Cognitive and cortical restructuring in the acquisition of negative number concepts.

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How do people develop well-structured representations for non-perceptual, quantitative concepts? For example, when mathematicians reason about five-dimensions, do they depend on internal spatial representations, do they apply a series of symbolic rules, or do they use a combination of both? The current research addresses this question in the context of children learning about zero and the negative numbers. By the time most children begin learning the integers, they have an internal spatial representation that supports their abilities to reason about natural number magnitude, even when presented symbolically as digits. Recent evidence, however, indicates that children?s reasoning with zero and negative numbers relies on the application of syntactic rules. This contrasts with most adults who have developed a spatial representation of negative numbers in their own right. A combination of instructional, behavioral, and fMRI methods are examining the relative influences of spatial and symbolic experiences on brain reorganization and children?s development of integer concepts.