Formal Reasoning: A Reappraisal

  • E. A. Lunzer
Part of the Topics in Cognitive Development book series (TOPCOGDEV, volume 2)


A Backward Look In a paper that appeared over 10 years ago (Lunzer, 1965), this author spoke of a

desire to arrive at a clearer understanding of the kinds of advances in reasoning that appear as the child approaches adolescence. Are these advances sufficiently homogeneous and distinctive to warrant the use of the general term “formal reasoning” in opposition to the term “concrete reasoning” to characterize the achievements belonging to the years between six and nine? (p. 19)


Correct Solution Logical Thinking Logical Inference Formal Reasoning True Sentence 
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. Bartlett, F. C. Thinking: An experimental and social study. London: Allen and Unwin, 1958.Google Scholar
  2. Brown, R. Psycholinguistics: Selected papers. New York: Free Press, 1970.Google Scholar
  3. Calvert, W. M. A short-term longitudinal study: The development of classificatory behaviour in children at the pre-operational and concrete operational stages. M.Ed. thesis, University of Birmingham, 1971.Google Scholar
  4. Campbell, R. N., & Young, B. M. Some aspects of classificatory behaviour in pre-school children. Paper read to the Annual Congress of the British Psychological Society, Education Section, September 1968.Google Scholar
  5. Chapman, L. J., & Chapman, J. P. Atmosphere effect re-examined. Journal of Experimental Psychology, 1959, 58, 220–226.PubMedCrossRefGoogle Scholar
  6. Collis, K. A study of concrete and formal operations in school mathematics. Ph.D. thesis, University of Newcastle, New South Wales, 1972.Google Scholar
  7. Covington, M. V. The cognitive curriculum: A process-oriented approach to education. In J. Hellmuth (Ed.), Cognitive studies, Vol. 1. New York: Branner/Mazel, 1970, 491–502.Google Scholar
  8. Dienes, Z. P. Six stages in the process of learning mathematics. Unpublished monograph, 1972.Google Scholar
  9. Halford, G. S. An investigation of concept learning. Ph.D. thesis, University of Newcastle, New South Wales, 1968.Google Scholar
  10. Herriot, P. An introduction to the psychology of language. London: Methuen, 1970.Google Scholar
  11. Hill, R., Kapadia, R., Dadds, M., Lunzer, E. A., & Armitage, V. The child’s conception of the structure of numbers. Interim report to the Social Sciences Research Council (unpublished manuscript), 1973.Google Scholar
  12. Inhelder, B., & Piaget, J. The growth of logical thinking. New York: Basic Books, 1958.Google Scholar
  13. Inhelder, B., & Piaget, J. The early growth of logic in the child. London: Routledge, 1964.Google Scholar
  14. Jackson, S. The growth of logical thinking in normal and subnormal children. British Journal of Educational Psychology, 1965, 35, 255–258.PubMedCrossRefGoogle Scholar
  15. Jensen, A. R. Hierarchical theories of mental ability. In W. B. Dockrell (Ed.), On intelligence. London: Methuen, 1970.Google Scholar
  16. Karplus, E. F., & Karplus, R. Intellectual development beyond elementary school, I: Deductive logic. School Science and Mathematics, 1970, 70, 398–406.CrossRefGoogle Scholar
  17. Karplus, R., & Peterson, R. W. Intellectual development beyond elementary school, II: Ratio, a survey. School Science and Mathematics, 1970, 70, 813–820.CrossRefGoogle Scholar
  18. Keats, J. A. Formal and concrete thought processes. Educational Testing Service Research Bull. No. 17, Princeton, 1955.Google Scholar
  19. Lovell, K. A follow-up study of Inhelder and Piaget’s The growth of logical thinking. British Journal of Psychology, 1961, 52, 143–153.Google Scholar
  20. Lunzer, E. A. Problems of formal reasoning in test situations. In P. H. Mussen (Ed.), European research in cognitive development. Monographs of the Society for Research in Child Development, 1965, 30 (2, Whole No. 100), 19–46.Google Scholar
  21. Lunzer, E. A. Formal reasoning. In E. A. Lunzer and J. F. Morris (Eds.), Development in human learning. New York: American Elsevier, 1968.Google Scholar
  22. Lunzer, E. A. On children’s thinking(University of Nottingham, Inaugural lecture). London: National Foundation for Educational Research, 1970.Google Scholar
  23. Lunzer, E. A. The development of formal reasoning: Some recent experiments and their implications. In K. Frey and M. Lang (Eds.), Cognitive processes and science instruction. Baltimore: Williams and Wilkins, 1973.Google Scholar
  24. Lunzer, E. A., Harrison, C., & Davey, M. The four-card problem and the generality of formal reasoning. Quarterly Journal of Experimental Psychology, 1972, 24, 326–339.CrossRefGoogle Scholar
  25. Lunzer, E. A., & Pumfrey, P. D. Understanding proportionality. Mathematics Teaching, 1966, 34, 7–12.Google Scholar
  26. Matalon, A. Etude günütique de l’implication. In E. W. Beth, J. B. Grize, R. Martin, B. Matalon, A. Naess, and J. Piaget (Eds.), Implication, formalisation et logique naturelle. Etudes d’üpistümologie günütique, 1962, 16, 69–93. Paris: Presses Universitaires de France.Google Scholar
  27. McLaughlin, G. H. Psycho-logic: A possible alternative to Piaget’s formulation. British Journal of Educational Psychology, 1963, 33, 61–67.CrossRefGoogle Scholar
  28. O’Brien, T. C. Logical thinking in college students. Educational Studies in Mathematics, 1973, 5, 71–79.CrossRefGoogle Scholar
  29. O’Brien, T. C., Shapiro, B. J., & Reali, N. C. Logical thinking: Language and context. Educational Studies in Mathematics, 1971, 4, 201–209.CrossRefGoogle Scholar
  30. Peel, E. A. A study of differences in the judgments of adolescent pupils. British Journal of Educational Psychology, 1966, 36, 77–86.PubMedCrossRefGoogle Scholar
  31. Peel, E. A. A method for investigating children’s understanding of certain logical connectives used in binary propositional thinking. British Journal of Mathematical and Statistical Psychology, 1967, 20, 81–92.PubMedCrossRefGoogle Scholar
  32. Peel, E. A. The nature of adolescent judgment. London: Staples, 1971.Google Scholar
  33. Piaget, J. Les notions de mouvement et de vitesse chez l’enfant. Paris: Presses Universitaires de France, 1946.Google Scholar
  34. Piaget, J. Piaget’s theory. In P. H. Mussen (Ed.), Carmichael’s manual of child psychology, Vol. 1. New York: Wiley, 1970. Pp. 703–732.Google Scholar
  35. Piaget, J., Inhelder, B., & Szeminska, A. The child’s conception of geometry. London: Routledge, 1960.Google Scholar
  36. Piaget, J., Grize, J. B., Szeminska, A., & Vinh Bang. Epistümologie et psychologie de la fonction. Etudes d’üpistümologie günütique, 1968, 23. Paris: Presses Universitaires de France.Google Scholar
  37. Reichard, S., Schneider, M., & Rappaport, D. The development of concept formation in children. American Journal of Orthopsychiatry, 1944, 14, 156–162.CrossRefGoogle Scholar
  38. Rhys, W. T. The development of logical thought in the adolescent with reference to the teaching of geography in the secondary school. M.Ed. thesis, University of Birmingham, 1964.Google Scholar
  39. Roberge, J. J., & Paulus, D. H. Developmental patterns for children’s class and conditional reasoning abilities. Developmental Psychology, 1971, 4, 191–199.CrossRefGoogle Scholar
  40. Sells, S. B. The atmosphere effect: An experimental study of reasoning. Archives of Psychology, 1936, 29, 3–72.Google Scholar
  41. Shapiro, B. J., & O’Brien, T. C. Quasi-child logics. Educational Studies in Mathematics, 1973, 5, 181–184.CrossRefGoogle Scholar
  42. Thouless, R. H. Map of educational research. London: National Foundation for Educational Research, 1969.Google Scholar
  43. Wason, P. C., & Johnson-Laird, P. N. Psychology of reasoning, structure, and content. London: Batsford, 1972.Google Scholar
  44. Wason, P. C., & Shapiro, D. Natural and contrived experience in a reasoning problem. Quarterly Journal of Experimental Psychology, 1971, 23, 63–71.CrossRefGoogle Scholar
  45. White, S. A. Evidence for a hierarchical arrangement of learning processes. In L. P. Lipsitt & C. C. Spiker (Eds.), Advances in child behavior development, Vol. 2. New York: Academic Press, 1965. Pp. 187–220.Google Scholar

Copyright information

© Jean Piaget Society 1978

Authors and Affiliations

  • E. A. Lunzer
    • 1
  1. 1.University of NottinghamNottinghamEngland

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