Mechanisms Underlying Numerical and Mathematical Cognition

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As world economies are becoming increasingly more reliant on scientific and technological innovation, understanding the factors that influence success in science, technology, engineering, and mathematics (STEM) fields is becoming increasingly more important. Proficiency in spatial processing and numerical/mathematical processing are important components of STEM and people who perform better on spatial tasks also have higher mathematical ability (e.g., Lubinski & Benbow, 1992). However, despite the thorough investigation of this link, there are not well-articulated explanations for it (Mix & Cheng, 2012). There are undoubtedly many ways that spatial processing can be related to mathematics. In this proposal, I present a novel theory explaining one component of why spatial processing is related to numerical processing and, more specifically, which elements of spatial processing are involved. Using this theoretical framework, I derive and test specific predictions.****** Central to the theory developed and tested within this proposed research is the idea that numbers are represented along an internal mental number line with small numbers on the left and large numbers on the right (e.g., Dehaene, 2011). The theoretical framework adopted here views the mental number line as being constructed as a function of the task and held in working memory (WM) wherein people systematically map the numbers onto an internal mental number line that is held in WM (Van Dijck & Fias, 2011). Importantly, the more precise one's number lines are, the higher their mathematical ability tends to be (Holloway & Ansari, 2009; Siegler & Ramani, 2009). The proposed research examines the novel idea that this mapping process is, at least partially, responsible for the observed relation between spatial processing and numerical processing, arguing that spatial resources are engaged in the creation of the mental number line (e.g., Gunderson, Ramirez, Beilock, & Levine, 2012).****** The research within this proposal serves to examine the role of spatial processing in numerical and mathematical tasks that do and do not require comparisons of numerical magnitude, test the hypothesis that spatial processing is involved in the generation of a linear representation onto which constructs are mapped and examine how individual differences in various types of spatial abilities relate to performance on numerical and mathematical tasks that do and do not require the comparisons of numerical magnitude. This work has the potential to not only garner insights into the basic cognitive mechanisms underlying numerical and mathematical cognition, but also to inform spatial-processing-based interventions aimed at improving achievement in mathematics and increasing the number of candidates qualified to enter and succeed in STEM careers.*****