A first category consists of semantic models, according to which the number word is first transformed into a semantic magnitude representation, and then into its constituent Arabic digits (e.g., McCloskey et al., 1985 Power and Dal Martello, 1990 McCloskey, 1992). Syntactic errors, in which the number's elements are correct but its magnitude is not (e.g., “ one hundred twenty-three” → 10023) are generally more frequent in children's performance than are lexical errors, in which a number's elements are incorrect (e.g., “ one hundred twenty-three” → 124) ( Seron et al., 1992 Sullivan et al., 1996).Ĭognitive models of number transcoding offer a useful framework to understand and investigate number transcoding. Using this task, it has been shown that error rates are high, but decline across development: 49–54% in 6-year-olds, 22–54% in 7-year-olds, and 16–36% in 8-year-olds ( Power and Dal Martello, 1990 Noël and Turconi, 1999 Camos, 2008 Zuber et al., 2009 Krinzinger et al., 2011 Pixner et al., 2011 Simmons et al., 2011). The most widely used task to study number transcoding is writing Arabic numbers to dictation. Errors against these rules would result in 100, respectively.Ĭognitive research into number transcoding was rather scarce, but gained renewed attention recently. Examples are additive rules (e.g., “ one hundred and sixty” → 100 + 60 = 160) and multiplicative rules (e.g., “ four hundred” → 4 × 100 = 400). Most lexicons also entail particulars such as “ eleven” and “ twelve.” Because only a few quantities can be designated by a single word, a syntax provides the rules for making larger word sequences. They rely on a limited lexicon, organized in different lexical classes such as units (“ one” to “ nine”), decades (“ ten” to “ ninety”), hundreds, and thousands. Verbal number systems, in contrast, are much more complicated. The Arabic number system is rather simple, as it consists of only 10 elements (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) and one principle (i.e., the place value principle, according to which the value of a digit increases by a power of 10 with each step to the left). Throughout development, children learn to map the early-learned number words onto the respective Arabic symbols, increasing the overlap between the different formats ( Kucian and Kaufmann, 2009). Although these tasks are usually faultlessly performed by adults, they pose significant problems to young children. Examples are writing down a dictated number or saying aloud an Arabic digit. Number transcoding refers to the process in which a number is “translated” from one format into another one. Numbers come in various formats, such as Arabic digits (e.g., 46) and number words (e.g., “ forty-six”). The present study focuses on one of these building blocks, number transcoding or the ability to translate between number formats (verbal to Arabic or Arabic to verbal). Given the crucial role of numeracy, researchers started to search for its building blocks. Numeracy is extremely important in our everyday life (e.g., banking, cooking, shopping) and it gets even more important given the challenges of our modern society (e.g., population control, stock market crashes, climate change, and health risks, e.g., Reyna and Brainerd, 2007). Given the observed relation between number transcoding and mathematics grades, current findings may provide useful information for educational and clinical settings. Less-skilled transcoders also differed from more-skilled transcoders in that they used semantic rather than asemantic transcoding routes. Executive resources were important in all children. Working-memory components, in contrast, were the only significant predictors of transcoding errors. Regression analyses confirmed that language was the only significant predictor of inversion errors. Although the number of transcoding errors (e.g., hearing 46 but writing 56) was equal in both groups, the number of inversion errors (e.g., hearing 46 but writing 64) was significantly higher in Dutch-speaking than in French-speaking children. We also tested their IQ and their phonological, visuospatial, and executive working memory. In the present study, children speaking Dutch (an inversed number language) and French (a non-inversed number language) wrote Arabic digits to dictation. Number transcoding (e.g., writing 64 when hearing “ sixty-four”) is a basic numerical skill rather faultlessly performed in adults, but difficult for children. 3Code, Expertise Centre for Development and Learning and Department of Applied Psychology, Thomas More University College, Antwerp, Belgium.2Department of Experimental-Clinical and Health Psychology, Ghent University, Ghent, Belgium.1Department of Experimental Psychology, Ghent University, Ghent, Belgium.Ineke Imbo 1 *, Charlotte Vanden Bulcke 2, Jolien De Brauwer 3 and Wim Fias 1
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