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

preschoolers aged 4). However, the developmental trajectories of this spatial representation of
number magnitude and the determining factors are still under debate (Booth, & Siegler, 2006;
Ebersbach, Luwel, Frick, Onghena, & Verschaffel, 2008; Moeller, Pixner, Kaufmann, &
Nuerk, 2009a; Barth & Paladino, in press).
The typical task to assess children’s spatial representation of number magnitude
requires them to determine the spatial position of a specific number on a physical line flanked
by two numbers denoting the range of this hypothetical number line (e.g., 0-to-100; see
Siegler & Opfer, 2003; Siegler & Booth, 2004; Booth & Siegler, 2006; Muldoon, Simms,
Towse, Burns, & Yue, this issue; see also Opfer & Siegler, 2007; Opfer & Thompson, 2008
for the 0-to-1,000, and Thompson & Opfer, in press, for the 0-to-10,000 number range). In the
context of this so-called number line task, children’s ability to estimate a number’s spatial
position on this line is assumed to reflect their internal representation of numbers along the
MNL. It is suggested that the coding of number magnitude in children changes gradually from
logarithmic to linear representation as a function of age and experience (e.g., Booth & Siegler,
2008; Opfer & Siegler, 2007). This means that at first the spatial mapping of number
magnitude is best conceptualized as being logarithmically compressed so that the perceived
distances between two adjacent numbers on the MNL decrease as their magnitudes increase
(e.g., Dehaene, 1992; 2001). With increasing age and experience the MNL is suggested to be
organized in a linear fashion so that distances between two adjacent numbers become
invariant to increasing magnitude (e.g., Gibbon & Church, 1981; Brannon, Wusthoff,
Gallistel, & Gibbon, 2001).
However, two recent studies suggest the alternative view that performance in a
number line task may not necessarily reflect a change from logarithmic to linear coding of
number magnitude, but rather a change from a two-linear representation to a linear one
(Ebersbach et al., 2008; Moeller et al., 2009a, see also Barth & Paladino, in press for an
account based on a power model of proportion judgements). Using segmented regression
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