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

all numbers the overlap for larger numbers is suggested to be gets relatively larger. Due to
this larger overlap more interference with the magnitude representations of neighbouring
numbers occurs slowing down magnitude comparison of larger numbers compared to
magnitude comparison of two smaller numbers with the same absolute distance.
Alternatively, when linear coding with scalar variability is assumed, numbers are mapped
with equal separations onto the mental number line but the variability of their entries
increases with their size. Again, the overlap between two larger numbers is relatively larger
and the comparison is slowed down correspondingly.
2. The decomposed model
The decomposition model (e.g., Verguts & De Moor, 2005) predicts that the
magnitudes in two-digit numbers are represented separately for each of the constituting digits.
Thus, the magnitude of a two-digit number is not mapped onto one mental number line as an
entity. Instead, each digit constituting a two-digit number is mapped onto its own number
line. Considering the base-10 structure of the Arabic number system, these mental number
lines must then be labelled by referring to the place-value of the digit represented. In number
comparison, separate comparisons of corresponding digits at equivalent positions (e.g., units,
tens, etc.) within the to-be-compared numbers are assumed. The representation of the
individual numbers (i.e., 0 - 9) on the separate number lines is supposed to be organized in an
analogue way comparable to the one postulated by the holistic model of magnitude
representation. This assumption allows accounting for the problem size effect based on the
increasing magnitude of the individual digits on their respective number lines (see above for
the distinction between linear coding with scalar variability and logarithmic coding with fixed
variability).
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