Development of Arithmetic Fluency: A Direct Effect of Reading Fluency?

The present longitudinal study investigated the developmental trajectories of addition, subtraction, and multiplication fluency; their relationships to general cognitive functions; and potential interrelations between reading fluency and growth in arithmetic fluency for different operations. The central prediction was that measures of arithmetic fluency for different operations would be differentially related to reading fluency because of variations in the timing and format of arithmetic instruction. Panel data on children's arithmetic fluency and reading fluency performance were collected twice per year in third, fourth, and fifth grades (N = 449). For each operation tested (addition, subtraction, and multiplication), a series of bivariate (reading/arithmetic) latent growth and autoregressive latent trajectory models were constructed. After controlling for background cognitive variables, significant short- and long-term relationships to reading fluency were observed only for multiplication fluency. Specifically, reading fluency in early third grade predicted both immediately subsequent multiplication fluency scores and the slope of growth in multiplication fluency across subsequent grade levels. Exploratory analyses of covariate effects showed that whole number line estimation accuracy was related to growth in multiplication and subtraction fluency, while general verbal ability had a unique relationship to subtraction fluency that was not observed for either addition or multiplication. Overall, results indicate that children's level of reading fluency and differences among arithmetic operations should be considered both when conducting research and when making instructional decisions about how to build students' arithmetic fluency.