Numerical Building Blocks: Exploring Domain Specific Cognitive Predictors of Mathematics
This dissertation includes three studies examining individual differences in domain specific quantitative skills as predictors of adults' mathematical performance. Quantitative skills included subitizing, counting, approximate number system (ANS) and symbolic skills. Subitizing is the ability to quickly and exactly enumerate small sets without counting (1 to 3 or 4) whereas the ANS facilitates discrimination between large quantities. Given the evidence for their presence among human infants and other animals, the subitizing and approximate number systems are considered core quantitative systems leading to theories that one or both systems scaffold the acquisition of symbolic quantity representations. Counting is the process of enumerating sets beyond the subitizable range to determine exact quantity; learning to count is the first step in acquiring the symbolic system. The present research was framed by three theoretical accounts, each of which emphasize the subitizing, counting, or approximate number system as the key contributor to mathematical success. Compared to the ANS literature, very little research has examined subitizing and counting skills in relation to mathematics performance with adult samples. To address this issue, the current research included subitizing, counting, and ANS as well as symbolic skills. These domain specific quantitative skills were examined in relation to each other and as relative contributors to mathematics outcomes via path analyses (Studies 1 and 2) and structural equation modeling (Study 3) ANS skill did not uniquely predict mathematical outcomes requiring exact calculation, but did predict symbolic and nonsymbolic number line performance. Counting predicted symbolic quantitative skills, but not mathematical outcomes. Subitizing emerged as a predictor of arithmetic fluency across all three studies, but did not predict other mathematical outcomes. As hypothesized, symbolic quantitative skill tended to be the strongest predictor of all mathematical outcomes, except for nonsymbolic number line. Experiential factors also predicted mathematical outcomes across all three studies. These findings suggest that the subitizing system scaffolds the development of counting and symbolic quantitative skills, and continues to predict arithmetic fluency in adulthood. It is recommended that future research explore the role of subitizing in the development of symbolic quantitative skills, to gain understanding of this developmental trajectory.