Instructional Science

, Volume 12, Issue 1, pp 67–82 | Cite as

A curriculum to improve thinking under uncertainty

  • Ruth Beyth-Marom
  • Shlomit Dekel


Recent evidence indicates that people's intuitive judgments are sometimes affected by systematic biases that can lead to bad decisions. Much of the value of this research depends on its applicability, i.e., showing people when and how their judgments are wrong and how they can be improved. This article describes one step toward that goal, i.e., the development of a curriculum for junior high school students aimed at improving thought processes, specifically, those necessary in uncertain situations (probabilistic thinking). The relevant psychological literature is summarized and the main guidelines in the curriculum development are specified: (a) encouraging students to introspect and examine their own (and others') thought processes consciously, (b) indicating the circumstances in which common modes of thinking may cause fallacies, and (c) providing better tools for coping with the problems that emerge. Two detailed examples are given. In addition, the problem of training teachers is briefly discussed and a small-scale evaluation effort is described.


High School Student Systematic Bias Training Teacher Good Tool Common Mode 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Armstrong, J. S., Denniston, W. B. and Gordon, M. M. (1975). “The use of the decomposition principle in making judgments,” Organizational Behavior and Human Performance 14: 257–263.Google Scholar
  2. Bar-Hillel, M. (1980). “The base-rate fallacy in probability judgments,” Acta Psychologica 44: 211–233.Google Scholar
  3. Brown, J. S. and Burton, R. R. (1978). “Diagnostic models for procedural bugs in basic mathematical skills,” Cognitive Science 2: 155–192.Google Scholar
  4. Bruner, J. S., Goodnow, J. J. and Austin, G. A. (1956). A Study of Thinking. New York: Wiley.Google Scholar
  5. Caramazza, A., McCloskey, M. and Green, B. (1981). “Naive beliefs in ‘sophisticated’ subjects: Misconceptions about trajectories of objects,” Cognition 9: 117–123.Google Scholar
  6. Champagne, A. B., Klopfer, L. E., Solomon, C. A. and Cahn, A. D. (1980). Interactions of students' knowledge with their comprehension and design of science experiments. A LRDS Report, University of Pittsburgh.Google Scholar
  7. Chapman, L. J. and Chapman, J. P. (1969). “Illusory correlation as an obstacle to the use of valid psychodiagnostic signs,” Journal of Abnormal Psychology 74: 271–280.Google Scholar
  8. Dowie, J. (1980). U201 Risk: Course Handbook. Milton Keynes: Open University Press.Google Scholar
  9. Falk, R., Falk, R. and Levin, I. (1980). “A potential for learning probability in young children,” Educational Studies in Mathematics 11.Google Scholar
  10. Fama, E. F. (1965). “Random walks in stock market prices,” Financial Analysts Journal 21: 55–60.Google Scholar
  11. Feuerstein, R., Rand, Y., Hoffman, M. D. and Miller, R. (1980). Instrumental Enrichment. Baltimore: University Park Press.Google Scholar
  12. Fischbein, E. (1975). The Intuitive Sources of Probabilistic Thinking in Children. New York: D. Reidel.Google Scholar
  13. Fischhoff, B. (1982). “Debiasing,” in D.Kahneman, P.Slovic and A.Tversky (eds.) Judgment under Uncertainty: Heuristics and Biases. New York: Cambridge University Press.Google Scholar
  14. Fischhoff, B. and Bar-Hillel, M. (1982). “Focusing techniques as aids to inference,” Decision Research Report 82-4.Google Scholar
  15. Fischhoff, B., Slovic, P. and Lichtenstein, S. (1979). “Subjective sensitivity analysis”, Organizational Behavior and Human Performance 23: 339–359.Google Scholar
  16. Fischhoff, B., Slovic, P. and Lichtenstein, S. (1981). “Lay foibles and expert fables in judgments about risk,” in T.O'Riordan and R. K.Turner (eds.), Progress in Resource Management and Environmental Planning, Vol 3. Chichester: Wiley.Google Scholar
  17. Fletcher, G. H. and Wooddell, G. (1981). “Educating for a changing world,” The Journal of Thought 16 (3).Google Scholar
  18. Fong, G. T., Krantz, D. H. and Nisbett, R. E. (1982). “Improving Inference Through Statistical Training,” paper presented at the meeting of the American Psychological Association, Washington, D. C., August 1982.Google Scholar
  19. Furby, L. (1973). “Interpreting regression toward the mean in developmental research,” Developmental Psychology 8: 172–179.Google Scholar
  20. Goodlad, J. I. (1973). “A concept of the school in 200 A.D.,” in R. W.Holstrop (ed.), Foundations of Futurology in Education. Homewood, Illinois: ETC Publications.Google Scholar
  21. Hayes, J. R. (1981). The Complete Problem Solver. Philadelphia: The Franklin Institute Press.Google Scholar
  22. Johnson-Laird, P. N. and Wason, P. C. (eds.) (1977). Thinking. New York: Cambridge University Press.Google Scholar
  23. Kahneman, D. and Tversky, A. (1972). “Subjective probability: A judgment of representativeness,” Cognitive Psychology 3: 430–454.Google Scholar
  24. Kahneman, D. and Tversky, A. (1973). “On the psychology of prediction,” Psychological Review 80: 237–251.Google Scholar
  25. Kahneman, D. and Tversky, A. (1979). “Intuitive predictions: Biases and corrective procedures,” TIMS Studies in Management Science 12: 313–327.Google Scholar
  26. Kahneman, D., Slovic, P. and Tversky, A. (eds.) (1982). Judgment under Uncertainty: Heuristics and Biases. New York: Cambridge University Press.Google Scholar
  27. Knight, F. H. (1921). Risk, Uncertainty, and Profit. Boston and New York: Houghton-Miflin.Google Scholar
  28. Lefrere, P., Dowie, J. and Whalley, P. (1980). “Educating for justified uncertainty,” in R.Winterburn and L.Evans (eds.) Aspects of Educational Technology 14. London: Kogan Page.Google Scholar
  29. Lichtenstein, S., Slovic, P., Fischhoff, B., Layman, M. and Combs, B. (1978). “Judged frequency of lethal events,” Journal of Experimental Psychology: Human Learning and Memory 4: 551–578.Google Scholar
  30. Lipman, M. Philosophy for Children. Unpublished manuscript, undated, Montclair State College, p. 9.Google Scholar
  31. McCloskey, M., Caramazza, A. and Green, B. (1980). “Curvilinear motion in the absence of external forces: Naive beliefs about the motion of objects,” Science 210: 1139–1141.Google Scholar
  32. Michael, D. (1968). The Unprepared Society: Planning for a Precarious Future. New York: Basic Books.Google Scholar
  33. Miller, G. A. (1965). “The magical number seven, plus or minus two: Some limits on our capacity for processing information,” Psychological Review 63: 81–97.Google Scholar
  34. Newell, A. and Simon, H. A. (1972). Human Problem Solving. Englewood Cliffs, N.J.: Prentice-Hall.Google Scholar
  35. Sieber, T., Epstein, M. and Petty, C. (1970). “The effectiveness of modelling and concept-learning procedures in teaching children to indicate uncertainty,” The Irish Journal of Education 4 (2): 90–106.Google Scholar
  36. Sieber, J., Clark, R. E., Smith, H. M. and Sanders, N. (1976). “The effects of learning to be uncertain on children's knowledge and use of drugs,” R & D Memo 144, Stanford Center for Research and Development in Teaching.Google Scholar
  37. Seif, E. (1981). “Thinking and education: A futures approach.” The Journal of Thought 16 (3).Google Scholar
  38. Slovic, P., Fischhoff, B. and Lichtenstein, S. (1977). “Behavioral decision theory,” Annual Review of Psychology 28: 207–232.Google Scholar
  39. Tversky, A. and Kahneman, D. (1971). “The belief in the ‘law of small numbers,” Psychological Bulletin 76: 105–110.Google Scholar
  40. Tversky, A. and Kahneman, D. (1973). “Availability: A heuristic for judging frequency and probability,” Cognitive Psychology 4: 207–232.Google Scholar
  41. Tversky, A. and Kahneman, D. (1974). “Judgment under uncertainty: Heuristics and biases” Science 185: 1124–1131.Google Scholar
  42. Underwood, B. J. (1969). “Attributes of memory,” Psychological Review 76: 559–573.Google Scholar
  43. Vye, N. J. and Bransford, J. D. (1981). “Programs for teaching thinking,” Educational Leadership (October) pp. 26–28.Google Scholar
  44. Wason, P. C. and Johnson-Laird, P. N. (1972). Psychology of reasoning: Structure and Content. London: Batsford.Google Scholar
  45. Whimbey, A. and Lochhead, J. (1980). Problem Solving and Comprehension: A Short Course in Analytical Reasoning. Philadelphia: The Franklin Institute Press.Google Scholar
  46. Young, R. M. and O'Shea, T. (1981). “Errors in children's subtractions,” Cognitive Science 5: 153–177.Google Scholar

Copyright information

© Elsevier Science Publishers B.V 1983

Authors and Affiliations

  • Ruth Beyth-Marom
    • 1
  • Shlomit Dekel
    • 2
  1. 1.Decision ResearchA Branch of Perceptronics, Inc.EugeneU.S.A.
  2. 2.School of EducationThe Hebrew UniversityJerusalemIsrael

Personalised recommendations