Formal Representation of Qualitative and Quantitative Reversible Operations

  • Colleen F. Surber
Part of the Springer Series in Cognitive Development book series (SSCOG)

Abstract

In this chapter I present an approach using contemporary mathematical models of human judgment to explore the issue of whether the relations among a set of variables are conceptualized reversibly. Specifically, are the judgments of each of a set of variables based on a single, fully reversible set of mental operations?1 This topic is important to psychologists for three reasons. Piaget (1947/1960) proposed that reversible mental operations distinguish true intelligence from intuition and perception. If the transition to reversible thought is an important developmental event, then there is a need for precise representations of knowledge that is reversible. It is equally important to describe states of irreversible and partially reversible knowledge in order to describe the transition from irreversible to reversible thought.

Keywords

Torque Income Coherence Beach Posit 

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References

  1. Acredolo, C. (1981). Acquisition of conservation: A clarification of Piagetian terminology, some recent findings, and an alternative formulation. Human Development, 24, 120–137.CrossRefGoogle Scholar
  2. Anderson, J. R. (1982). Acquisition of cognitive skill. Psychological Review, 89, 369–406.CrossRefGoogle Scholar
  3. Anderson, J. R. (1983). The architecture of cognition. Cambridge, MA: Harvard.Google Scholar
  4. Anderson, N. H. (1974). Cognitive algebra. In L. Berkowitz (Ed.), Advances in experimental social psychology (Vol. 7, pp. 1–101). New York: Academic.Google Scholar
  5. Anderson, N. H. (1977). Note on functional measurement and data analysis. Perception and Psychophysics, 21, 201–215.CrossRefGoogle Scholar
  6. Anderson, N. H. (1979). Algebraic rules in psychological measurement. American Scientist, 67, 555–563.Google Scholar
  7. Anderson, N. H. (1980). Information integration theory in developmental psychology. In F. Wilkening, J. Becker, & T. Trabasso (Eds.), Information integration by children (pp. 1–45). Hillsdale, NJ: Erlbaum.Google Scholar
  8. Anderson, N. H., & Butzin, C. A. (1974). Performance = motivation × ability: An integration-theoretical analysis. Journal of Personality and Social Psychology, 30, 598–604.CrossRefGoogle Scholar
  9. Anderson, N. H., & Butzin, C. A. (1978). Integration theory applied to children’s judgments of equity. Developmental Psychology, 14, 593–606.CrossRefGoogle Scholar
  10. Anderson, N. H., & Cuneo, D. O. (1978). The height + width rule in children’s judgments of quantity. Journal of Experimental Psychology,’ General, 107, 335–378.CrossRefGoogle Scholar
  11. Birnbaum, M. H. (1974a). The nonadditivity of personality impressions. Journal of Experimental Psychology, 102, 543–561.PubMedCrossRefGoogle Scholar
  12. Birnbaum, M. H. (1974b). Using contextual effects to derive psychophysical scales. Perception and Psychophysics, 15, 89–96.CrossRefGoogle Scholar
  13. Birnbaum, M. H. (1976). Intuitive numerical prediction. American Journal of Psychology, 89, 417–429.CrossRefGoogle Scholar
  14. Birnbaum, M. H. (1978). Differences and ratios in psychological measurement. In N. J. Castellan & F. Restle (Eds.), Cognitive theory (Vol. 3, pp. 33–74). Hillsdale, NJ: Erlbaum.Google Scholar
  15. Birnbaum, M. H. (1982). Controversies in psychological measurement. In B. Wegener (Ed.), Social attitudes and psychophysical measurement (pp. 401–485). Hillsdale, NJ: Erlbaum.Google Scholar
  16. Birnbaum, M. H., Parducci, A., & Gifford, R. K. (1971). Contextual effects in information integration. Journal of Experimental Psychology, 88, 155–170.CrossRefGoogle Scholar
  17. Birnbaum, M. H., & Viet, C. (1974). ’Scale convergence as a criterion for rescaling: Information integration with difference, ratio, and averaging tasks. Perception and Psychophysics, 15, 7–15.CrossRefGoogle Scholar
  18. Bogartz, R. S. (1976). On the meaning of statistical interactions. Journal of Experimental Child Psychology, 22, 178–183.CrossRefGoogle Scholar
  19. Bogartz, R. S., & Wackwitz, J. H. (1970). Transforming response measures to remove interactions or other sources of variance. Psychonomic Science, 19, 87–89.Google Scholar
  20. Brainerd, C. J. (1976). Does prior knowledge of the compensation rule increase susceptibility to conservation training? Developmental Psychology, 12, 1–5.CrossRefGoogle Scholar
  21. Brehmer, B. (1974). Hypotheses about relations between scaled variables in the learning of probabilistic inference tasks. Organizational Behavior and Human Performance, 11, 1–27.CrossRefGoogle Scholar
  22. Brehmer, B., & Slovic, P. (1980). Information integration in mUltiple cue judgments. Journal of Experimental Psychology: Human Perception and Performance, 6, 302–308.CrossRefGoogle Scholar
  23. Busemeyer, J. R. (1980). Importance of measurement theory, error theory, and experimental design for testing the significance of interactions. Psychological Bulletin, 88, 237–244.CrossRefGoogle Scholar
  24. Butzin, C. A., & Anderson, N. H. (1973). Functional measurement of children’s judgments. Child Development, 44, 529–537.CrossRefGoogle Scholar
  25. Chandler, J. D. (1969). Subroutine STEP IT-Finds local minima of a smooth function of several parameters. Behavioral Science, 14, 81–82.Google Scholar
  26. Graesser, C. A., & Anderson, N. H. (1974). Cognitive algebra of the equation Gift size = generosity x income. Journal of Experimental Psychology, 103, 692–699.CrossRefGoogle Scholar
  27. Haines, B. A., Surber, C. F., Walden, J., & Gzesh, S. M. (1985, April). Reversibility of intuitive versus analytic mental operations. Paper presented at the biennial meeting of the Society for Research in Child Development, Toronto, Canada.Google Scholar
  28. Heider, F. (1958). The psychology of interpersonal relations. New York: Wiley.CrossRefGoogle Scholar
  29. Hoffman, P. J. (1960). The paramorphic representation of clinical judgment. Psychological Bulletin, 57, 116–131.PubMedCrossRefGoogle Scholar
  30. Inhelder, B., & Piaget, J. (1958). The growth of logical thinking from childhood to adolescence. New York: Basic Books.CrossRefGoogle Scholar
  31. Karabenick, J. D., & Heller, K. A. (1976). A developmental study of effort and ability attributions. Developmental Psychology, 12, 559–560.CrossRefGoogle Scholar
  32. Kelley, H. H. (1972). Causal schemata and the attribution process. New York: General Learning Press.Google Scholar
  33. Kelley, H. H. (1973). The processes of causal attribution. American Psychologist, 28, 107–128.CrossRefGoogle Scholar
  34. Krantz, D. H., & Tversky, A. (1971). Conjoint-measurement analysis of composition rules in psychology. Psychological Review, 78, 151–169.CrossRefGoogle Scholar
  35. Kruskal, J., & Cannone, F. (1969). MONANOV A: A FORTRAN-IV program for monotone analysis of variance. Behavioral Science, 14, 165–166.Google Scholar
  36. Kun, A. (1977). Development of the magnitude-covariation and compensation schemata in ability and effort attributions of performance. Child Development, 48, 862–873.CrossRefGoogle Scholar
  37. Kun, A., Parsons, J., & Ruble, D. (1974). Development of integration processes using ability and effort information to predict outcome. Developmental Psychology, 10, 721–732.CrossRefGoogle Scholar
  38. Kun, A., & Weiner, B. (1973). Necessary versus sufficient causal schemata for success and failure. Journal of Research in Personality, 7, 197–207.CrossRefGoogle Scholar
  39. Larsen, G. Y., & Flavell, J. H. (1970). Verbal factors in compensation performance and the relation between conservation and compensation. Child Development, 41, 965–977.PubMedCrossRefGoogle Scholar
  40. Marks, L. E. (1982). Psychophysical measurement: Procedures, tasks, scales. In B. Wegener (Ed.), Social attitudes and psychophysical measurement (pp. 43–71). Hillsdale, NJ: Erlbaum.Google Scholar
  41. Mellers, B. (1982). Equity judgment: A revision of Aristotelian views. Journal of Experimental Psychology: General, 111, 242–270.CrossRefGoogle Scholar
  42. Mellers, B., & Birnbaum, M. H. (1982). Loci of contextual effects in judgment. Journal of Experimental Psychology: Human Perception and Performance, 8, 582–601.PubMedCrossRefGoogle Scholar
  43. Mellers, B., & Birnbaum, M. H. (1983). Context effects in social judgment. Journal of Experimental Social Psychology, 19, 157–171.CrossRefGoogle Scholar
  44. Norman, K. L., & Schemmer, F. M. (1977). Functional processing in information integration tasks (Tech. Rep. No. 14). University of Maryland, Center for Language and Cognition.Google Scholar
  45. Oden, G. C. (1977). Integration offuzzy logical information. Journal of Experimental Psychology: Human Perception and Performance, 3, 565–575.CrossRefGoogle Scholar
  46. Parducci, A. (1974). Context effects: A range-frequency analysis. In E. C. Carterette and M. P. Friedman (Eds.), Handbook of perception: Vol 2. Psychophysicaljudgment and measurement (pp. 127–141). New York: Academic.Google Scholar
  47. Peterson, C. R., & Beach, L. R. (1967). Man as an intuitive statistician. Psychological Bulletin, 68, 29–46.PubMedCrossRefGoogle Scholar
  48. Piaget, J. (1941/1965). The child’s conception of number. New York: Norton.Google Scholar
  49. Piaget, J. (1947/1960). The psychology of intelligence. Totowa, NJ: Littlefield, Adams & Co.CrossRefGoogle Scholar
  50. Shatz, M. (1978). The relationship between cognitive processes and the development of communication skills. In C. B. Keasey (Ed.), Nebraska symposium on motivation 1977 (Vol. 25, pp. 1–42). Lincoln: University of Nebraska Press.Google Scholar
  51. Siegler, R. S. (1976). Three aspects of cognitive development. Cognitive Psychology, 8, 481–520.CrossRefGoogle Scholar
  52. Siegler, R. S. (1981). Developmental sequences within and between concepts. Monographs of the Society for Research in Child Development 46 (2, Serial No. 189).Google Scholar
  53. Singh, R., Gupta, M., & Dalal, A. K. (1979). Cultural difference in attribution of performance: An integration-theoretical analysis. Journal of Personality and Social Psychology, 37, 1342–1351.CrossRefGoogle Scholar
  54. Slovic, P., & Lichtenstein, S. C. (1971). Comparison of Bayesian and regression approaches to the study of information processing in judgment. Organizational Behavior and Human Performance, 6, 649–744.CrossRefGoogle Scholar
  55. Smith, E. R. (1984). Model of social inference processes. Psychological Review, 91, 392–413.CrossRefGoogle Scholar
  56. Surber, C. F. (1978). Organization in social inference: Is there a schema for judgments of ability, effort, and task performance? Unpublished doctoral dissertation, University of Illinois afUrbana-Champaign.Google Scholar
  57. Surber, C. F. (1980). The development of reversible operations in judgments of ability, effort and performance. Child Development, 51, 1018–1029.CrossRefGoogle Scholar
  58. Surber, C. F. (1981a). Effects of information reliability in predicting task performance using ability and effort. Journal of Personality and Social Psychology, 40, 977–989.CrossRefGoogle Scholar
  59. Surber, C. F. (1981b). Necessary versus sufficient causal schemata: Attributions for achievement in difficult and easy tasks. Journal of Experimental Social Psychology, 17, 569–586.CrossRefGoogle Scholar
  60. Surber, C. F. (1982, November). Relationships between predictions and inferences. Paper presented at the meeting of the Psychonomic Society, 1982, Minneapolis, MN.Google Scholar
  61. Surber, C. F. (1984a). The development of achievement-related judgment processes. In J. Nicholls (Ed.), The development of achievement motivation. Greenwich, CT: JAI Press.Google Scholar
  62. Surber, C. F. (1984b). Inferences of ability and effort: Evidence for two different processes. Journal of Personality and Social Psychology, 46, 249–268.CrossRefGoogle Scholar
  63. Surber, C. F. (1984c). Issues in using quantitative rating scales in developmental research. Psychological Bulletin, 95, 226–246.CrossRefGoogle Scholar
  64. Surber, C. F. (1985a). Applications of information integration to children’s social cognitions. In J. B. Pryor & J. D. Day (Eds.), The development of social cognition (pp. 59–94). New York: Springer-Verlag.CrossRefGoogle Scholar
  65. Surber, C. F. (1985b). Developmental changes in inverse compensation in social and nonsocial attributions. In S. Yussen (Ed.), The growth of reflection in children (pp. 149–166). New York: Academic.Google Scholar
  66. Surber, C. F. (1985c). Measuring the importance of information in judgment: Individual differences in weighting ability and effort. Organizational Behavior and Human Decision Processes, 35, 156–178.CrossRefGoogle Scholar
  67. Surber, C. F., Gzesh, S. M. (1984). Reversible operations in the balance scale task. Journal of Experimental Child Psychology, 38, 254–274.CrossRefGoogle Scholar
  68. Wilkening, F. (1981). Integrating velocity, time and distance information: A developmental study. Cognitive Psychology, 13, 231–247.PubMedCrossRefGoogle Scholar

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© Springer-Verlag New York Inc. 1987

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  • Colleen F. Surber

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