Evidence from Normal Adults

In studies of normal adults, researchers Elizabeth Spelke and Stanislas Dehaene and their colleagues have found evidence that precise arithmetic facts are stored in a language-specific format, whereas approximate number facts and knowledge appear to be language-independent. In several experiments, bilingual subjects were trained on precise number facts (e.g., they had to choose which of two answers was the correct sum to an addition problem when given the correct answer versus a distractor answer very close in magnitude to the correct answer) and on approximate number facts (e.g., they had to choose the correct sum when given the choice between the correct answer and an answer that was much farther off from the correct sum, such that an idea of the approximate result would be sufficient to rule out the latter). After training, subjects were tested on these facts in the language in which the facts were trained and in the subjects' other language. The acquisition of the exact number facts did not transfer to the untrained language, whereas acquisition of the approximate number facts did: performance was equally good in both the trained and untrained language for the approximate facts. Thus, precise number facts appear to be stored in the same language in which they are learned, whereas approximate number facts, which engage subjects' magnitude sense of number, are represented in a language-independent format.

Brain-imaging experiments on normal adults also show that these two systems engage distinct brain regions. Several fMRI studies examined the brain structures recruited while subjects were engaged in precise number calculations and compared them with those structures activated during the processing of approximate number calculations. In accordance with the model, both left and right parietal lobes (along with some additional areas associated with visuospatial and analogical mental transformations) showed greater activation for approximate than for exact calculation. In contrast, the left inferior frontal lobe showed greater activation for exact calculation than for approximate.

The preceding sources of evidence all suggest that number processing rests on a variety of different mechanisms: some visuospatial, some highly language-dependent, and some involving a sense of numerical magnitude. Clearly, the visual and verbal representational systems for number are acquir-ed—we are not born knowing the number words of our language or the Arabic numeral system. But where does our magnitude sense of number come from? If it is truly independent of language, we might see evidence of this component of numerical understanding in prelinguistic and nonlinguistic subjects, such as human infants and nonhuman animals. Before turning to empirical evidence addressing this question, however, let us look at this component of number knowledge in closer detail, in particular, the mental structures that underlie our sense of numerical magnitude.

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