Four and twenty blackbirds: how transcoding ability mediates the relationship between visuospatial working memory and math in a language with inversion

Writing down spoken number words (transcoding) is an ability that is predictive of math performance and related to working memory ability. We analysed these relationships in a large sample of over 25,000 children, from kindergarten to the end of primary school, who solved transcoding items with a computer adaptive system. Furthermore, we investigated the nature of transcoding difficulty of over 300 two- and three-digit numbers. All data come from a Dutch sample, meaning that transcoding is complicated by decade-unit inversion: 24 is pronounced as ‘four-and-twenty’. Omission to invert the digits of a spoken number when writing it down is an inversion error: the incidence of these declined but did not disappear in later elementary school. Furthermore, transcoding ability mediated the relationship between visuospatial working memory and mathematics performance, a strong effect that declined with age. Inversion error making mediated this same relationship in an inverted U-shaped curve, peaking around grade 2 (8 years old). At the item level, structural characteristics related to inversion and irregular pronunciation of units and decades explained a large part of the variance in item difficulty. We conclude that number transcoding is an important ability to develop mathematical proficiency and discuss the implications of these findings.