Making Sense of Number Sense : Implications for Children With Mathematical Disabilities

Does the human capacity for mathematical intuition depend on linguistic competence or on visuo-spatial representations? A series of behavioral and brain-imaging experiments provides evidence for both sources. Exact arithmetic is acquired in a language-specific format, transfers poorly to a different language or to novel facts, and recruits networks involved in word-association processes. In contrast, approximate arithmetic shows language independence, relies on a sense of numerical magnitudes, and recruits bilateral areas of the parietal lobes involved in visuo-spatial processing. Mathematical intuition may emerge from the interplay of these brain systems.

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 but inaccurately generated by the Meck and Church (1983) preverbal counting mechanism. We suggest the following. (1) The preverbal counting mechanism 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) Subitizing 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 experiments 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.