Evidence for the Phase Transition from Rule I to Rule II on the Balance Scale Task

Akaike, 1974, A new look at the statistical model identification, IEEE Transactions on Automatic Control, 19, 716, 10.1109/TAC.1974.1100705 Azzelini, 1996 Brainerd, 1979, Markovian interpretations of conservation learning, Psychological Review, 86, 181, 10.1037/0033-295X.86.3.181 Brainerd, 1981, Working memory and the developmental analysis of probability judgment, Psychological Review, 88, 463, 10.1037/0033-295X.88.6.463 Brainerd, 1985, Three-state models of memory development: A review of advances in statistical methodology, Journal of Experimental Child Psychology, 40, 375, 10.1016/0022-0965(85)90072-4 Brainerd, 1993, Cognitive development is abrupt (but not stage-like), Monographs of the Society for Research in Child Development, 58, 170, 10.1111/j.1540-5834.1993.tb00460.x Chletsos, 1986 Dolan, 1998, Fitting multivariate normal finite mixtures subject to structural equation modeling, Psychometrika, 63, 227, 10.1007/BF02294853 Eckstein, 1999, A dynamic model of cognitive growth in a population: Spatial tasks and conservation, Journal of Mathematical Psychology, 43, 34, 10.1006/jmps.1998.1219 Eckstein, 2000, Growth of cognitive abilities: Dynamic models and scaling, Developmental Review, 20, 1, 10.1006/drev.1999.0485 Ferretti, 1985, The classification of children's knowledge: Development on the balance-scale and inclined-plane tasks, Journal of Experimental Child Psychology, 39, 131, 10.1016/0022-0965(85)90033-5 Flavell, 1985 Gilmore, 1981 Heinen, 1996 Hosenfeld, 1997, Indicators of discontinuous change in the development of analogical reasoning, Journal of Experimental Child Psychology, 64, 367, 10.1006/jecp.1996.2351 Jansen, 1997, Statistical test of the rule assessment methodology by latent class analysis, Developmental Review, 17, 321, 10.1006/drev.1997.0437 Kelso, 1995 Langeheine, 1994, Latent variables Markov models Langeheine, 1995 McCutcheon, 1987 Mislevy, 1996, Marginal maximum likelihood estimation for a psychometric model of discontinuous development, Psychometrika, 61, 41, 10.1007/BF02296958 Molenaar, 1986, Issues with a rule-sampling theory of conservation learning from a structuralist point of view, Human Development, 29, 137, 10.1159/000273037 Molenaar, 1986, On the impossibility of acquiring more powerful structures: A neglected alternative, Human Development, 29, 245, 10.1159/000273061 Normandeau, 1989, The balance-scale dilemma: Either the subject or the experimenter muddles through, Journal of Genetic Psychology, 150, 237, 10.1080/00221325.1989.9914594 Poston, 1978 Raftery, 1995, Bayesian model selection in social research (with Discussion), Sociological Methodology, 25, 111, 10.2307/271063 Richards, 1981, Very young children's acquisition of systematic problem-solving strategies, Child Development, 52, 1318, 10.2307/1129523 Rost, 1990, Rasch models in latent classes: An integration of two approaches to item analysis, Applied Psychological Measurement, 14, 271, 10.1177/014662169001400305 Rost, 1991, A logistic mixture distribution model for polychotomous item responses, British Journal of Mathematical and Statistical Psychology, 44, 75, 10.1111/j.2044-8317.1991.tb00951.x Schwarz, 1978, Estimating the dimension of a model, Annals of Statistics, 6, 461, 10.1214/aos/1176344136 Siegal, 1991 Siegler, 1976, Three aspects of cognitive development, Cognitive Psychology, 8, 481, 10.1016/0010-0285(76)90016-5 Siegler, 1981, Developmental sequences within and between concepts, Monographs of the Society for Research in Child Development, 46, 10.2307/1165995 Siegler, 1998, Developmental differences in rule learning: A microgenetic analysis, Cognitive Psychology, 36, 273, 10.1006/cogp.1998.0686 Ta'eed, 1988, Determinants involved in the perception of the Necker cube: An application of catastrophe theory, Behavioral Science, 33, 97, 10.1002/bs.3830330203 Thom, 1975 Thomas, 1993, Modeling growth and individual differences in spatial tasks, Monographs of the Society for Research in Child Development, 58, 10.2307/1166121 Thomas, 1999, Stability and change in longitudinal water-level task performance, Developmental Psychology, 35, 1024, 10.1037/0012-1649.35.4.1024 Van der Heijden, 1997, A parametric bootstrap procedure to perform statistical tests in a latent class analysis of anti-social behavior Van der Maas, 1992, Stagewise cognitive development: An application of catastrophe theory, Psychological Review, 99, 395, 10.1037/0033-295X.99.3.395 Van der Maas, 1996, Catastrophe analysis of discontinuous development Van Geert, 1991, A dynamic systems model of cognitive and language growth, Psychological Review, 98, 3, 10.1037/0033-295X.98.1.3 Van Geert, 1998, A dynamic systems model of basic developmental mechanisms: Piaget, Vygotsky, and beyond, Psychological Review, 105, 634, 10.1037/0033-295X.105.4.634-677 Van Maanen, 1989, The linear logistic test model and heterogeneity of cognitive strategies, 267 Wilkening, 1982, Comparison of two rule-assessment methodologies for studying cognitive development and knowledge structure, Psychological Bulletin, 92, 215, 10.1037/0033-2909.92.1.215 Wilson, 1989, Saltus: A psychometric model of discontinuity in cognitive development, Psychological Bulletin, 105, 276, 10.1037/0033-2909.105.2.276 Zeeman, 1976, Catastrophe theory, Scientific American, 234, 65, 10.1038/scientificamerican0476-65