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

distance. And indeed, such a distinction may be useful. Consider the latter case of distance to
the middle number when the following interval should be bisected e.g., 29_52_75. In such an
instance rejecting an incorrect middle number should be harder when the probe differs at the
unit digit only as when it differs at the tens position as well; even when overall difference
were the same (e.g., 29_56_75 vs. 29_48_75, respectively; please note that absolute overall
distance to the middle is 4 for both probes). Thus, it may be more appropriate to operatinalize
the distance between the correct middle number and the probe in terms of its distance at the
tens as well as the unit position rather than computing an overall distance measure (i.e.,
29_56_75 decade distance: 0, unit distance 4; 29_48_75 decade distance: 1, unit
distance: 6). Similarly, in addition verification (cf. Study 2) it might be the case that for the
problem 18 + 24 = 32 the probe 35 may be harder to reject as incorrect when compared to the
probe 29 since it shares the correct tens digit even though overall split between both probes
and the correct result is identical (i.e., 3 in this example). Again, the results of the current
thesis imply that it should be more suitable to account for the split in terms of decade and unit
distance as compared to an overall distance measure not accounting for place-value related
differences of the probes. In light of the longitudinal results of Study 4 the latter distinction
becomes even more relevant as it would provide an additional way of analyzing place-value
influences not only for the correctly solved problems (e.g., 18 + 24 = 32, requiring a “yes”
response) but also for those solved incorrectly (e.g., 18 + 24 = 35, requiring a “no” response;
actually representing 50% of all items). So far, incorrect probes have been chosen to differ at
either the tens or the unit position but did not discern between above introduced decadeconsistent
and decade-inconsistent probes. However, Domahs, Nuerk, and Delazer (2006;
Domahs et al., 2007) were already able to show that such kind of decade consistency had a
reliable effect on performance in simple multiplication: participants produced more decadeconsistent
than inconsistent faulty responses and it took them longer to reject a decadeconsistent
as compared to a decade-inconsistent probe (see introduction for a more elaborate
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