Numerical Predictors of Arithmetic Skills in Early Elementary and Middle School

• In Event: Policy Implications for Science and Math Education, Visual Spatial Learning, and Neuromyth

Abstract

Math education is crucial to the physical and psychological well-being of individuals, as well as the competitiveness of national economies. Unfortunately, research on the predictors of math achievement lags far behind that in other areas such as reading development. While recent years have seen some increase in the publications on this topic, results have been drawn from relatively small samples of children with considerable differences in age ranges and methods across studies, and the few studies with larger sample sizes have focused exclusively on only one or two basic numerical skills. Accordingly, conclusions have been disjointed and often contradictory. Worse, this has in turn produced a series of premature and inchoate recommendations for math educators, several of which have proved ineffective upon wider testing. For both educational and theoretical purposes, a unifying perspective on the relationship between basic numerical competencies and the acquisition of school math is sorely needed. In this talk, I report results from a large-scale study that I believe fills this void.
I present data from a single sample of 1391 children in grades 1-6 (n>200 in each), comparing the unique contributions of 8 different basic numerical processing measures and 3 different non-numerical control measures to the development of early arithmetic skills, both across and within grade levels. This combination of measures and large sample-size is unprecedented within a field that is receiving ever increasing national and global attention. Consistent with prior work, we initially found that judging the relative numerical magnitude of collections of dots was predictive of arithmetic ability. However, once we accounted for the variance explained by other basic numerical processes, we found that this ability was not uniquely predictive of math ability at any grade. In contrast, we show that mastery of basic symbolic number processing was uniquely predictive of math ability. Moreover, these symbolic predictors of math ability changed dynamically from grades 1-6, shifting from cardinal (‘How many?’) to ordinal (‘What position?’) understanding of symbolic numbers. These results are the first to comprehensively characterize developmental changes in how basic numerical abilities relate to early arithmetic skills, and highlight the need to consider dynamic developmental processes when drawing conclusions about the numerical foundations of more complex mathematics.

Author

• Ian M Lyons, University of Western Ontario