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

the rules applied, participants needed to determine the mean of the interval and compare it
with the magnitude of the central number 1 . However, in the case of non-bisectable triplets the
number that correctly bisects the interval is not an integer. Therefore, per definition the
central number of the triplet cannot be the correct mean of the interval. In this particular case,
there is no need to compare the magnitudes of the central number and the correct mean of the
interval. In other words, the procedure of comparing the magnitude of the central number with
the correct mean of the interval becomes meaningless in the case of non-bisectable triplets.
Changes in the relevance of mental rules are associated with the activation of a specific region
in the ventrolateral prefrontal cortex.
Ventrolateral prefrontal cortex
Imaging and patient studies show that the ventrolateral prefrontal cortex is associated
with controlled retrieval of mental rule meanings and generation of alternative solutions for a
problem (Donohue,Wendelken, Crone, & Bunge, 2005, Miller & Tippet, 1996). Miller and
1 Note that the NBT can be solving using different strategies: participants may for instance subtract the first
number from the central, add the result to the central number again and compare it with the third number.
Alternatively, participants may calculate the mean of the two outer numbers and compare the result with the
central one. In both cases, triplets with small bisection ranges may be solved by recruiting fact retrieval while
trials large bisection ranges and/or decade crossing may be more demanding and may result in stronger
activation of the fronto-parietal network. However, there are important similarities between the two strategies: in
both cases, a distance is computed and compared with a standard. In the first case, the distance to the third
number, in the other case the distance to the middle is calculated. Independently of the strategy used, however, in
both cases an effect of decade crossing, problem size, range, bisection possibility and distance to mean are
expected. Finally, it is possible that the underscore character used to separate the numbers in the NBT induced
the use of subtraction strategies in the present study. Since subtraction strategies are associated with magnitude
manipulation, the use of procedural rules may be even stronger when the underscore character is not utilized. In
follow-up studies, this aspect should be investigated further.
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