An Application of Configural Frequency Analysis
The Development of Children’s Class Reasoning
Abstract
Development of class reasoning was investigated using configural frequency analysis (CFA). We administered class inclusion, vicariant inclusion, and law of duality tasks to a sample of 540 Chinese second through fifth graders. In each task, children were asked to compare two classes and make a choice from four alternative answers while the number of classes was not given. Results showed that (1) children’s performance on both class inclusion and vicariant inclusion tasks improved significantly from Grade 2 to Grade 3 and from Grade 3 to Grade 4, but children did not tend to give correct answers to class inclusion items until Grade 4 and to vicariant inclusion items until Grade 5; (2) children from Grades 2 to 5 performed poorly on the law of duality task, but fifth graders were more likely to respond correctly than the general population; and (3) second graders tended to give wrong answers such as “equal number” and “not sure.” A discussion of the development of class reasoning followed.
References
1994). Schematic or taxonomic organization of the reality and development of class logic. International Journal of Psychology, 29, 183–212. doi 10.1080/00207599408246541
(1994). Understanding categorical hierarchies: The earliest level of skill. Child Development, 65, 1279–1298. doi 10.1111/j.1467-8624.1994.tb00817.x
(1974). Training and transfer of transitivity, conservation, and class inclusion of length. Child Development, 45, 324–334. doi 10.2307/1127952
(1992). Beyond competence and performance: Children’s class inclusion strategies, superordinate class cues, and verbal justifications. Developmental Psychology, 28, 319–327. doi 10.1037/0012-1649.28.2.319
(1999). Interference and inhibition in cognition and behavior: Unifying themes for education psychology. Educational Psychology Review, 11(1), 1–88. doi 10.1023/A:1021992632168
(1993). The ontogeny of inhibition mechanisms: A renewed approach to cognitive development. In , Emerging themes in cognitive development (Vol. 1, pp. 28–49). New York: Springer.
(1996). Intending to forget: The development of cognitive inhibition in directed forgetting. Journal of Experimental Child Psychology, 62, 292–315. doi 10.1006/jecp.1996.0032
(1987). Performance model analysis in class inclusion: An illustration with two language conditions. Developmental Psychology, 23, 683–689. doi 10.1037/0012-1649.23.5.683
(2000). Inhibition and cognitive development: Object, number, categorization, and reasoning. Cognitive Development, 15(1), 63–73. doi 10.1016/S0885-2014(00)00015-0
(1964). The early growth of logic in the child: Classification and seriation. London, UK: Routledge and Kegan Paul.
(2002). The development of children’s rule use on the balance scale task. Journal of Experimental Child Psychology, 81, 383–416. doi 10.1006/jecp.2002.2664
(1992). Beyond modularity: A developmental perspective on cognitive science. Cambridge, MA: MIT.
(1975). Configural frequency analysis as a statistical tool for defining types. Educational and Psychological Measurement, 35, 231–238. doi 10.1177/ 001316447503500201
(1978). Empirical versus logical solutions to part-whole comparison problems concerning classes and collections. Child Development, 49, 168–177. doi 10.2307/1128605
(1999). Developmental sequences in class reasoning and propositional reasoning. Journal of Experimental Child Psychology, 74(2), 69–106. doi 10.1006/jecp.1999.2510
(2006). Enhancing academic performance by strengthening class-inclusion reasoning. The Journal of Psychology: Interdisciplinary and Applied, 140, 603–613. doi 10.3200/JRLP.140.6.603-613
(2003). Respective contributions of inhibition and knowledge levels in class inclusion development: A negative priming study. Developmental Science, 6, 283–288. doi 10.1111/1467-7687.00284
(1980). Experiments in contradiction. Chicago, IL: University of Chicago Press.
(1985). The equilibration of cognitive structures: The central problem of intellectual development. Chicago, IL: University of Chicago Press.
(1994). The inferential structure of class-inclusion tasks. British Journal of Developmental Psychology, 12, 209–233. doi 10.1111/j.2044-835X.1994.tb00629.x
(1985). Piaget’s grouping II: The model, its assessment, and the effect of training. Developmental Review, 5, 289–308. doi 10.1016/0273-2297(85)90015-2
(1979). The class-inclusion task: Question form and distributive comparisons. Journal of Psycholinguistic Research, 8, 301–331. doi 10.1007/BF01067136
(2006). What leads children to adopt new strategies? A microgenetic/cross-sectional study of class inclusion. Child Development, 77, 997–1015. doi 10.1111/j.1467-8624.2006.00915.x
(1999). Necessary knowledge in number conservation. Developmental Science, 2(1), 23–27. doi 10.1111/1467-7687.t01-1-00049
(2008). Children’s knowledge of the earth: A new methodological and statistical approach. Journal of Experimental Child Psychology, 100, 276–296. doi 10.1016/j.jecp.2008.03.004
(1995). Modeling class inclusion strategies. Developmental Psychology, 31, 170–179. doi 10.1037/0012-1649. 31.2.170
(1997). Competency criteria and the class inclusion task: Modeling judgments and justifications. Developmental Psychology, 33, 1060–1073. doi 10.1037/0012-1649.33.6.1060
(1996). Catastrophe analysis of discontinuous development. In , Categorical variables in developmental research: Methods of analysis (pp. 77–105). San Diego, CA: Academic Press.
C. M. (1976). Deux expériences à propos de l’extension dans l’épreuve de la quantification de l’inclusion [
(Two experiments about “extension” in the class inclusion problem ]. Revue Suisse de Psychologie, 35, 269–284.2001). Configural frequency analysis – Version 2000: A program for 32-bit Windows operating systems. Methods of Psychological Research, 6(1). www.dgps.de/fachgruppen/methoden/mpr-online/issue14/art1/article.html
(2002). Configural frequency analysis: Methods, Models, and Applications. Mahwah, NJ: Erlbaum.
(2008). Temporal patterns of variable relationships in person-oriented research: Longitudinal models of configural frequency analysis. Developmental Psychology, 44, 437–445. doi 10.1037/0012-1649.44.2.437
(1974). An analysis of verbal facilitation of class-inclusion reasoning. Child Development, 45, 224–227. doi 10.2307/1127776
(1980). Class-inclusion reasoning in children: A review of the empirical literature. Child Development, 51, 309–328. doi 10.2307/1129264
(