fact that symmetry facilitates calculation or estimation. We found systematic evidence for the use of heuristics in solving mathematical tasks, and we discuss how these findings relate to a processing-fluency account of intuition in mathematical judgment.


Correct Rejection Symmetric Pattern Intuitive Judgment Asymmetric Pattern Processing Fluency 
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  1. Alter, A. L., & Oppenheimer, D. M. (2006). Predicting short-term stock fluctuations by using processing fluency. Proceedings of the National Academy of Sciences, 103, 9369–9372.CrossRefGoogle Scholar
  2. Ben-Zeev, T. (1996). When erroneous mathematical thinking is just as “correct”: The oxymoron of rational errors. In R. J. Sternberg & T. Ben-Zeev (Eds.), The nature of mathematical thinking (pp. 55–79). Mahwah, NJ: Erlbaum.Google Scholar
  3. Bolte, A., & Goschke, T. (2005). On the speed of intuition: Intuitive judgments of semantic coherence under different response deadlines. Memory & Cognition, 33, 1248–1255.CrossRefGoogle Scholar
  4. Bowers, K. S., Regehr, G., Balthazard, C., & Parker, K. (1990). Intuition in the context of discovery. Cognitive Psychology, 22, 72–110.CrossRefGoogle Scholar
  5. Campbell, J. I. D. (Ed.) (2005). Handbook of mathematical cognition. New York: Psychology Press.Google Scholar
  6. Campbell, J. I. D., & Austin, S. (2003). Effects of response time deadlines on adults’ strategy choices for simple addition. Memory & Cognition, 30, 988–994.CrossRefGoogle Scholar
  7. Chandrasekhar, S. (1987). Truth and beauty: Aesthetics and motivations in science. Chicago: University of Chicago Press.Google Scholar
  8. Cole, K. C. (1998). The universe in a teacup: The mathematics of truth and beauty. New York: Harcourt, Brace.Google Scholar
  9. Dehaene, S. (1997). The number sense: How the mind creates mathematics. New York: Oxford University Press.Google Scholar
  10. Draine, S. C., & Greenwald, A. G. (1998). Replicable unconscious semantic priming. Journal of Experimental Psychology: General, 127, 286–303.CrossRefGoogle Scholar
  11. Gangestad, S. W., Thornhill, R., & Yeo, R. A. (1994). Facial attractiveness, developmental stability, and fluctuating asymmetry. Ethology & Sociobiology, 15, 73–85.CrossRefGoogle Scholar
  12. Garner, W. R. (1974). The processing of information and structure. Potomac, MD: Erlbaum.Google Scholar
  13. Gilovich, T., Griffin, D., & Kahneman, D. (Eds.) (2002). Heuristics and biases: The psychology of intuitive judgment. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  14. Greenwald, A. G., Draine, S. C., & Abrams, R. L. (1996). Three cognitive markers of unconscious semantic activation. Science, 273, 1699–1702.CrossRefPubMedGoogle Scholar
  15. Hadamard, J. (1954). The psychology of invention in the mathematical Field. Princeton, NJ: Princeton University Press.Google Scholar
  16. Jacoby, L. L., & Dallas, M. (1981). On the relationship between autobiographical memory and perceptual learning. Journal of Experimental Psychology: General, 110, 306–340.CrossRefGoogle Scholar
  17. Kalick, S. M., Zebrowitz, L. A., Langlois, J. H., & Johnson, R. M. (1998). Does human facial attractiveness honestly advertise health? Longitudinal data on an evolutionary question. Psychological Science, 9, 8–13.CrossRefGoogle Scholar
  18. Lee, A. Y., & Labroo, A. A. (2004). The effect of conceptual and perceptual fluency on brand evaluation. Journal of Marketing Research, 41, 151–165.CrossRefGoogle Scholar
  19. McColm, G. (2007). A metaphor for mathematics education. Notices of the American Mathematical Society, 54, 499–502.Google Scholar
  20. McGlone, M. S., & Tofighbakhsh, J. (2000). Birds of a feather flock conjointly (?): Rhyme as reason in aphorisms. Psychological Science, 11, 424–428.CrossRefPubMedGoogle Scholar
  21. Palmer, S. E. (1991). Goodness, Gestalt, groups, and Garner: Local symmetry subgroups as a theory of figural goodness. In G. R. Lockhead & J. R. Pomerantz (Eds.), The perception of structure (pp. 23–39). Washington, DC: American Psychological Association.Google Scholar
  22. Parks, C. M., & Toth, J. P. (2006). Fluency, familiarity, aging, and the illusion of truth. Aging, Neuropsychology, & Cognition, 13, 225–253.CrossRefGoogle Scholar
  23. Posner, M. I., & Keele, S. W. (1968). On the genesis of abstract ideas. Journal of Experimental Psychology, 77, 353–363.CrossRefPubMedGoogle Scholar
  24. Reber, A. S. (1967). Implicit learning of artificial grammars. Journal of Verbal Learning & Verbal Behavior, 6, 855–863.CrossRefGoogle Scholar
  25. Reber, R. (2002). Reasons for the preference for symmetry. Behavioral & Brain Sciences, 25, 415–416.CrossRefGoogle Scholar
  26. Reber, R., & Schwarz, N. (1999). Effects of perceptual fluency on judgments of truth. Consciousness & Cognition, 8, 338–342.CrossRefGoogle Scholar
  27. Reber, R., Schwarz, N., & Winkielman, P. (2004). Processing fluency and aesthetic pleasure: Is beauty in the perceiver’s processing experience? Personality & Social Psychology Review, 8, 364–382.CrossRefGoogle Scholar
  28. Reber, R., Winkielman, P., & Schwarz, N. (1998). Effects of perceptual fluency on affective judgments. Psychological Science, 9, 45–48.CrossRefGoogle Scholar
  29. Rhodes, G., Proffitt, F., Grady, J. M., & Sumich, A. (1998). Facial symmetry and the perception of beauty. Psychonomic Bulletin & Review, 5, 659–669.CrossRefGoogle Scholar
  30. Royer, F. (1981). Detection of symmetry. Journal of Experimental Psychology: Human Perception & Performance, 7, 1186–1210.Google Scholar
  31. Silver, E. A. (1986). Using conceptual and procedural knowledge: A focus on relationships. In J. Hiebert (Ed.), Conceptual and procedural knowledge (pp. 181–198). Hillsdale, NJ: Erlbaum.Google Scholar
  32. Stewart, I. (2007). Why beauty is truth: The history of symmetry. New York: Basic Books.Google Scholar
  33. Topolinski, S., & Strack, F. (in press). The analysis of intuition: Processing fluency and affect in judgments of semantic coherence. Cognition & Emotion.Google Scholar
  34. Unkelbach, C. (2007). Reversing the truth effect: Learning the interpretation of processing fluency in judgments of truth. Journal of Experimental Psychology: Learning, Memory, & Cognition, 33, 219–230.Google Scholar
  35. VanLehn, K. (1986). Arithmetic procedures are induced from examples. In J. Hiebert (Ed.), Conceptual and procedural knowledge (pp. 133–179). Hillsdale, NJ: Erlbaum.Google Scholar
  36. Whittlesea, B. W. A. (1993). Illusions of familiarity. Journal of Experimental Psychology: Learning, Memory, & Cognition, 19, 1235–1253.Google Scholar
  37. Winkielman, P., Halberstadt, J., Fazendeiro, T., & Catty, S. (2006). Prototypes are attractive because they are easy on the mind. Psychological Science, 17, 799–806.CrossRefPubMedGoogle Scholar

Copyright information

© Psychonomic Society, Inc. 2008

Authors and Affiliations

  • Rolf Reber
    • 1
  • Morten Brun
    • 1
  • Karoline Mitterndorfer
    • 1
  1. 1.Department of Biological and Medical Psychology, Cognitive Neuroscience GroupUniversity of BergenBergenNorway

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