PREVERBAL AND VERBAL COUNTING AND COMPUTATION

We describe the preverbal system of counting and arithmetic reasoning revealed by experiments on numerical representations in animals. In th is system, numerosities are represented by magnitudes, which are rapid ly but inaccurately generated by the Meck and Church (1983) preverbal counting mechanism. We suggest the following. (1) The preverbal counti ng mechanism is the source of the implicit principles that guide the a cquisition of verbal counting. (2) The preverbal system of arithmetic computation provides the framework for the assimilation of the verbal system. (3) Learning to count involves, in part, learning a mapping fr om the preverbal numerical magnitudes to the verbal and written number symbols and the inverse mappings from these symbols to the preverbal magnitudes. (4) Subitizing is the use of the preverbal counting proces s and the mapping from the resulting magnitudes to number words in ord er to generate rapidly the number words for small numerosities. (5) Th e retrieval of the number facts, which plays a central role in verbal computation, is mediated via the inverse mappings from verbal and writ ten numbers to the preverbal magnitudes and the use of these magnitude s to find the appropriate cells in tabular arrangements of the answers . (6) This model of the fact retrieval process accounts for the salien t features of the reaction time differences and error patterns reveale d by experiments on mental arithmetic. (7) The application of verbal a nd written computational algorithms goes on in parallel with, and is t o some extent guided by, preverbal computations, both in the child and in the adult.