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

INTRODUCTION
The internal representation of numerical magnitude is a central component in all
cognitive models of number processing in humans (e.g., Campbell, 1994; Cipolotti &
Butterworth, 1995; Dehaene & Cohen, 1995, 1997; Dehaene, Piazza, Pinel, & Cohen, 2003;
McCloskey, 1992; for an overview see Deloche & Willmes, 2000). These models differ in the
number and kind of postulated representations and their interactions, but the goal of all
attempts was to develop a model that is sufficiently detailed to explain magnitude processing
in both normal and cognitively impaired persons. There are at least two empirical findings
that any proposed form of number magnitude representation should account for: the distance
effect and the problem size effect. First, the distance effect indicates increased speed and
precision in discriminating between two numbers with increasing numerical distance between
them (e.g., Hinrichs, Yurko, & Hu, 1981; Moyer & Landauer, 1967). Second, the problem
size effect denotes that performance in number processing or calculation worsens with
increasing numerical magnitude of the numbers involved (e.g., Brysbaert, 1995; see also
Zbodroff & Logan, 2005 for a review).
However, the specifics of mental number magnitude representation, which can
account for these basic effects in numerical cognition, are still under debate. On the one hand,
most models of number processing agree about (or at least do not oppose) the existence of
one (or several) mentally represented number line(s) involved in numerical tasks such as
magnitude comparison or mental arithmetic. On the other hand, the way this number line is
organized in detail as well as the characteristics driving the mapping of numbers onto this
mental number line is subject to controversial discussions among researchers. To address this
issue, the case of two-digit numbers will be dealt with in the following section.
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