Human adults' numerical representation is spatially oriented; consequently, participants are faster to respond to small/large numerals with their left/right hand, respectively, when doing a binary classification judgment on numbers, known as the SNARC (spatial-numerical association of response codes) effect. Studies on the emergence and development of the SNARC effect remain scarce. The current study introduces an innovative new paradigm based on a simple color judgment of Arabic digits. Using this task, we found a SNARC effect in children as young as 5.5 years. In contrast, when preschool children needed to perform a magnitude judgment task necessitating exact number knowledge, the SNARC effect started to emerge only at 5.8 years. Moreover, the emergence of a magnitude SNARC but not a color SNARC was linked to proficiency with Arabic digits. Our results suggest that access to a spatially oriented approximate magnitude representation from symbolic digits emerges early in ontogenetic development. Exact magnitude judgments, on the other hand, rely on experience with Arabic digits and, thus, necessitate formal or informal schooling to give access to a spatially oriented numerical representation.

A specific instance of the association between numerical and spatial representations is the SNARC (Spatial Numerical Association of Response Codes) effect. The SNARC effect describes the finding that during binary classification of numbers participants are faster to respond to small/large numbers with the left/right hand respectively. Even though it has been frequently replicated, important inter-individual variability has also been reported. Mathematical proficiency is an obvious candidate source for inter-individual variability in numerical judgments, but studies investigating its influence on the SNARC effect remain scarce. The present experiment included a total of 95 University students, divided into three groups differing significantly in their mathematical proficiency levels. Using group analyses, it appeared that the three groups differed significantly in the strength of their number-space associations in a parity judgment task. This result was further confirmed on an individual level, with higher levels in arithmetic leading to relatively weaker SNARC effects. To explain this negative relationship we propose accounts based on differences in access to qualitatively different numerical representations and also consider more domain general factors, with a focus on inhibition capacities.

Numerical and spatial representations are tightly linked, i.e., when doing a binary classification judgment on Arabic digits, participants are faster to respond with their left/right hand to small/large numbers, respectively (Spatial-Numerical Association of Response Codes, SNARC effect, Dehaene et al. in J Exp Psychol Gen 122:371-396, 1993). To understand the underlying mechanisms of the well-established SNARC effect, it seems essential to explore the considerable inter-individual variability characterizing it. The present study assesses the respective roles of inhibition, age, working memory (WM) and response speed. Whereas these non-numerical factors have been proposed as potentially important factors to explain individual differences in SNARC effects, none (except response speed) has so far been explored directly. Confirming our hypotheses, the results show that the SNARC effect was stronger in participants that had weaker inhibition abilities (as assessed by the Stroop task), were relatively older and had longer response times. Interestingly, whereas a significant part of the age influence was mediated by cognitive inhibition, age also directly impacted the SNARC effect. Similarly, cognitive inhibition abilities explained inter-individual variability in number-space associations over and above the factors age, WM capacity and response speed. Taken together our results provide new insights into the nature of number-space associations by describing how these are influenced by the non-numerical factors age and inhibition.

Given the considerable prevalence of math anxiety, it is important to identify the factors contributing to it in order to improve mathematical learning. Research on math anxiety typically focusses on the effects of more complex arithmetic skills. Recent evidence, however, suggests that deficits in basic numerical processing and spatial skills also constitute potential risk factors of math anxiety. Given these observations, we determined whether math anxiety also depends on the quality of spatial-numerical associations. Behavioral evidence for a tight link between numerical and spatial representations is given by the SNARC (spatial-numerical association of response codes) effect, characterized by faster left-/right-sided responses for small/large digits respectively in binary classification tasks. We compared the strength of the SNARC effect between high and low math anxious individuals using the classical parity judgment task in addition to evaluating their spatial skills, arithmetic performance, working memory and inhibitory control. Greater math anxiety was significantly associated with stronger spatio-numerical interactions. This finding adds to the recent evidence supporting a link between math anxiety and basic numerical abilities and strengthens the idea that certain characteristics of low-level number processing such as stronger number–space associations constitute a potential risk factor of math anxiety.

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