Early markers for arithmetic difficulties

Abstract

The development of six prenumerical abilities and the relationship with numerical facility and arithmetic reasoning was explored in a longitudinal study (n = 108) for children in preschool (age 5 to 6) and Grade 1. ‘Procedural knowledge about counting’ was assessed using accuracy in counting objects. ‘Conceptual knowledge about counting’ was assessed by asking children to make judgments about unusual right-to-left counts and reflections on why procedure work. To assess the logical knowledge children completed ‘seriation’, ‘conservation’ and ‘classification’ tasks. The ‘representation of number size’ was assessed by subitising or dot and number comparison tasks. The results showed that about half of the variance in mathematical reasoning (as measured by a standardised test at age 6 to 7) was associated with the prenumerical skills of children in preschool. Especially conceptual counting knowledge and the seriation performances in preschool, and the procedural counting knowledge in grade 1 were important for early arithmetic reasoning. Numerical facility in grade 1 (as measured by a standardised test) was associated for a smaller proportion with the prenumerical skills of children. Moreover, it was possible to correctly classify in almost ninety percent performance in grade 1 based on the six prenumerical skills in preschool. Again especially conceptual knowledge about counting and seriation were suitable early markers for arithmetic difficulties.