Commentary on Le Corre & Carey

Abstract

The experiments reported by Le Corre and Carey were designed to test a form of the analog mapping hypothesis, but not to test the hypothesis advanced by Gallistel and Gelman (1992). Our hypothesis is that very early in the prolonged process of learning verbal counting children recognize 2 that the structure and function of verbal counting are the same as the structure and function of their pre-verbal counting system. Both processes honor the one-one, stable order, and cardinal principles, and both processes deliver symbols that are subject to arithmetic processing. Gelman and her coauthors (Gelman, 1998; Gelman & Lucariello, 2002; Gelman & Williams, 1998) have argued that this recognition of common structure and function is mediated by a more general process that she calls structure mapping, which plays an important role in many other aspects of cognitive development. The Gallistel and Gelman (1992) hypothesis is that it is the early recognition that there is a mapping of both structure and function that drives the long, slow process of learning the bidirectional maps – the mapping from the mental magnitudes to the corresponding count words and the mapping from the count words to the corresponding mental magnitudes. The process of learning these two mappings never goes to completion in that count words like ‘million’, ‘billion’, and ‘trillion’ probably do not map to useable mental magnitudes in most adults. On our hypothesis, counting is a numerically meaningful activity even in children who are very bad counters. They already understand that counting yields a word that represents cardinality and that words representing cardinality are principal players in talk about arithmetic operations, such as addition and subtraction. Thus, we take