Number transcoding ability mediates the relation between working memory and mathematics performance

Visuospatial working memory is strongly related to mathematics in young children, but the strength of this relation declines with age (De Smedt et al., 2009; Holmes & Adams, 2006; Van der Ven et al., 2013). This has been explained by the hypothesis that young children predominantly rely on (imaginary) object manipulation while solving math problems, whereas other children apply verbal routines. An alternative explanation is, however, that young children still struggle with writing down or transcoding the numbers properly. This is especially challenging in languages like German, Dutch, and Arab, that have decade-unit inversion: 24 is pronounced as ‘four-and-twenty’. Children learning to transcode in these languages make many inversion errors. Inversion error making is also related to visuospatial working memory (Zuber et al., 2009), and to math performance (Moeller et al., 2011). Since the decline in relation between visuospatial working memory and mathematics has especially been found in children speaking languages with inversion, we tested whether transcoding ability in general and inversion error making in particular mediated the relation between visuospatial working memory and math performance and explained the decline with age. We made use of Math Garden, a large Dutch web-based computer learning environment used in schools to practice math. Computer Adaptive Technology based on Item Response Theory estimates the ability of each child and uses these estimates to present each child with items tailored to their ability. Data from the Transcoding game, the Visuospatial working memory game and the Addition game, obtained between February and May 2013, were analyzed. In this period, 25,620 children from kindergarten to grade 6 (approximately age 5-12) played the games. Their ability ratings from the three games, as well as the proportion of inversion errors in the incorrect answers of the Transcoding game were analyzed. The results showed an increase in transcoding ability and a decline in inversion error making with age, especially around grade 2, although at all ages most children made inversion errors occasionally. In each grade separately, two mediation analyses were performed (Figure 1). In the first analysis, transcoding ability in general was included as a mediator; in the second analysis, proportion correct of the items with an inversion. The size of the beta coefficients of the paths are displayed graphically, adjacent to each path, and the proportion mediated is displayed in the center. The upper panel shows that transcoding ability partially mediated the relationship between working memory and mathematics, and this mediation was reduced in higher grades, removing the age trend between working memory and math ability. The lower panel shows that the relation between inversion error making and both visuospatial working memory and mathematics shows an inverted U-shape, with the strongest relations around grade 2. The results thus confirmed the mediating role of transcoding ability in the relation between working memory and mathematics which explained the decline with age. Inversion error making in particular played a role around grade 2; although inversion mistakes were made at later ages, they are no longer predicted mathematical performance.