Abstract
Spatial representations of number, such as a left-to-right oriented mental number line, are well documented in Western culture. Yet, the functional significance of such a representation remains unclear. To test the prominent hypothesis that a mental number line may support mathematical development, we examined the relation between spatial-numerical associations (SNAs) and math proficiency in 5- to 7-year-old children. We found evidence of SNAs with two tasks: a non-symbolic magnitude comparison task, and a symbolic “Where was the number?” (WTN) task. Further, we found a significant correlation between these two tasks, demonstrating convergent validity of the directional mental number line across numerical format. Although there were no significant correlations between children’s SNAs on the WTN task and math ability, children’s SNAs on the magnitude comparison task were negatively correlated with their performance on a measure of cross-modal arithmetic, suggesting that children with a stronger left-to-right oriented mental number line were less competent at cross-modal arithmetic, an effect that held when controlling for age and a set of general cognitive abilities. Despite some evidence for a negative relation between SNAs and math ability in adulthood, we argue that the effect here may reflect task demands specific to the magnitude comparison task, not necessarily an impediment of the mental number line to math performance. We conclude with a discussion of the different properties that characterize a mental number line and how these different properties may relate to mathematical ability.
Highlights
Interest in the spatial nature of numerical representations can be traced back as early as 1880 to Francis Galton’s work on “number forms.” In this work, Galton demonstrated that individuals visualized numbers in spatial format, albeit in an idiosyncratic manner across individuals (Galton, 1880)
Scores on the was the number?” (WTN) task were transformed for the correlation analyses reported ; skewness on the WTN task was in an acceptable range following the transformation
When the WTN task served as the spatial-numerical associations (SNAs) measure, we found no significant correlations between children’s slopes on the WTN task and their accuracy on any math task
Summary
Interest in the spatial nature of numerical representations can be traced back as early as 1880 to Francis Galton’s work on “number forms.” In this work, Galton demonstrated that individuals visualized numbers in spatial format, albeit in an idiosyncratic manner across individuals (Galton, 1880). In the 25 years since the publication of this work, there have been ongoing efforts to understand the ontogenetic and phylogenetic origins of such a number line (for alternative perspectives, Gevers et al, 2003; Abrahamse et al, 2016) Because this initial work dealt primarily with symbolic numerical stimuli (Dehaene et al, 1993), and because it has since been shown that there is cross-cultural variation in the direction of these effects (Zebian, 2005; Shaki et al, 2009), it was hypothesized that the mental number line arose from experience with linguistic conventions (i.e., reading and writing). Cultural experience certainly modulates the directionality of one’s mental number line (Shaki et al, 2009; McCrink et al, 2014), recent research using nonsymbolic stimuli demonstrates directional effects in non-human animals (Drucker and Brannon, 2014; Rugani et al, 2015) and preliterate children (Patro and Haman, 2012; de Hevia et al, 2014), though the specific orientation of these directional effects may vary (Cooperrider et al, 2017; Gazes et al, 2017)
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