Cognitive, Neural, and Educational Contributions to Mathematics Performance: A Closer Look at the Roles of Numerical and Spatial Skills

The principal aims of this thesis were to (1) provide new insights into the cognitive and neural associations between spatial and mathematical abilities, and (2) translate and apply findings from the field of numerical cognition to the teaching and learning of early mathematics. Study 1 investigated the structure and interrelations amongst cognitive constructs related to numerical, spatial, and executive function (EF) skills and mathematics achievement in 4- to 11-year old children (N=316). Results revealed evidence of highly related, yet separable, cognitive constructs. Together, numerical, spatial, and EF skills explained 84% of the variance in mathematics achievement (controlling for chronological age). Only numerical and spatial skills, but not EF, were unique predictors of mathematics performance. Spatial visualization was an especially strong predictor of mathematics. Study 2 examined where and under what conditions spatial and numerical skills converge and diverge in the brain. An fMRI meta-analysis was performed to identify brain regions associated with basic symbolic number processing, mental arithmetic, and mental rotation. All three cognitive processes were associated with activity in and around the bilateral intraparietal sulcus (IPS). There was also evidence of overlap between symbolic number and arithmetic in the left IPS and overlap between mental rotation and arithmetic in the middle frontal gyri. Together, these findings provide a process-based account of common and unique relations between spatial and numerical cognition. Study 3 addressed the research-to-practice gap in the areas of numerical cognition research and mathematics education. A 25-hour Professional Development (PD) model for teachers of Kindergarten–3rd Grade was designed, implemented, and tested. Results indicated that the PD was effective at increasing teachers’ self-perceived numerical cognition knowledge and students’ general numeracy skills. However, there were notable differences in the effects of the PD across the two sites studied, with much stronger effects at one site than the other. Thus, critical questions remain as to when and why the model may be effective in some school contexts but not others. Together, these studies contribute to an improved understanding of the underlying relations amongst spatial, numerical, and mathematical skills and a viable new approach to better integrate research and practice