Basic and advanced numerical performances relate to mathematical expertise but are fully mediated by visuospatial skills.

Abstract

Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic number line task, which required mapping positive and negative numbers on a physical horizontal line, and has been shown to correlate with more advanced numerical abilities and mathematical achievement. We found that mathematicians were more accurate compared with nonmathematicians when mapping positive, but not negative numbers, which are considered numerical primitives and cultural artifacts, respectively. Moreover, performance on positive number mapping could predict whether one is a mathematician or not, and was mediated by more advanced mathematical skills. This finding might suggest a link between basic and advanced mathematical skills. However, when we included visuospatial skills, as measured by block design subtest, the mediation analysis revealed that the relation between the performance in the number line task and the group membership was explained by non-numerical visuospatial skills. These results demonstrate that relation between basic, even specific, numerical skills and advanced mathematical achievement can be artifactual and explained by visuospatial processing.

Prenatal and postnatal polybrominated diphenyl ether exposure and visual spatial abilities in children

“…There is no clear association between performance on the Virtual Morris Water Maze and cognitive function. However, impairments in visual spatial abilities, measured by other assessment tools, are related to poorer mathematical abilities and achievement, which have been associated with higher risk of unemployment and lower lifetime earnings (Dumontheil and Klingberg, 2012; Li and Geary, 2013; Sella et al, 2016; Slot et al, 2016; Wei et al, 2012). Deficits in visual spatial abilities can also affect quality of life and activities of daily living, including navigational ability, vestibular function, autobiographical memory, and social interactions in terms of recognizing social signals and interpersonal space (Bigelow et al, 2015; Janssen et al, 2015; Rodriguez et al, 2015).…”

Mastering algebra retrains the visual system to perceive hierarchical structure in equations

“…Category Theory, a branch of modern mathematics, relies on a proof technique known as “diagram chasing” that relies entirely on the creation and interpretation of diagrams in which spatial locations indicate mathematical relations. Indeed, visuospatial ability is significantly greater among professional mathematicians compared to non-mathematicians, and it completely mediates the relation between basic numerical abilities and the attainment of advanced mathematical expertise (Sella, Sader, Lolliot, & Cohen Kadosh, 2016). Thus, while algebra has been our case study, we propose that mathematics more generally depends for its accomplishment on the cultural regimentation of our perceptual apparatus.…”

What Expertise Can Tell About Mathematical Learning and Cognition

“…The implementation of different strategies in mathematicians has been also found in the case of fractions comparison (Obersteiner, Van Dooren, Van Hoof, & Verschaffel, ) and for the solution of algebraic problems (Star & Newton, ). Mathematicians also possess a more efficient processing of symbolic numerical information as indexed by their ability to quickly compare two‐digit numbers, superior numerosity estimation skills (Castronovo & Göbel, ) and more accurate spatial mapping of numbers, even though the latter ability appears to be mediated by visuospatial skills (Sella, Sader, Lolliot, & Cohen Kadosh, ; see also Wei, Yuan, Chen, & Zhou, ). Mathematicians' representation of symbolic numbers may lack a robust spatial connotation, which was instead found in professionals who regularly use math for their job and doctoral students from humanities (Cipora et al, ; for similar results see Hoffmann, Mussolin, Martin, & Schiltz, ).…”

“…Cognitive Excellent computational estimation skills and use of arithmetic strategies (Dowker, 1992;Dowker et al, 1996;Obersteiner et al, 2013) Rapid number comparison (Castronovo & Göbel, 2012) Accurate spatial mapping of numbers (Sella et al, 2016) Flexible spatial representation of numbers (Cipora et al, 2015;Hoffmann et al, 2014) Neural Increased gray matter in the parietal cortex (Aydin et al, 2007) Larger surface area and thinner cortex in the frontal and parietal regions (Navas-Sánchez et al, 2014, 2016 Neural efficiency in frontal areas (Jeon & Friederici, 2016;Zhang, Gan, & Wang, 2015) Greater frontoparietal and interhemispheric connectivity (Prescott, Gavrilescu, Cunnington, O'Boyle, & Egan, 2010) Enhanced activation in frontal and parietal areas during reasoning and executive function tasks (Desco et al, 2011) 2007), which constitutes the primary brain area responsible for processing of numerical and visuospatial information (Cohen Kadosh, Lammertyn, & Izard, 2008;Dehaene, Piazza, Pinel, & Cohen, 2003;Klingberg, Forssberg, & Westerberg, 2002) (see Table 1). Significant differences also emerge in the frontoparietal network, which plays a crucial role in the development of arithmetical and mathematical competencies (Evans et al, 2015;Kucian et al, 2014;Rotzer et al, 2008;Tsang, Dougherty, Deutsch, Wandell, & Ben-Shachar, 2009).…”