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

number system as formalized by its 10 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) is formally simple
because assembling a number by its constituting digits follows the so called place-value
principle (Zhang & Norman, 1995). The place-value concept signifies that the value of a digit
is defined by its position within the sequence of digits constituting the respective number
(Zhang & Norman, 1995): Starting from the rightmost digit the power of 10 is increasing by
one with each step to the left (e.g., 368 = {3} 10 2 {6} 10 1 {8} 10 0 ; cf. McCloskey, 1992).
Taking this into account, complex addition requires quite elaborate understanding of the
place-value concept. For instance, consider the problem 36 + 57. Here, unit and decade digits
need to be manipulated and arranged correctly to obtain the result 93, i.e., considering the
carry, overwriting of zeros: 90 93. Thus, more advanced mathematical skills might not
only be predicted by a general activation of magnitude representations, but might, in
particular, rely on the understanding of the place-value system and the integration of
constituting digits in this system as well (Kaufmann & Nuerk, 2007; Nuerk et al., 2004a;
Nuerk et al., 2006).
In what follows children’s difficulties in the acquisition of the understanding of the
place-value system will be briefly sketched and the possible impact on the specific
characteristics of complex addition problems will be outlined to allow for a deduction of
specific longitudinal hypotheses later.
Understanding the Arabic place-value concept
Several studies indicated that children experience specific difficulties acquiring this
principle. One of these difficulties is reflected by problems in mastering the correspondence
between verbal number words and the place-value principles for Arabic digits (e.g., Camos,
2008; Power & Dal Martello, 1990; 1997; Zuber, Pixner, Moeller, & Nuerk, 2009). These
problems seem to be mainly driven by the fact that in most Western languages the verbal
number-word system is not structured along place-value constraints (cf. Comrie, 2005). This
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