ABSTRACT

Knowledge about operators, about the conditions of their applicability, and about their effects is essential for effective interaction with the physical world. By combining two defining dimensions of this knowledge – abstractness of content and directionality of access – we can distinguish four classes of representational units: rules, instances, episodes, and structures. We present a multinomial model that measures the characteristics of these units. This model was applied to an experiment on the acquisition and use of alphabet-arithmetic operators (Müller & Gehrke, 2002). The multinomial model could be fitted very well to the data and allows calculating the proportions of the different kinds of mental operators. To compare these findings with a simulation of the specific cognitive processes, we developed an ACT-R model. Separating four cases of information processing in correspondence to the knowledge units in the multinomial model confirmed the estimates of the multinomial analysis. This finding demonstrates the usefulness of multinomial modeling as a statistical tool to investigate cognitive processes. Also, it provides converging evidence for the use of different kinds of knowledge, even in simple tasks.