2 Mathematics
3.4 Inter-Individual Differences and Development of Number-Space Associations
Despite the well-documented relation between numerical and spatial representations, the directionality and strength of these number-space associations considerably vary between individuals depending on cultural factors and cognitive skills. The size of the parity SNARC effect for instance depends on mathematical proficiency (see also next section termed “the relation between number-space associations and mathematics”). Individuals scoring lower on arithmetic measures usually display more pronounced number-space associations in the parity judgment task (Hoffmann, Mussolin, Martin, & Schiltz, 2014; but see Cipora & Nuerk,
math controls (i.e., people not studying math-related topics), while the weakest parity SNARC effect is evidenced in professional mathematicians (Hoffmann, Mussolin et al., 2014;
see also Cipora et al., 2016). The SNARC effect in the parity judgment task also relates to spatial abilities in that individuals with weaker mental rotation skills display stronger parity SNARC effects (Viarouge, Hubbard, & McCandliss, 2014). The latter effect is also shown to be stronger in individuals with weaker inhibition capacities and that are relatively older (Hoffmann, Pigat, & Schiltz, 2014).
In addition to these inter-individual differences in the strength of number-space associations, Shaki, Fischer, and Petrusic (2009) showed that Canadians, reading from left-to-right, associated small/large numbers with the left/right side of space respectively, while the number-space associations of Palestinians, reading from right-to-left, were reversed (see also Zebian, 2005). The orientation of the MNL thus seems to depend on culturally mediated reading habits. This initially led to the assumption that number-space mappings on the MNL only develop after formal schooling through reading acquisition. Support for this idea was provided by studies observing a parity SNARC effect only in 9-year-old children, but not prior to this age (Berch et al., 1999; van Galen & Reitsma, 2008).
The assumption of such a reading account for number-space associations was, however, refuted by studies evidencing spatial-numerical interactions also prior to reading acquisition.
Namely, Hoffmann et al. (2013) reported a SNARC effect in 5.5-year-old preschool children, while performing binary color judgments on single Arabic digits. A SNARC effect was also observed in the classical parity judgment task in Chinese kindergarteners at the age of 5.8 years (Yang et al., 2014). Patro and Haman (2012) even observed a SNARC-like effect in 4-year-olds in that they preferentially associated small/large non-symbolic numerosities with the left/right side of space respectively. These findings thus provide evidence against the idea that the association between numerical and spatial concepts is entirely built on the acquisition of reading skills.
However, such evidence for number-space associations prior to formal schooling is not sufficient to claim their innateness. Since the directionality of spatial-numerical interactions was also shown to depend on directionally-relevant cultural experiences other than reading direction, those factors could give rise to the MNL prior to reading acquisition but postnatally.
Shaki, Fischer, and Göbel (2012) for instance showed that 3- to 6-year-old preschoolers growing up in England counted from left-to-right, while Palestinian children counted from right-to-left. Individuals whose finger-counting routines started with the right hand were then also less likely to show a regular SNARC effect (Fischer, 2008). In addition, the orientation of number-space associations in preliterates was modulated by spatial-directional training in that left-to-right attentional non-numerical training led to a subsequent left-to-right SNARC-like effect, while right-to-left training reversed it (Patro, Fischer, Nuerk, & Cress, 2016).
The importance of such directionally-relevant cultural experiences for the development of the MNL is, however, more difficult to reconcile with studies reporting number-space associations already in infants and even neonates (de Hevia, Girelli, Addabbo, & Macchi Cassia, 2014; de Hevia, Girelli, & Vallar, 2006; de Hevia, Izard et al., 2014; de Hevia &
Spelke, 2009, 2010; Lourenco & Longo, 2010). Nonetheless, these preverbal populations mostly associate numbers and space in an undifferentiated manner without any directional bias or specific linear relation. Namely, infants and neonates merely mapped numerical quantities onto length or size (de Hevia, Izard et al., 2014; de Hevia & Spelke, 2010;
Lourenco & Longo, 2010). Moreover, while 7-month-olds preferred increasing magnitudes presented in a left-to-right orientation, no preference was observed for decreasing magnitudes depicted from right-to-left (de Hevia, Girelli et al., 2014). At these earlier developmental stages, numerical magnitudes might thus not yet relate to lateralized spatial codes (i.e., small/left versus large/right), as it is the case in adults. Consequently, number-space associations in infants and neonates might not arise from a left-to-right oriented MNL, which only gradually develops through cultural experiences. This gradual emergence of the MNL agrees with the four-step developmental model by von Aster and Shalev (2007).
Accordingly, the numerical quantity system in the IPS can be subdivided into an implicit core representation of numerical magnitudes and an explicit MNL. While the former inherited system represents the basic meaning of numbers, the later explicit MNL develops only as a final step following linguistic and Arabic symbolization.
Conversely, although the aforementioned findings suggest that the left-to-right oriented MNL might only develop postnatally, some studies have highlighted its potential innateness. Bulf and colleagues (2015) for instance evidenced directional left-to-right mappings also in 8-month-old infants. Namely, the central display of smaller/larger non-symbolic numerosities facilitated the detection of left-/right-sided targets respectively, indicating that even infants spontaneously associate small/large quantities with the left/right side of space respectively.
Further evidence for the innateness of the MNL comes from studies reporting such directional spatial-numerical mappings also in animals. For instance, 3-day-old chicks spontaneously associated relatively smaller/larger digits with the left/right space respectively (Rugani, Vallortigara, Priftis et al., 2015). Some authors, however, suggested that the latter direction-specific number-space associations could be explained by a right hemispheric dominance in visuospatial and/or numerical tasks (Emerson & Cantlon, 2015; Hyde, Boas, Blair, & Carey, 2010; Rugani, Vallortigara, & Regolin, 2016) rather than an innate left-to-right oriented MNL (de Hevia et al., 2012; de Hevia, Girelli et al., 2014; Rugani, Vallortigara, &
Regolin, 2015). Accordingly, a leftward attention bias in physical and numerical space would explain the preferential association of small/large numerosities with the left/right side respectively. Nonetheless, functional neuroimaging studies have reported a topographical arrangement of numerical magnitudes in the human parietal cortex (Harvey, Klein, Petridou,
& Dumoulin, 2013), thereby probably indicating a biological predisposition to organize numerical representations spatially in the brain. This neural map might then determine the organization of numerical quantities on the MNL (see Drucker & Brannon, 2015), thus emphasizing its innateness. As such, cultural experiences might merely calibrate the directionality of an innate MNL, eventually strengthening or counteracting a biological bias.