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

The current study follows up and extends the effect approach used in the innovative
study of Holloway and Ansari (2009). It aims at extending the study of Holloway and Ansari
(2009) in four aspects: (i) Holloway and Ansari (2009) used an effect approach only on the
side of the predictor variable (i.e., the symbolic distance effect), while we will use numerical
effects as the predictor and the dependent variable. Thus, not only the representation
predicting later performance is measured within-task, but also the processes and
representations indexed by the criterion variables are measured by specific numerical effects
in addition to overall performance measures. (ii) While Holloway and Ansari (2009) tested a
cross-sectional sample of children, the present study presents longitudinal data on the
developmental trajectories from basic numerical competencies (first grade) to later arithmetic
performance (third grade). (iii) The stimulus sets used to assess basic numerical competencies
in this study (i.e., transcoding and magnitude comparison) were almost entirely composed of
at least two-digit numbers while single-digit numbers were employed by Holloway and
Ansari (2009). This directly relates to the last point: (iv) As Holloway and Ansari (2009) only
used single-digit stimuli they could not address the issue of place-value understanding as an
important precursor of later arithmetic ability in their study. Contrarily, the issue of mastery
of the place-value structure of the Arabic number system will be the central question of the
current study. Therefore, the relevance of the place-value concept as well as children’s
difficulties in acquiring this concept will be reviewed in the remainder of this introduction.
The place-value structure of the Arabic number system
Obviously, complex (multi-digit) arithmetic does not only require an activation of
number magnitude (e.g., Dehaene & Cohen, 1995; Holloway & Ansari, 2009), but also
requires at least basic understanding of the place-value structure of the Arabic number system
(Moeller, Pixner, Kaufmann, & Nuerk, 2009a; Nuerk, Kaufmann, Zoppoth, & Willmes,
2004a; Nuerk, Graf, & Willmes, 2006; Nuerk & Willmes, 2005, for a review). The Arabic
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