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

analyses Ebersbach and colleagues (2009) observed that the breakpoint of the two-linear
representation was correlated to children’s counting abilities. The authors interpreted this
finding to suggest two separate representations of numbers within and outside the children’s
counting range with an identifiable change point reflected by the breakpoint of a two-linear
fitting function. Picking up on the idea of an initially two-linear representation of number
magnitude, Moeller and coworkers (2009a) argued that performance changes with age and
experience can also be interpreted as an improvement in integrating the single digits’
magnitudes of tens and units in compliance with the place-value structure of the Arabic
number system. That is, to correctly solve the number line task, one has to be aware that the
distance between 0 and 40 is ten times as large as the distance between 0 and 4, as this is an
attribute of the base-10 structure of the Arabic number system. However, when children have
not yet acquired a comprehensive understanding of this relationship, they may consequently
overestimate one-digit number intervals (i.e., misplacing them towards the right).
Consequently, the remaining two-digit numbers (in the case of the 0-to-100 interval is
assessed) have to be located in a compressed manner upon a relatively short segment of the
hypothetical number line. This would suggest two linear representations in a number line task
from 0-to-100 with a theoretically fixed breakpoint at 10: one for single digit numbers and
one for two-digit numbers. In segmented regression analyses Moeller et al. (2009a) observed
that a two-linear model with an assumed breakpoint at 10 (reflecting two separate
representations for single- and two-digit numbers) fits the empirical data even better than a
logarithmic model. Based on this intriguing finding, Moeller et al. (2009a) concluded that to
estimate the magnitude of a given number in the number line task correctly, integration of the
single digits’ magnitude of tens and units complying with the place-value structure of the
Arabic number system is inevitable. In this view the magnitude of a two-digit number is not
represented holistically but built up by integrating tens and units into a coherent
representation: This decomposed account states that the magnitude of the constituting digits is
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