A REPRESENTATIONAL ANALYSIS OF NUMERATION SYSTEMS

This article explores the representational structures of numeration sy stems and the cognitive factors of the representational effect in nume rical tasks, focusing on external representations and their interactio ns with internal representations. Numeration systems are analyzed at f our levels: dimensionally, dimensional representations, bases, and sym bol representations. The representational properties at these levels a ffect the processes of numerical tasks in different ways and are respo nsible for different aspects of the representational effect. This hier archical structure is also a cognitive taxonomy that can classify near ly all numeration systems that have been invented across the world. Mu ltiplication is selected as an example to demonstrate that complex num erical tasks require the interwoven processing of information distribu ted across internal and external representations. Finally, a model of distributed numerical cognition is proposed and an answer to the quest ion of why Arabic numerals are so special is provided.