Educational Studies in Mathematics

, Volume 15, Issue 1, pp 1–24 | Cite as

Does the teaching of probability improve probabilistic intuitions?

An exploratory research study
  • E. Fischbein
  • A. Gazit


The paper analyzes the effects of a teaching programme in probability devised for junior high school pupils (grades 5, 6 and 7). It was found that most of the notions were too difficult for the fifth grade pupils. In contrast, about 60–70% of the sixth graders and about 80–90% of the seventh graders were able to understand and use correctly most of the concepts contained in the programme. It was also found that, as an indirect effect the course on probability had a beneficial effect on some intuitively based misconceptions of the subjects, like: the “representiveness” effect; the positive recency effect; the notion of “a lucky choice”; the superstitious belief in the possibility of influencing the course of events by some particular behaviour.


High School Beneficial Effect Indirect Effect Teaching Programme Recency Effect 
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. Falk, R., Falk, R., and Levin, J.: 1980, ‘A potential for learning probability of young children’, Educational Studies in Mathematics 11, 181–204.Google Scholar
  2. Feller, W.: 1968, An Introduction To Probability Theory and its Applications, John Wiley, New York.Google Scholar
  3. Fischbein, E.: 1975, The Intuitive Sources of Probabilistic Thinking in Children, D. Reidel, Dordrecht.Google Scholar
  4. Goldberg, E.: 1966, ‘Probability judgements by pre-school children: task conditions and performance’, Child Development 37, 157–167.Google Scholar
  5. Hart, K. M. (ed.): 1981, Children's Understanding of Mathematics, John Murray, London.Google Scholar
  6. Kahneman, D. and Tversky, A.: 1972, ‘Subjective probability: a judgement of representativeness’, Cognitive Psychology 3, 430–454.Google Scholar
  7. Karplus, R. and Karplus, E.: 1971, Proportional reasoning and control of variables, Division for Study and Research in Education, Cambridge, Mass.Google Scholar
  8. Lecoutre, M. E.: 1981, ‘Etudes des représentations probabilistes: Formation en théorie des probabilite; pratique des jeux du hasard’, Technical Report, Groupe Mathematique et Psychologie, Paris.Google Scholar
  9. Ojemann, R. H., Maxey, E. J., And Snider, B. C.: 9165, ‘Effects of guided learning experiences in developing probability concepts at the fifth grade level’, Perceptual and Moto Skills 21, 415–427.Google Scholar
  10. Piaget, J. and Inhelder, B.: 1951, La Genese de L'Idée de Hasard chez l'Enfant. P.U.F., Paris.Google Scholar
  11. Tversky, A. and Kahneman, D.: 1973, ‘Availability: a heuristic for judging frequency and probability’, Cognitive Psychology 5, 207–232.Google Scholar
  12. Yost, P., Siegel, A. E., and Andrews, J. N.: 1962, ‘Non-verbal probability judgement by young children’, Child Development 33, 768–780.Google Scholar

Copyright information

© D. Reidel Publishing Company 1984

Authors and Affiliations

  • E. Fischbein
    • 1
  • A. Gazit
    • 1
  1. 1.School of EducationTel Aviv UniversityTel AvivIsrael

Personalised recommendations