Intuitive Rules: A way to Explain and Predict Students’ Reasoning



Through our work in mathematics and science education we have observed that students react similarly to a wide variety of conceptually unrelated situations. Our work suggests that many responses which the literature describes as alternative conceptions could be interpreted as evolving from common, intuitive rules. This paper describes and discusses one such rule, manifested when two systems are equal with respect to a certain quantity A but differ in another quantity B. We found that in such situations, students often argue that ‘Same amount of A implies same amount of B’. Our claim is that such responses are specific instances of the intuitive rule ‘Same A—same B’. This approach explains common sources for students’ conceptions and has strong predictive power.


Science Education Alternative Conception Comparison Task Proportional Reasoning Logical Scheme 
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.


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  1. Cough, E.E. and Driver, R.: 1986, ‘A study of consistency in the use of students’ conceptual frameworks across different task contexts’, Science Education 70 (4), 473–496.CrossRefGoogle Scholar
  2. Dembo, Y., Levin, I. and Siegler, R.S.: 1997, ‘A comparison of the geometric reasoning of students attending Israeli ultraorthodox and rain stream schools’, Developmental Psychology 33 (1), 92–103.CrossRefGoogle Scholar
  3. Erickson, G.L.: 1979, ‘Children’s conceptions of heat and temperature’, Science Education 63 (2), 221–230.CrossRefGoogle Scholar
  4. Fischbein, E.: 1987, Intuition in science and mathematics: An educational approach, D. Reidel, Dordrecht, The Netherlands.Google Scholar
  5. Fischbein, E. and Schnarch, D.: 1997, ‘The evolution with age of probabilistic, intuitively based misconceptions’, Journal for Research in Mathematics Education 28 (1), 96–105.CrossRefGoogle Scholar
  6. Hirstein, J.: 1981, ‘The second area assessment in mathematics: Area and volume’, Mathematics Teacher 74, 704–708.Google Scholar
  7. Hoffer, A.R. and Hoffer, S.A.K.: 1992, ‘Geometry and visual thinking’, in T.R. Post, (ed.), Teaching Mathematics in Grades K-8: Research-Based Methods ( 2nd ed. ), Allyn and Bacon, Boston.Google Scholar
  8. Linchevsky, L.: 1985, ‘The meaning attributed by elementary school teachers to terms they use in teaching mathematics and geometry’, Unpublished doctoral dissertation, Hebrew University, Jerusalem, Israel (in Hebrew).Google Scholar
  9. Livne, T.: 1996, ‘Examination of high school students’ difficulties in understanding the change in surface area, volume and surface area/ volume ratio with the change in size and/or shape of a body’, Unpublished Master’s thesis, Tel-Aviv University, Tel Aviv, Israel (in Hebrew).Google Scholar
  10. Meged, H.: 1978, ‘The development of the concept of density among children ages 6–16’. Unpublished Master’s thesis, Tel-Aviv University, Tel Aviv, Israel (in Hebrew).Google Scholar
  11. Noelting, G.: 1980a, ‘The development of proportional reasoning and the ratio concept: Part I–differentiation of stages’, Educational Studies in Mathematics 11, 217–253.CrossRefGoogle Scholar
  12. Noelting, G.: 1980b, ‘The development of proportional reasoning and the ratio concept: Part II - problem structure at successive stages: problem solving strategies and the mechanism of adaptive restructuring’, Educational Studies in Mathematics 11, 331–363.Google Scholar
  13. Noss, R.: 1987, ‘Children’s learning of geometrical concepts through LOGO’, Journal for Research in Mathematics Education 18 (3), 343–362.CrossRefGoogle Scholar
  14. Nunes, T., Schliemann, A.D. and Carraher, D.W.: 1993, Street Mathematics and School Mathematics, Cambridge University Press, Cambridge.Google Scholar
  15. Piaget, J. and Inhelder, B.: 1974, The Child’s Construction of Quantities, Routledge & K. Paul, London.Google Scholar
  16. Piaget, J.,Inhelder, B. and Szeminska, A.: 1960, The Child’s Conception of Geometry,Routledge & K. Paul, London.Google Scholar
  17. Rojhany, L.: 1997, ‘The use of the intuitive rule ‘The more of A, the more of B’: The case of comparison angles’, Unpublished Master’s thesis, Tel Aviv University, Tel Aviv, Israel (in Hebrew).Google Scholar
  18. Ronen, E.: 1996, ‘Overgeneralization of conservation’, Unpublished Master’s thesis, Tel Aviv University, Tel Aviv, Israel (in Hebrew).Google Scholar
  19. Schrage, G.L.: 1983, ‘(Mis-)interpretation of stochastic models’, in R. Scholz (ed.), Decision Making Under Uncertainty, North-Holland, Amsterdam, pp. 351–361.Google Scholar
  20. Shultz, T., Dover, A. and Amsel, E.: 1979, ‘The logical and empirical bases of conservation judgments’, Cognition 7, 99–123.CrossRefGoogle Scholar
  21. Stavy, R. and Berkovitz, B.: 1980, ‘Cognitive conflict as a basis for teaching quantitative aspects of the concept of temperature’, Science Education 64, 679–692.CrossRefGoogle Scholar
  22. Stavy, R., Strauss, S., Orpaz, N. and Carmi, C.: 1982, ‘U-shaped behavioral growth in ratio comparisons, or that’s funny I would not have thought you were u-ish’, in S. Strauss with R. Stavy (eds.), U-Shaped Behavioral Growth, Academic Press, New York, pp. 11–36.Google Scholar
  23. Stavy, R. and Tirosh, D.: 1996, ‘Intuitive rules in mathematics and science: The case of ’The more of A — the more of B’, International Journal of Science Education 18 (6), 653–667.CrossRefGoogle Scholar
  24. Strauss, S. and Stavy, R.: 1982, ‘U-shaped behavioral growth: ’Implications for theories of development, in W.W. Hartup (ed.), Review of Child Development Research, University of Chicago Press, Chicago, pp. 547–599.Google Scholar
  25. Tirosh, D.: ‘Inconsistencies in students’ mathematical constructs’ Focus on Learning Problems in Mathematics 12(1), 111–129. Google Scholar
  26. Tirosh, D. and Stavy, R.: 1996, ‘Intuitive rules in science and mathematics: The case of ‘Everything can be divided by two’,’ International Journal of Science Education 18 (6), 669–683.CrossRefGoogle Scholar
  27. Tversky, A. and Kahneman, D.: 1983, ‘Extensional versus intuitive reasoning: ’The conjunction fallacy in probability judgment, Psychological Review 90, 293–315.Google Scholar
  28. Walter, N.: 1970, ‘A common misconception about area’, Arithmetic Teacher 17, 286–289.Google Scholar
  29. Wiser, M. and Carey, S.: 1983, ‘When heat and temperature were one’, in D. Gentner and A.L. Stevens (eds.), Mental Models,Lawrence Erlbaum, Hillsdale, New Jersey, pp. 267–296.Google Scholar
  30. Woodward, E. and Byrd, F.: 1983, ‘Area: Included topic, neglected concept’ School Science and Mathematics 83, 343–347.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1999

Authors and Affiliations

  1. 1.School of EducationTel Aviv UniversityTel AvivIsrael

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