Journal of Experimental Child Psychology vol:133 pages:29-46
The current longitudinal study tried to capture profiles of individual differences in children’s arithmetic fact development. We used a model-based clustering approach (Banfield & Raftery, 1993) to delineate profiles of arithmetic fact development, based upon empirically derived differences in parameters of arithmetic fact mastery repeatedly assessed at the start of three subsequent school years, i.e. third, fourth and fifth grade. This cluster analysis revealed three profiles in a random sample – slow and variable (n = 8), average (n = 24) and efficient (n = 20) ‒ that were marked by differences in children’s development in arithmetic fact mastery from third to fifth grade. These profiles did not differ in terms of age, sex, socioeconomic status and intellectual ability. We, additionally, explored whether these profiles varied in cognitive skills that have been associated with individual differences in single-digit arithmetic. The three profiles differed in nonsymbolic and symbolic numerical magnitude processing as well as phonological processing, but not in digit naming or working memory. After cluster differences in general mathematics achievement and reading ability were additionally controlled for, only differences in symbolic numerical magnitude processing remained significant. Taken together, our longitudinal data reveal that symbolic numerical magnitude processing represents an important variable that contributes to subject variability in children’s acquisition of arithmetic facts.