Transcranial direct current stimulation (tDCS) is an innovative method to explore the causal structure-function relationship of brain areas. We investigated the specificity of bilateral bi-cephalic tDCS with two active electrodes of the same polarity (e.g., cathodal on both hemispheres) applied to intraparietal cortices bilaterally using a combined between- and within-task approach. Regarding between-task specificity, we observed that bilateral bi-cephalic tDCS affected a numerical (mental addition) but not a control task (colour word Stroop), indicating a specific influence of tDCS on numerical but not on domain general cognitive processes associated with the bilateral IPS. In particular, the numerical effect of distractor distance was more pronounced under cathodal than under anodal stimulation. Moreover, with respect to within-task specificity we only found the numerical distractor distance effect in mental addition to be modulated by direct current stimulation, whereas the effect of target identity was not affected. This implies a differential influence of bilateral bi-cephalic tDCS on the recruitment of different processing components within the same task (number magnitude processing vs. recognition of familiarity). In sum, this first successful application of bilateral bi-cephalic tDCS with two active electrodes of the same polarity in numerical cognition research corroborates the specific proposition of the Triple Code Model that number magnitude information is represented bilaterally in the intraparietal cortices.

The unit-decade compatibility effect describes longer response times and higher error rates for incompatible (e.g., 37_52) than compatible (e.g., 42_57) number comparisons. Recent research indicated that the effect depends on the percentage of same-decade filler items. In the present study, we further examined this relationship by recording participants' eye-fixation behaviour. In four conditions, participants had to compare item sets with different filler item types (i.e., same-decade and same-unit filler items) and different numbers of same-decade filler items (i.e., 25, 50, and 75%). We found a weaker unit-decade compatibility effect with most fixations on tens in the condition with same-unit filler items. Moreover, the compatibility effect increased with the percentage of same-decade filler items which was accompanied by less fixations on tens and more fixations on units. Thus, our study provides first eye-tracking evidence for the influence of cognitive control in number processing.

The inversion of number words influences numerical cognition even in seemingly non-verbal tasks, such as Arabic number comparison. However, it is an open question whether inversion of decades and units also influences number processing beyond the two-digit number range. The current study addresses this question by investigating compatibility effects in both German- (a language with inverted) and English-speaking (a language with non-inverted number words) university students (mean age 22 years) in a three-digit number comparison task. We observed reliable hundred-decade as well as hundred-unit compatibility effects for three-digit number comparison. This indicates that, comparable two-digit numbers, three-digit numbers are processed in a parallel decomposed fashion. However, in contrast to previous results on two-digit numbers as well as on children’s processing of three-digit numbers, no reliable modulation of these compatibility effects through language was observed in adults. The present data indicate that inversion-related differences in multi-digit number processing are limited. They seem to be restricted to the number range involving those digits being inverted (i.e., tens and units in two-digit numbers) but do not generalize to neighboring digits. Possible reasons for this lack of generalization are discussed.

In early numerical development, children have to become familiar with the Arabic number system and its place-value structure. The present review summarizes and discusses evidence for language influences on the acquisition of the highly transparent structuring principles of digital-Arabic digits by means of its moderation through the transparency of the respective language's number word system. In particular, the so-called inversion property (i.e., 24 named as “four and twenty” instead of “twenty four”) was found to influence number processing in children not only in verbal but also in non-verbal numerical tasks. Additionally, there is first evidence suggesting that inversion-related difficulties may influence numerical processing longitudinally. Generally, language-specific influences in children's numerical development are most pronounced for multi-digit numbers. Yet, there is currently only one study on three-digit number processing for German-speaking children. A direct comparison of additional new data from Italian-speaking children further corroborates the assumption that language impacts on cognitive (number) processing as inversion-related interference was found most pronounced for German-speaking children. In sum, we conclude that numerical development may not be language-specific but seems to be moderated by language.

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To process a multi-digit number its constituting digits need to be integrated into the place-value structure of the Arabic number system. For two-digit numbers, processes of unit-decade integration are reflected by the compatibility effect in magnitude comparison. Recent research in adults indicated that the size of the compatibility effect increases when stimuli prevent to focus on the decade digits as achieved by the inclusion of within-decade items (43_47). In the present study within- and between-decade items (47_62) were used to assess the compatibility effect in children. We observed reliable compatibility effects that increased with grade level and that were larger than in a previous study without within-decade stimuli. Furthermore, evaluation of the developmental trajectories showed that two-digit number processing develops to more automatic parallel processing of the constituent digits of tens and units. From these results we conclude that (i) even for children attentional processes can strongly influence multi-digit number processing and (ii) with increasing age and experience more parallel and automated understanding of two-digit numbers develops which seems to remain relatively stable once achieved.

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