The Importance of Additive Reasoning in Children's Mathematical Achievement: A Longitudinal Study

This longitudinal study examines the relative importance of counting ability, additive reasoning, and working memory in children's mathematical achievement (calculation and story problem solving). In Hong Kong, 115 Chinese children aged 6 years old participated in 2 waves of assessments (T1 = first grade and T2 = second grade). Multiple regression analyses showed that counting ability explained a significant amount of variance in T1 and T2 calculation beyond the effects of age, IQ, and working memory, in which conceptual knowledge of counting, but not procedural counting, was a unique predictor. However, counting ability did not contribute significantly to story problem solving at both time points. Additive reasoning explained a substantial and significant amount of variance in calculation and story problem solving at both time points after the effects of age, IQ, working memory, and counting ability were controlled for: Both knowledge of the commutativity and complement principles were unique predictors. Working memory also accounted for a significant amount of variance in calculation and story problem solving at both time points beyond the influence of age, IQ, counting ability, and additive reasoning. Among the 3 components of working memory, only the central executive was a unique predictor for all measures of mathematical achievement. Autoregressive analyses provided further evidence for the strong predictive powers of additive reasoning and working memory. Overall, additive reasoning accounted for the greatest amount of variance in mathematical achievement both concurrently and longitudinally. This finding underscores the importance of additive reasoning in children's mathematical development.