Stagewise cognitive development: An application of catastrophe theory.
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In this article an overview is given of traditional methodological approaches to stagewise cognitive developmental research. These approaches are evaluated and integrated on the basis of catastrophe theory. In particular, catastrophe theory specifies a set of common criteria for testing the discontinuity hypothesis proposed by Piaget. Separate criteria correspond to distinct methods used in cognitive developmental research. Such criteria are, for instance, the detection of spurts in development, bimodality of test scores, and increased variability of responses during transitional periods. When a genuine stage transition is present, these criteria are expected to be satisfied. A revised catastrophe model accommodating these criteria is proposed for the stage transition in cognitive development from the preoperational to the concrete operational stage.
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A dynamic systems model of cognitive and language growth.
van Geert, P. (1991) · Psychological Review · doi:10.1037/0033-295x.98.1.3 · Cited by 464 · cited 1× · see citing works
“That is, instead of the normal Verhulst equation, X^{ = r Xn (1 - Xn), the equation X^{ = r X, (1 - X\) + N must be used, van Geert (1991) already gave an interpretation for the additional variable N.”
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- Brainerd, C. J. (1973). Judgments and explanations as criteria for the presence of cognitive structures. Psychological Bulletin, 79, 172–179.
- Brainerd, C. J. (1979). Markovian interpretations ofconservation learning. Psychological Review, 86, 181–213.
- Brainerd, C. J., & Allen, T. (1971). Experimental inductions of the conservation of "first-order" quantitative invariants. Psychological Bulletin, 75, 128–144.
- Bruner, J. S. (1967). On the conservation of liquids. In J. S. Bruner, R. R. Olver, & P. M. Greenfield (Eds.), Studies in cognitive growth (pp. 183–207). New York: Wiley.
- Campbell, R. L., & Bickhard, M. H. (1986). Contributions to human development: Volume 16. Knowing levels and developmental stages (J. A. Meacham, Ed.). Basel, Switzerland: Karger.
- Cantor, G. N. (1983). Conflict, learning, and Piaget: Comments on Zimmerman and Blom's "toward an empirical test of the role of cognitive conflict in learning." Developmental Review, 3, 39–53.
- Case, R. (1985). Intellectual development: Birth to adulthood. San Diego, CA: Academic Press.
- Cobb, L. (1980). Estimation theory for the cusp catastrophe model. Proceedings of the Section on Survey Research Methods (pp. 772– 776). Washington, DC: American Statistical Association.
- Cobb, L., & Zacks, S. (1985). Applications of catastrophe theory for statistical modeling in the biosciences. Journal of the American Statistical Association, 80, 793–802.
- Connell, J. P., & Furman, W. (1984). The study of transitions: Conceptual and methodological issues. In R. N. Emde & R. J. Harmon (Eds.), Continuities and discontinuities in development (pp. 153–174). New York: Plenum Press.
- Emde, N. R., & Harmon, R. J. (Eds.). (1984). Continuities and discontinuities in development. New York: Plenum Press.
- Field, D. (1987). A review of preschool conservation training: An analysis of analyses. Developmental Review, 7, 210–251.
- Fischer, K. W. (1983). Developmental levels as periods of discontinuity. In K. W. Fischer (Ed.), Levels and transitions in children's development: New directions for child development (Vol. 21, pp. 5-20). San Francisco: Jossey-Bass.
- Fischer, K. W., & Bullock, D. (1981). Patterns of data: Sequence, synchrony, and constraint in cognitive development. In K. W. Fischer (Ed.), Cognitive development: New directions forchild development (Vol. 12, pp. 1–20). San Francisco: Jossey-Bass.
- Fischer, K. W., Pipp, S. L., & Bullock, D. (1984). Detecting developmental discontinuities: Methods and measurement. In R. N. Emde & R. J. Harmon (Eds.), Continuities and discontinuities in development (pp. 95–122). New York: Plenum Press.
- Fischer, K. W, & Silvern, L. (1985). Stages and individual differences in cognitive development. Annual Review of Psychology, 36, 613648.
- Flavell, J. H., & Wohlwill, J. F. (1969). Formal and functional aspects of cognitive development. In D. Elkind & J. H. Flavell (Eds.), Studies in cognitive development: Essays in honor of Jean Piaget (pp. 67–120). New York: Oxford University Press.
- Freedle, R. (1977). Psychology, thomian topologies, deviant logics, and human development. In N. Datan & H. W. Reese (Eds.), Life-span development psychology: Dialectical perspectives on experimental research (pp. 317–342). San Diego, CA: Academic Press.
- Gilmore, R. (1981). Catastrophe theory for scientists and engineers. New York: Wiley.
- Globerson, T. (1985). Field dependence/independence and mental capacity: A developmental approach. Developmental Review, 5, 261– 273.
- Globerson, T., & Zelniker, T. (1989). Introduction. In T. Globerson & T. Zelniker (Eds.), Human development: Cognitive style and cognitive development (Vol. 3, pp. 1–9). Norwood, NJ: Ablex.
- Guastello, S. J. (1988). Catastrophe modeling of the accident process: Organizational subunit size. Psychological Bulletin, 103, 246–255.
- Jackson, E. A. (1989). Perspectives on nonlinear dynamics (Vol. 1). Cambridge, England: Cambridge University Press.
- Kenny, S. L. (1983). Developmental discontinuities in childhood and adolescence. In K. W. Fischer (Ed.), Levels and transitions in children's development: New directions for child development (Vol. 21, pp. 81–96). San Francisco: Jossey-Bass.
- Kingma, J. (1984). Criterion problem in conservation research reconsidered from a psychometric point of view. Journal of General Psychology, 111, 109–129.
- Levin, I. L. (Ed.). (1986). Stage and structure: Reopening the debate. Norwood, New Jersey: Ablex.
- Lewis, M. (1990). Development, time, and catastrophe: An alternative view of discontinuity. In P. Baltes, D. L. Featherman, & R. Lerner (Eds.), Life span development and behavior series (Vol. 10, pp. 325– 350). Hillsdale, NJ: Erlbaum.
- McCall, R. B. (1983). Exploring developmental transitions in mental performance. In K. W. Fischer (Ed), Levels and transitions in children's development: New directions for child development (Vol. 21, pp. 65-80). San Francisco: Jossey-Bass.
- McShane, J. (1991). Cognitive development: An information processing approach (lst ed.). Oxford, England: Basil Blackwell.
- Murray, F. B. (1983). Equilibration as cognitive conflict. Developmental Review, 3, 54–61.
- Odom, R. D. (1972). Effects on perceptual salience on the recall of relevance and incidental dimensional values: A developmental study. Journal of Experimental Psychology, 92, 185–291.
- Odom, R. D. (1978). A perceptual salience account of décalage relations and developmental change. In L. S. Siegel, & C. J. Brainerd (Eds.), Alternatives to Piaget: Critical essays on the theory (pp. 11– 130). San Diego, CA: Academic Press.
- Pascual-Leone, J. (1989). An organismic process model of Witkin's field-Dependency-Independency. In T. Globerson, & T. Zelniker (Eds.), Cognitive style and cognitive development (Vol. 3, pp. 36–70). Norwood, New Jersey: Ablex.
- Pascual-Leone, J., & Morra, S. (in press). Horizontality of water level: A neopiagetian developmental review. Advances in Child Development and Behavior.
- Pinard, A. (1981). The conservation of conservation: The child's acquisition of a fundamental concept. Chicago: University of Chicago Press. Poston, T., & Stewart, I. (1978). Catastrophe theory and its applications.
- Rutter, M. (1984). Continuities and discontinuities in socioemotional development: Empirical and conceptual perspectives. In R. N. Emde & R. J. Harmon (Eds.), Continuities and discontinuities in development (pp. 41–68). New York: Plenum Press.
- Saari, D. G. (1977). A qualitative model for the dynamics of cognitive processes. Journal of Mathematical Psychology, 15, 145–168.
- Sommerhoff, G. (1969). The abstract characteristics of living systems. In F. E. Emery (Ed.), System thinking (4th ed., pp. 147–202). Middlesex, England: Penguin Books.
- Stauder, J. E. A., Molenaar, P. C. M., & van der Molen, M. W. (in press). Event related brain potentials elicited in an Piagetian conservation task analogue. Child Development. Submitted
- Stewart, I. N., & Peregoy, P. L. (1983). Catastrophe theory modeling in psychology. Psychological Bulletin, 94, 336–362.
- Tabor, L. E., & Kendler, T. S. (1981). Testing for developmental continuity or discontinuity: Class inclusion and reveral shifts. Developmental Review, 1, 330–343.
- Thomas, H. (1 989). A binomial mixture model for classification performance: A commentary on Waxman, Chambers, Yntema, and Gelman (1989). Journal of Experimental Child Psychology, 48, 423–430.
- Wilson, M. (1989). Saltus: A psychometric model of discontinuity in cognitive development. Psychological Bulletin, 105, 276–289.
- Wohlwill, J. F. (1973). The study of behavioral development. San Diego, CA: Academic Press.
- Zeeman, E. C. (1976). Catastrophe theory. Scientific American, 234(4), 65-83.
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- Authors
- Van der Maas, H. L., & Molenaar, P. C.
- ORCID
- Molenaar, Peter C.
- Venue
- Psychological Review
- Published
- 1992
- Volume
- 99
- Issue
- 3
- Pages
- 395-417
- ISSN
- 0033-295X (ISSN-L)
- 1939-1471
- OpenAlex
- W2165983682
- Cited by
- 433
- References
- 1
- Citations by year
- 2026: 6 · 2025: 8 · 2024: 7 · 2023: 11 · 2022: 11 · 2021: 8 · 2020: 8 · 2019: 10 · 2018: 11 · 2017: 11 · 2016: 14 · 2015: 17 · 2014: 22 · 2013: 16 · 2012: 16
- FWCI
- 27.17
- Type
- journal article
- Language
- en
- Open access
- green
- handle.uba.uva.nl
- Locations
- Psychological Review (publishedVersion)
- PubMed (publishedVersion)
- UvA-DARE (University of Amsterdam) (submittedVersion)
- Data Archiving and Networked Services (DANS) (submittedVersion, other-oa)
- Topics
- Social Sciences › Psychology › Developmental and Educational Psychology › Child and Animal Learning Development
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Chaos, Complexity, and Education
- Social Sciences › Psychology › Clinical Psychology › Ego Development and Educational Practices
- Keywords
- catastrophe theory, Piaget, stage transitions, preoperational stage, concrete operational stage, response variability
- MeSH terms
- Adaptation, Psychological, Child, Child Development, Cognition, Humans, Models, Psychological, Thinking
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