Reading and calculating with familiar and unfamiliar numerical symbols
The term 'binumeralism' is introduced to describe people who use more than one numeral system. Different forms of the condition are distinguished. From previous work on bilingualism and calculation a distinction is derived between combination and auxiliary stages of calculation. Three sets of numerals, Western Arabic, Eastern Arabic and a specially devised set, are used in experiments on reading, identifying and transcribing digits, on rate of uptake of information (using Sperling's paradigm) and on addition (single pairs and multi-digit). The tests are given to subjects whose experience with their second numeral system ranges from 60 seconds to 5 years. The effects of the extra auxiliary stages involved in second numeral performance are shown to be strongly interactive with the combination stage in early, much less so in intermediate binumeralism. Advanced binumerals are as proficient as monolinguals at simple arithmetic in both their first and second numeral systems. However even advanced binumerals have lower rate of uptake of items with their second numerals. (This effect is shown to be independent of language of report.) An information processing analysis is offered to explain the relation between these two results. A new approach to the comparison situation which considers addends and sum as a triplet is outlined and applied to these experiments and earlier work; in particular to the question of why ties normally produce faster RTs, but in these experiments did not. The experiments in general support the view that no single theory of calculation can apply to all subjects and situations. Advanced binumerals seem to adapt more slowly to new situations with their second numerals. This has implications for existing studies of calculation in bilinguals. Incidental results include a confirmation of Allport's speculation that both visual features and accessibility of names affect rate of uptake of items in the Sperling paradigm, and the discovery of learning without current external information using the specially devised numerals. Relation between these investigations and practical situations are discussed.