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

Different Language Modalities Yet Similar Cognitive Processes in Arithmetic Fact Retrieval

Does experience with signed language impact the neurocognitive processes recruited by adults solving arithmetic problems? We used event-related potentials (ERPs) to identify the components that are modulated by operation type and problem size in Deaf American Sign Language (ASL) native signers and in hearing English-speaking participants. Participants were presented with single-digit subtraction and multiplication problems in a delayed verification task. Problem size was manipulated in small and large problems with an additional extra-large subtraction condition to equate the overall magnitude of large multiplication problems. Results show comparable behavioral results and similar ERP dissociations across groups. First, an early operation type effect is observed around 200 ms post-problem onset, suggesting that both groups have a similar attentional differentiation for processing subtraction and multiplication problems. Second, for the posterior-occipital component between 240 ms and 300 ms, subtraction problems show a similar modulation with problem size in both groups, suggesting that only subtraction problems recruit quantity-related processes. Control analyses exclude possible perceptual and cross-operation magnitude-related effects. These results are the first evidence that the two operation types rely on distinct cognitive processes within the ASL native signing population and that they are equivalent to those observed in the English-speaking population

The unexplored role of handshape similarity in processing numbers on the hands

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Implicit versus explicit interference effects in a number-color synesthete

A fundamental question in the study of consciousness is the connection between subjective report and objective measures. We explored this question by testing NM, a grapheme-color synesthete, who experiences colors when viewing digits but not dot patterns. Synesthesia research has traditionally used variants of the Stroop paradigm as an objective correlate of these subjective synesthetic reports. We used both a classical synesthetic Digit Stroop task and a novel Numerosity Stroop task, in which random dot patterns were colored either congruently or incongruently with the colors NM reported for digits. We observed longer response times in the incongruent condition for both tasks, despite the fact that NM denied experiencing colors for random dot patterns, constituting a clear dissociation between subjective and objective measures of synesthetic experience. We argue that distinguishing synesthesia from learned synesthesia-like associations (pseudosynesthesia) should depend primarily on the presence of subjective reports, validated by objective measures. More generally, we suggest that consciously and unconsciously mediated interference may arise from qualitatively different mechanisms

The Unexplored Role of Handshape Similarity in Processing Numbers on the Hands

With two simple experiments we investigate the overlooked influence of handshape similarity for processing numerical information conveyed on the hands. In most finger-counting sequences there is a tight relationship between the number of fingers raised and the numerical value represented. This creates a possible confound where numbers closer to each other are also represented by handshapes that are more similar. By using the American Sign Language (ASL) number signs we are able to dissociate between the two variables orthogonally. First, we test the effect of handshape similarity in a same/different judgment task in a group of hearing non-signers and then test the interference of handshape in a number judgment task in a group of native ASL signers. Our results show an effect of handshape similarity and its interaction with numerical value even in the group of native signers for whom these handshapes are linguistic symbols and not a learning tool for acquiring numerical concepts. Because prior studies have never considered handshape similarity, these results open new directions for understanding the relationship between finger-based counting, internal hand representations and numerical proficiency

Neuropsychology is nothing without control: a potential fallacy hidden in clinical studies

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Neural evidence of core foundations and conceptual change in preschool numeracy

Children learn the meanings of number words before entering school and this knowledge forms the foundation for lifelong numeracy. Here we test competing theories of early numeracy development by measuring event-related brain potentials during a novel number word-quantity comparison task in a convenience sample of North American 3-4 year old preschool children. We find differences in early attention-related parietal electrophysiology by conceptual stage of development, with less conceptually advanced children more likely to process individual objects and advanced children more likely to refocus attention over sets of multiple-item arrays. Subsequently, only more advanced children showed later frontal brain electrophysiology sensitive to exact rather than approximate number word meaning. These results suggest that while children may learn the first few number words through parallel individuation, they ultimately create new exact number concepts not defined in terms of core, non-verbal number systems