Professional mathematicians differ from controls in their spatial-numerical associations

Abstract

While mathematically impaired individuals have been shown to have deficits in all kinds of basic numerical representations, among them spatial-numerical associations, little is known about individuals with exceptionally high math expertise. They might have a more abstract magnitude representation or more flexible spatial associations, so that no automatic left/small and right/large spatial-numerical association is elicited. To pursue this question, we examined the Spatial Numerical Association of Response Codes (SNARC) effect in professional mathematicians which was compared to two control groups: Professionals who use advanced math in their work but are not mathematicians (mostly engineers), and matched controls. Contrarily to both control groups, Mathematicians did not reveal a SNARC effect. The group differences could not be accounted for by differences in mean response speed, response variance or intelligence or a general tendency not to show spatial-numerical associations. We propose that professional mathematicians possess more abstract and/or spatially very flexible numerical representations and therefore do not exhibit or do have a largely reduced default left-to-right spatial-numerical orientation as indexed by the SNARC effect, but we also discuss other possible accounts. We argue that this comparison with professional mathematicians also tells us about the nature of spatial-numerical associations in persons with much less mathematical expertise or knowledge.

Space in numerical and ordinal information: A common construct?

“…In this context, the reliabilities of comparison SNARC effects (Cipora et al, 2016;Viarouge, Hubbard, & McCandliss, 2014) In this study, we observed that the ordinal and cardinal SNARC indices were weakly correlated, but the obtained correlation vanished for standardized SNARC estimates and also especially if we extracted slope coefficients according to the best fit, categorical for ordinality and linear for numerosity. Thus, the data from this study suggest poor (if any) convergent validity for a single common construct beyond the spatial alignment of numbers and weekdays, exemplifying two cardinal and ordinal item ranges.…”

How and why do number-space associations co-vary in implicit and explicit magnitude processing tasks?

“…Similarly, participants with math difficulties revealed stronger SNAs than math controls (i.e., people not studying mathrelated topics; Hoffmann, Mussolin, et al, 2014), while the weakest parity SNAs were evidenced in math professionals (Cipora et al, 2016). In addition to this, number-space associations in the parity judgment task were shown to relate to spatial visualization ability, such that individuals with weaker mental rotation skills displayed stronger parity SNAs (Viarouge et al, 2014).…”

“…One possible explanation for this is that number-space associations in the magnitude classification task do not depend (or to a lesser extent) on executive control, which might mediate the relationship between the parity SNAs and arithmetic performance (see Cipora et al, 2016 for the effects of mediating variables). Less involvement of executive control during magnitude classifications might well be the case, if one assumes that activation rather than inhibition of the magnitude-associated spatial code is helpful for successful task Georges,Hoffmann,& Schiltz 201 completion.…”

“…The relatively low reliability of this variable could for instance be explained by the small number of repetitions per digit for each response side (i.e., 9 repetitions), since a considerably higher split-half reliability of r = .698 was reported for the parity SNARC regression slopes when using 20 repetitions per digit (Cipora & Nuerk, 2013; see also Cipora & Wood, 2012;Cipora et al, 2016). Nonetheless, a shorter task length cannot account for the significant difference in reliabilities between the parity judgment and magnitude classification tasks, since both tasks were equally short.…”

“…We thus need to be careful before drawing conclusions about task-dependent spatial coding mechanisms with a specific contribution of visuospatial coding mechanisms only to explicit SNAs (at the population level) solely based on the present correlation and regression analyses outcomes. Even though moderation analyses enabled us to shed further light onto the mechanisms actually underlying number-space associations in implicit and explicit tasks, the present investigation should ideally be repeated with longer tasks (i.e., 20 instead of 9 repetitions per stimulus for each response side, see Cipora & Nuerk, 2013;Cipora & Wood, 2012;Cipora et al, 2016) and consequently more reliable measurements.…”