Indicators of Discontinuous Change in the Development of Analogical Reasoning

In a longitudinal study, five indicators of a transition in the development of analogical reasoning were examined in young elementary school children, (a) bimodality and (b) inaccessibility in the frequency distributions of test performance, and in the responses of the transitional subjects, respectively, (c) sudden jumps, (d) anomalous variance, and (e) critical slowing down. An open-ended geometric-analogies test was administered eight times during a period of six months to eighty children in Grades 1 and 2 (six- to eight-year-olds). Strong evidence for bimodality was found in the distribution of the test scores and weaker evidence for inaccessibility. In the performance curves of the transitional subjects sudden jumps were demonstrated. Furthermore, the transitional subjects displayed a temporary increase of inconsistent solution behavior and solution time near the sudden jump. The characteristic changes in the analogy performance of the transitional subjects were interpreted as a strategy shift.

[1]  R. Thom.  Structural stability and morphogenesis , 1977, Pattern Recognition.

[2]  H.L.J. van der Maas,et al.  Detecting Bimodality in the Analogical Reasoning Performance of Elementary Schoolchildren , 1997 .

[3]  Ann L. Brown.  Analogical learning and transfer: what develops? , 1989 .

[4]  H. Thomas,et al.  Modeling growth and individual differences in spatial tasks. , 1993, Monographs of the Society for Research in Child Development.

[5]  H.L.J. van der Maas,et al.  Beyond the metaphor , 1995 .

[6]  R. Sternberg,et al.  The development of analogical reasoning processes. , 1979, Journal of experimental child psychology.

[7]  R. J. Mokken,et al.  A Theory and Procedure of Scale Analysis: With Applications in Political Research , 1971 .

[8]  Eric A. Jenkins,et al.  How Children Discover New Strategies , 1989 .

[9]  E. Thelen,et al.  Hidden skills: a dynamic systems analysis of treadmill stepping during the first year. , 1991, Monographs of the Society for Research in Child Development.

[10]  Patricia A. Alexander,et al.  Analogical reasoning in young children. , 1987 .

[11]  A. Cohen,et al.  Finite Mixture Distributions , 1982 .

[12]  久保 亮五,et al.  H. Haken: Synergetics; An Introduction Non-equilibrium Phase Transitions and Self-Organization in Physics, Chemistry and Biology, Springer-Verlag, Berlin and Heidelberg, 1977, viii+325ページ, 251×17.5cm, 11,520円. , 1978 .

[13]  Jacob Cohen.  A Coefficient of Agreement for Nominal Scales , 1960 .

[14]  Michelle Perry,et al.  Indexing transitional knowledge , 1993 .

[15]  B. Silverman,et al.  Using Kernel Density Estimates to Investigate Multimodality , 1981 .

[16]  Marc D. Lewis,et al.  Evidence for a Neo-Piagetian Stage Transition in Early Cognitive Development , 1992 .

[17]  A. F. Smith,et al.  Statistical analysis of finite mixture distributions , 1986 .

[18]  Susan R. Goldman,et al.  Developmental and Individual Differences in Verbal Analogical Reasoning. , 1982 .

[19]  H. Thomas.  A binomial mixture model for classification performance: A commentary on Waxman, Chambers, Yntema, and Gelman (1989) , 1989 .

[20]  U. Goswami.  Analogical Reasoning: What Develops? A Review of Research and Theory. , 1991 .

[21]  C. S. White,et al.  Development of analogical reasoning in 4- and 5-year-old children , 1989 .

[22]  Melanie Mitchell,et al.  The emergence of understanding in a computer model of concepts analogy-making , 1990 .

[23]  K. Fischer,et al.  Detecting Developmental Discontinuities , 1984 .

[24]  Robin R. Vallacher,et al.  Dynamical Systems in Social Psychology , 1994 .

[25]  I. Prigogine,et al.  Order out of chaos , 1984 .

[26]  Robert Gilmore,et al.  Catastrophe Theory for Scientists and Engineers , 1981 .

[27]  Robert J. Sternberg,et al.  Component Processes in Analogical Reasoning. , 1977 .

[28]  Kevin Crowley,et al.  The microgenetic method , 1996 .

[29]  U. Goswami.  Analogical reasoning in children , 1993 .

[30]  A. Ortony,et al.  Similarity and Analogical Reasoning , 1991 .

[31]  D. Gentner.  Children's Performance on a Spatial Analogies Task. , 1977 .

[32]  Paul van Geert,et al.  A dynamic systems model of cognitive and language growth. , 1991 .

[33]  H.L.J. van der Maas,et al.  Stagewise cognitive development: an application of catastrophe theory. , 1992, Psychological review.

[34]  S. Vosniadou.  Analogical reasoning as a mechanism in knowledge acquisition: a developmental perspective , 1988 .

[35]  H. Haken.  Synergetics: an Introduction, Nonequilibrium Phase Transitions and Self-organization in Physics, Chemistry, and Biology , 1977 .

[36]  W. Resing,et al.  Constructing Geometric Analogies for the Longitudinal Testing of Elementary School Children. , 1997 .

[37]  H. Thomas,et al.  Individual differences and development in water-level task performance , 1991 .