Varieties of Numerical Representations

A growing amount of evidence supports the hypothesis that humans are able, from the earliest age, to process numerical information in the absence of language. This work addresses the question of the nature of the internal representation for processing numerosities from three perspective: developmental, adults' skilled performance, and the peculiar case of synaesthesia. In our studies with children we addressed the development of the mental representation for numbers. In the first experiment we showed that, before formal teaching, preschoolers possess multiple numerical representations that follow a specific developmental trend. Indeed, they first rely on an intuitive representation where numbers are distributed logarithmically and progressively, with numerical practice and increasing knowledge, they shift to a formal and linear representation. Moreover, preschool children can exhibit both types of representations according to the familiarity with the context. In the second study, we tested the hypothesis that non-numerical sequences may also rely on a similar representation and follow the same developmental pattern. By studying children from the last year of kindergarten to 3rd grade we observed that numerical and non-numerical sequences have different mental representations. Indeed, only the numerical sequence shows the classical effects that support the hypothesis of a logarithmic representation. Moreover, we observed that children start to learn linearity in the numerical domain and then generalize the principle to all ordinal sequences. In our third study we investigated adults numerical representation of symbolic and non symbolic material. The aim was to test if the basic ability of discriminating between numerosities could explain higher level processes such as approximate calculation and symbolic number comparison. Indeed, if the preverbal approximate system of the numerical representation forms the basis of more complex numerical and mathematical knowledge, it should influence performance in other numerical tasks. Moreover, the crossing of symbolic and non-symbolic format of the stimuli for the approximate calculation task allowed us to qualify previous findings about the operational momentum effect in approximate arithmetic (i.e., the tendency to overestimate additions and underestimate subtractions). Indeed, we observed that the effect may be explained by the tendency to underestimate numerosities and that this bias is proportional to the set size. In the last experiment we investigated the relation between colour and numerical representation in NM, a number-colour synaesthete. Results showed that, in spite of not reporting colours for numerosities, our synaesthete was subject to interference effects. From these results we suggest a new model that accounts for the implicit and explicit synaesthetic effects by suggesting the existence of primary and secondary synaesthetic connections ("pseudo-synaesthesia"). Our results and model questions previous work on bi-directional effects and the operational definition of synaesthesia.