No abstract

Reading and writing multidigit numbers requires accurate switching between Arabic numbers and spoken number words. This is particularly challenging in languages with number-word inversion such as German (24 is pronounced as four-and-twenty), as reported by Zuber, Pixner, Moeller, and Nuerk (2009, https://doi.org/10.1016/j.jecp.2008.04.003). The current study aimed to replicate the qualitative error analysis by Zuber et al. and further extended their study: 1) A cross-linguistic (German, English) analysis enabled us to differentiate between language-dependent and more general transcoding challenges. 2) We investigated whether specific number structures influence accuracy rates. 3) To consider both transcoding directions (from Arabic numbers to number words and vice versa), we assessed performance for number reading in addition to number writing. 4) Our longitudinal design allowed us to investigate transcoding development between Grades 1 and 2. We assessed 170 German- and 264 English-speaking children. Children wrote and read the same set of 44 one-, two- and three-digit numbers, including the same number structures as Zuber et al. For German, we confirmed that a high amount of errors in number writing was inversion-related. For English, the percentage of inversion-related errors was very low. Accuracy rates were strongly related to number syntax. The impact of number structures was independent of transcoding direction or grade level and revealed cross-linguistic challenges of transcoding multidigit numbers. For instance, transcoding of three-digit numbers containing syntactic zeros (e.g., 109) was significantly more accurate than transcoding of items with lexical zeros (e.g., 190). Based on our findings, we suggest adaptations of current transcoding models.

No abstract

The nature of the relation between non-symbolic and symbolic magnitude processing in the prediction of arithmetic remains a hotly debated subject. This longitudinal study examined whether the influence of non-symbolic magnitude processing on arithmetic is mediated by symbolic processing skills. A sample of 130 children with age-adequate (N = 73) or below-average (N = 57) achievement in early arithmetic was followed from the end of Grade 1 (mean age: 86.9 months) through the beginning of Grade 4. Symbolic comparison of one-and two-digit numbers serially mediated the effect of non-symbolic comparison on later arithmetic. These results support a developmental model in which non-symbolic processing provides a scaffold for single-digit processing, which in turn influences multi-digit processing and arithmetic. In conclusion, both non-symbolic and symbolic processing play an important role in the development of arithmetic during primary school and might be valuable long-term indicators for the early identification of children at risk for low achievement in arithmetic.

No abstract

What are the cognitive mechanisms supporting non-symbolic and symbolic order processing? Preliminary evidence suggests that non-symbolic and symbolic order processing are partly distinct constructs. The precise mechanisms supporting these skills, however, are still unclear. Moreover, predictive patterns may undergo dynamic developmental changes during the first years of formal schooling. This study investigates the contribution of theoretically relevant constructs (non-symbolic and symbolic magnitude comparison, counting and storage and manipulation components of verbal and visuo-spatial working memory) to performance and developmental change in non-symbolic and symbolic numerical order processing. We followed 157 children longitudinally from Grade 1 to 3. In the order judgement tasks, children decided whether or not triplets of dots or digits were arranged in numerically ascending order. Non-symbolic magnitude comparison and visuo-spatial manipulation were significant predictors of initial performance in both non-symbolic and symbolic ordering. In line with our expectations, counting skills contributed additional variance to the prediction of symbolic, but not of non-symbolic ordering. Developmental change in ordering performance from Grade 1 to 2 was predicted by symbolic comparison skills and visuo-spatial manipulation. None of the predictors explained variance in developmental change from Grade 2 to 3. Taken together, the present results provide robust evidence for a general involvement of pair-wise magnitude comparison and visuo-spatial manipulation in numerical ordering, irrespective of the number format. Importantly, counting-based mechanisms appear to be a unique predictor of symbolic ordering. We thus conclude that there is only a partial overlap of the cognitive mechanisms underlying non-symbolic and symbolic order processing.

No abstract

No abstract