Abstract
Abstract. Knowledge about potential operators, about the preconditions of their applicability, and about their effects is essential to interact effectively with the physical world. Four classes of representational units of this knowledge can be distinguished: I) rules, II) structures, III) instances, and IV) episodes. Two important characteristics of these units are the abstractness of content and the directionality of access. A multinomial model is presented that enables the measurement of these characteristics. Three experiments were conducted to validate the parameters of the model. The multinomial model could be fitted very well to the empirical data of each experiment. Moreover, the parameter estimates showed the expected effects. The model allows the investigation of the influence of important variables (for example, knowledge domain, type of instruction, or amount of practice) on characteristics of mental operators without a strong commitment to any specific process theory. Debates regarding the contribution of different kinds of knowledge can be converted into statistical tests of the corresponding model parameters.
References
(1993). Rules of the mind. Hillsdale, NJ: Lawrence Erlbaum Associates.
(1994). Acquisition of procedural skills from examples. Journal of Experimental Psychology: Learning, Memory, and Cognition, 20, 1322– 1340
(1997). The role of examples and rules in the acquisition of a cognitive skill. Journal of Experimental Psychology: Learning, Memory, and Cognition, 23, 932– 945
(1998). The atomic components of thought. Mahwah, NJ: Lawrence Erlbaum Associates.
(1999). Theoretical and empirical review of multinomial process tree modeling. Psychonomic Bulletin and Review, 6, 57– 86
(1988). Statistical power analysis for the behavioral sciences. (2nd edition). Hillsdale, NJ: Lawrence Erlbaum.
(1983). Structure-mapping: A theoretical framework for analogy. Cognitive Science, 7, 155– 170
(1998). Induction of relational schemas: Common processes in reasoning and complex learning. Cognitive Psychology, 35, 201– 245
(1993). Vorhersage und Erkenntnis. [Prediction and cognition]. Göttingen: Hogrefe.
(1994). The statistical analysis of general processing tree models with the EM algorithm. Psychometrika, 59, 21– 47
(1987). Production system models of learning and development. Cambridge, MA: MIT Press.
(1988). Toward an instance theory of automatization. Psychological Review, 95, 492– 527
(1999). Use specificity of cognitive skills: Evidence for production rules?. Journal of Experimental Psychology: Learning, Memory, and Cognition, 25, 191– 207
(2002). Single-use versus mixed-use learning of transformations: Evidence for conceptual integration. Experimental Psychology, 49, 45– 56
(2002). Acquisition and use of mental operators: Effects of type of practice. Experimental Psychology, 49, 141– 152
(1990). Unified theories of cognition. Cambridge, Mass.: Harvard University Press.
(1972). Human Problem Solving.. Englewood Cliffs, NJ: Prentice-Hall.
(1997). Exemplar similarity and the development of automaticity. Journal of Experimental Psychology: Learning, Memory, and Cognition, 23, 324– 354
(1998). A theory of the measurement of knowledge content, access, and learning. Psychological Review, 105, 58– 82
(1988). Multinomial modeling and the measurement of cognitive processes. Psychological Review, 95, 318– 339
(1994). On the cognitive structure of basic arithmetic skills: Operation, order, and symbol transfer effects. Journal of Experimental Psychology: Learning, Memory, and Cognition, 20, 1139– 1153
(1999). AppleTree: A multinomial processing tree modeling program for Macintosh computers. Behavior-Research-Methods,-Instruments-and-Computers, 31, 696– 700
(1932). Purposive behavior in animal and men. New York: Appleton.