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We describe the preverbal system of counting and arithmetic reasoning revealed by experiments on numerical representations in animals. In this system, numerosities are represented by magnitudes, which are rapidly by inaccurately generated by the Meck and Church (1983) preverbal counting mechanism. We suggest the following. (1) The preverbal counting mechanisms is the source of the implicit principles that guide the acquisition 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 from the preverbal numerical magnitudes to the verbal and written number symbols and the inverse mappings from these symbols to the preverbal magnitudes. (4) Subitizings is the use of the preverbal counting process and the mapping from the resulting magnitudes to number words in order to generate rapidly the number words for small numerosities. (5) The retrieval of the number facts, which plays a central role in verbal computation, is mediated via the inverse mappings from verbal and written numbers to the preverbal magnitudes and the use of these magnitudes to find the appropriate cells in tabular arrangements of the answers. (6) This model of the fact retrieval process accounts for the salient features of the reaction time differences and error patterns revealed by expriments on mental arithmetic. (7) The application of verbal and written computational algorithms goes on in parallel with, and is to some extent guided by, preverbal computations, both in the child and in the adult.

The authors show that Ss can make a fast "countability" judgment indicating whether or not they could, if requested, give an accurate numerosity response. These judgments were fast and produced a "yes" response within the subitizing range and a "no" response thereafter. It is concluded, on the basis of 5 studies with 48 adults, that the RT function found in subitizing consisted of 3 processes: a response to arrays of 1-3 that was fast and accurate and was based on acquired canonical patterns; a response to arrays 4 to 6 or 7 that was based on mental counting; and an estimating response for arrays larger than 6 that could be held in consciousness for mental counting. (36 ref)

Abstract: Numerical cognition encompasses the concepts of quantity ('how many?') and serial order ('which position?'). Yet, although numbers can convey different meanings, a recent imaging study by Fias and coworkers showed that ranking letters in the alphabet is subserved by a cortical network highly similar to that involved in judging magnitudes. In terms of neural processing, quantity and rank might just be two sides of the same coin.

A Proposed Framework for Examining Basic Number Sense Two scenarios: Story of a boy adding two-digit numbers and clerk taking 50% off. JSTOR: For the Learning of Mathematics, Vol. 12, No. 3 (Nov., 1992), pp. 2-8, 44