Neural representational similarity between symbolic and non-symbolic quantities predicts arithmetic skills in childhood but not adolescence.

Mathematical knowledge is constructed hierarchically from basic understanding of quantities and the symbols that denote them. Discrimination of numerical quantity in both symbolic and non-symbolic formats has been linked to mathematical problem-solving abilities. However, little is known of the extent to which overlap in quantity representations between symbolic and non-symbolic formats is related to individual differences in numerical problem solving and whether this relation changes with different stages of development and skill acquisition. Here we investigate the association between neural representational similarity (NRS) across symbolic and non-symbolic quantity discrimination and arithmetic problem-solving skills in early and late developmental stages: elementary school children (ages 7-10 years) and adolescents and young adults (AYA, ages 14-21 years). In children, cross-format NRS in distributed brain regions, including parietal and frontal cortices and the hippocampus, was positively correlated with arithmetic skills. In contrast, no brain region showed a significant association between cross-format NRS and arithmetic skills in the AYA group. Our findings suggest that the relationship between symbolic-non-symbolic NRS and arithmetic skills depends on developmental stage. Taken together, our study provides evidence for both mapping and estrangement hypotheses in the context of numerical problem solving, albeit over different cognitive developmental stages.

Characterizing the neural coding of symbolic quantities.

How the brain encodes abstract numerical symbols is a fundamental question in philosophy and cognitive neuroscience alike. Here we probe the nature of symbolic number representation in the brain by characterizing the neural similarity space for symbolic quantities in regions sensitive to their semantic content. In parietal and occipital regions, the similarity space of number symbols was positively predicted by the lexical frequency of numerals in parietal and occipital areas, and was unrelated to numerical ratio. These results are more consistent with a categorical, frequency-based account of symbolic quantity encoding. In contrast, the similarity space of analog quantities was positively predicted by ratio in prefrontal, parietal and occipital regions. We thus provide an explanation for why previous work has indicated that symbolic and analog quantities are distinct: number symbols operate primarily like discrete categories sensitive to input frequency, while analog quantities operate more like approximate perceptual magnitudes. In addition, we find substantial evidence for related patterns of activity across formats in prefrontal, parietal and occipital regions. Crucially however, between-format relations were not specific to individual quantities, indicating common processing as opposed to common representation. Moreover, evidence for between-format processing was strongest for quantities that could be represented as exact, discrete values in both systems (quantities in the 'subitizing' range: 1-4). In sum, converging evidence presented here indicates that symbolic quantities are coded in the brain as discrete categories sensitive to input frequency and largely independent of approximate, analog quantities.

Cross-Format Integration of Auditory Number Words and Visual-Arabic Digits: An ERP Study.

Converting visual-Arabic digits to auditory number words and vice versa is seemingly effortless for adults. However, it is still unclear whether this process takes place automatically and whether accessing the underlying magnitude representation is necessary during this process. In two event-related potential (ERP) experiments, adults were presented with identical (e.g., "one" and 1) or non-identical (e.g., "one" and 9) number pairs, either unimodally (two visual-Arabic digits) or cross-format (an auditory number word and a visual-Arabic digit). In Experiment 1 (N=17), active task demands required numerical judgments, whereas this was not the case in Experiment 2 (N=19). We found pronounced early ERP markers of numerical identity unimodally in both experiments. In the cross-format conditions, however, we only observed late neural correlates of identity and only if the task required semantic number processing (Experiment 1). These findings suggest that unimodal pairs of digits are automatically integrated, whereas cross-format integration of numerical information occurs more slowly and involves semantic access.

Arabic digits and spoken number words: Timing modulates the cross-modal numerical distance effect.

Moving seamlessly between spoken number words and Arabic digits is common in everyday life. In this study, we systematically investigated the correspondence between auditory number words and visual Arabic digits in adults. Auditory number words and visual Arabic digits were presented concurrently or sequentially and participants had to indicate whether they described the same quantity. We manipulated the stimulus onset asynchronies (SOAs) between the two stimuli (Experiment 1: -500 ms to +500 ms; Experiment 2: -200 ms to +200 ms). In both experiments, we found a significant cross-modal distance effect. This effect was strongest for simultaneous stimulus presentation and decreased with increasing SOAs. Numerical distance emerged as the most consistent significant predictor overall, in particular for simultaneous presentation. However, physical similarity between the stimuli was often a significant predictor of response times in addition to numerical distance, and at longer SOAs, physical similarity between the stimuli was the only significant predictor. This shows that SOA modulates the extent to which participants access quantity representations. Our results thus support the idea that a semantic quantity representation of auditory and visual numerical symbols is activated when participants perform a concurrent matching task, while at longer SOAs participants are more likely to rely on physical similarity between the stimuli. We also investigated whether individual differences in the efficiency of the cross-modal processing were related to differences in mathematical performance. Our results are inconclusive about whether the efficiency of cross-format numerical correspondence is related to mathematical competence in adults.