Doctor of Philosophy
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.
Summary for Lay Audience
In the last two decades, research has revealed just how important mathematics is for school and occupational success, but also one’s opportunities to live a healthy and happy life. Indeed, there is a growing need to better understand factors that influence and contribute to mathematical thinking and development. The current thesis addresses this objective by focusing on how cognitive competencies, namely numerical and spatial skills, contribute to mathematical learning and performance.
Study 1 examines how numerical, spatial, and executive functioning (i.e., working memory, attention, and inhibitory control) skills relate to one another and predict children’s (4-11 year olds) mathematics achievement. Results indicated strong connections between all cognitive skills. Mathematics performance was predicted by both numerical and spatial skills, but not executive function skills. Spatial visualization skill (i.e., the ability to form and manipulate mental images) was found to be an especially strong predictor of mathematics achievement.
Study 2 investigates which brain regions underlie numerical and spatial reasoning. An fMRI meta-analysis was performed to identify brain regions associated with basic symbolic number processing (e.g., comparing the larger of two numbers), mental arithmetic, and mental rotation (e.g., judging objects as the same or different despite being presented at different orientations). Results revealed large areas of overlap in and around the bilateral intraparietal sulcus (IPS), as well as regions in the left IPS potentially more sensitive to numerical processes and regions in the prefrontal cortex potentially more sensitive to domain-general manipulation (mental manipulation of numbers and/or objects).
Study 3 concerns the design, implementation, and effectiveness of a new model of Professional Development (PD) for Kindergarten—3rd Grade teachers. Central to the model is the goal of better integrating numerical cognition research with the teaching and learning of early mathematics. The results revealed evidence that the model was effective at improving teachers’ self-perceived knowledge of numerical cognition research and students’ general numeracy skills. However, there was also evidence that model worked better at one school compared to another, indicating the need for further research.
Together, the current PhD provides new insights into the ways in which cognitive skills and educational experiences influence mathematical thought.
Hawes, Zachary C.K., "Cognitive, Neural, and Educational Contributions to Mathematics Performance: A Closer Look at the Roles of Numerical and Spatial Skills" (2019). Electronic Thesis and Dissertation Repository. 6623.
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