The highs and lows of mathematical ability: shared and distinct longitudinal predictors of mathematical ability grouping

The current study examines how kindergarten domain-general and domain-specific factors, mathematical skills at primary 1 (P1), and socioeconomic status (SES) predict high versus low (top and bottom 13th percentile) mathematical ability at primary 6 (P6). Four-hundred-and-seven P6 students had previously completed the measures. Logistic path analyses showed that SES, P1 mathematics, and fluid intelligence showed direct significant effects on P6 high achievement group membership. Visuospatial working memory, SES, reading, and P1 mathematics showed direct effects on P6 low group membership. Number sense, fine motor skills, and reading demonstrated indirect effects on both group memberships through P1 mathematics. No significant effect was found for executive functioning or verbal working memory. Findings suggest that there is a qualitative difference in mathematical ability across the performance spectrum. Assessment and instruction should be differentiated to account for predictors that are specific to either end of the ability spectrum. Educational relevance and implications of the research Mathematical ability plays a critical role in future academic success and quality of life, and also provides the foundational knowledge for engagement in STEM school subjects and careers. While we know there are some early cognitive and environmental factors that predict future mathematical outcomes, little is known about whether they predict both mathematical high and low achievers differently. This study is one of very few that uses a large-scale longitudinal design to track how early factors predict students' mathematical performance across the two ends of the achievement continuum over eight years. The findings add to the existing literature that cognitive factors predict mathematical competencies differently across developmental time, and that there are some common and unique predictors of performance at the two ends of the achievement continuum. The outcomes of the study inform educators that fine motor skills, basic reading skills, and number sense are likely to be important fundamental skills for early mathematical development, which may have a carry-effect on both mathematical success and failure in late primary school. Visuospatial working memory and basic reading skills are likely to be particularly important to prevent students from falling behind, whereas logical reasoning skills appear to be particularly important for mathematically talented students.