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

easily solve. As no backup strategies are necessary in such simple experiments in normally
developing children, a larger distance effect was observed to be associated with worse access
to the mental number line and – consequently – worse performance in complex arithmetic
task. In contrast, consider now the studies by Rousselle and Noël (2007) as well as the present
study. As laid out above, Rousselle and Noël (2007) argued that some dyscalculic children
may have used back-up strategies even for simple single-digit number comparison. These
back-up strategies increased error variance with respect to the distance effect and thus, the
distance effect decreased (see Figure 2). Comparably, in the current study the comparison task
involved two-digit numbers, of which not all have been taught at school by the time children
were assessed in first grade. Nevertheless, most children could do the task. However, for such
a complex task even normally developing children may have resorted to back-up strategies
similar to that employed by dyscalculic children in more simple tasks. Notably, Nuerk et al.
(2004a) report similar findings for children attending grades two to five. In particular,
children with a higher error rate (in the number comparison task) were found to exhibit a
smaller (decade) distance effect than children with a comparably lower error rate (see Fig. 4).
Following the above argument, the children relying on backup-strategies may have boosted
error variance and thereby, the distance effect diminished or even disappeared. Put differently,
those children able to produce an analogue distance effect in first grade could represent twodigit
numbers in an analogue way without major problems (or back-up strategies) and such
early magnitude representation of two-digit numbers may corroborate future arithmetic
development. To summarize, we suggest that the seemingly contradictory data can be
integrated if one postulates a curvilinear relation between distance effect and arithmetic
performance which relies on both, explained magnitude variance and disturbing error variance
with the latter depending on interactions of task difficulty and individual capability (and
especially the need for backup-strategies).
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