The influence of the place-value structure of the Arabic number ...

e adapted for the results of the present study (as well as for results reported by Nuerk et al.,
2004a). The number comparison task administered in grade one required children to single
out the larger of two two-digit numbers ranging from 12 to 98. As by the end of grade one
only the numbers up to 20 and their interrelations were taught at schools in Austria this opens
the possibility that some children may have employed strategies other than magnitude
comparisons (e.g., counting). Hence, when eliminating all participants with a negative
distance effect to account for this possibility (see Rousselle & Noël, 2007 for a similar
proceeding) the (decade) distance effect was no longer a reliable predictor of either overall
addition performance or error rate for non-carry problems (both t < 0.95, both p > .35). Thus,
the unexpected influence of the (decade) distance effect on arithmetic performance may be
associated with the difficulty of the number comparison task (for a similar argumentation see
Nuerk et al., 2004a).
In fact, in our view, these results suggest that the relationship between the distance
effect and arithmetic performance may not be monotone (see Figure 2). What are the
prerequisites to obtain such a monotone relation? One needs a large magnitude effect to
explain much variance of numerical distance and one needs low error variance attributable to
the fact that all participants need to process numerical magnitude in a similar analogue way,
without using any back-up strategies producing much error variance and thereby making the
effect more fuzzy. We assume that worse access to analogue magnitude is associated with a
larger distance effect (see Kaufmann & Nuerk, 2008, for an elaboration of that argument).
However, we also assume that when access to magnitude is not always possible anymore in
an analogue form this may result in much larger error variance (e.g., because of back-up
counting strategies). This increased error variance may then account for a reduction or even a
disappearance of the distance effect. So, in the study by Holloway and Ansari (2009) and that
by Kaufmann and Nuerk (2008) the children exhibited normal performance in arithmetic tasks
and were confronted with a rather simple single-digit magnitude comparison task they could
161