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

INTRODUCTION
Dealing with (multi-digit) numbers is maybe one of the most important abilities
learned at school as it has a wide range of everyday applications. As a consequence, impaired
numeracy poses substantial problems for children’s educational development (Bynner &
Parsons, 1997) as well as post-educational experiences throughout life (Parsons & Bynner,
1997; 2005). Thus, given the importance of these skills understanding their developmental
trajectories and their cognitive underpinnings seems crucial.
Indeed, in recent years the research interest in calculation processes, calculation
strategies as well as their underlying cognitive architecture increased steadily with a clear
focus on investigating addition (e.g., Adams & Hitch, 1997). Addition is the first arithmetic
operation taught at school. Moreover, according to Ashcraft (1992) successful mastery of
addition rules and procedures constitutes an essential building block for the development of
more advanced mathematical skills (e.g., multiplication; Cooney, Swanson, & Ladd, 1988).
When developmental trajectories of more advanced mathematical skills are
investigated, it is important to know which more basic cognitive characteristics underlie such
advanced mathematical skills. Recently, there has been intriguing research investigating
(multi-digit) addition identifying different characteristics of addition problems moderating
task difficulty such as problem size (Deschuyteneer, De Rammelaere, & Fias, 2005; Imbo &
Vandierendonck, 2007a; Stanescu-Cosson et al., 2000), carry over, (Klein, Nuerk, Wood,
Knops, & Willmes, 2009; Imbo, Vandierendonck, & De Rammelaere, 2007a), solution
strategies depending on these characteristics (Roussel, Fayol, & Barrouillet, 2002; Imbo,
Vandierendonck, & Rosseel, 2007b) and their relation to working memory (e.g., De Smedt et
al., 2009a; Imbo, Vandierendonck, & Vergauwe, 2007c).
On the other hand, knowledge of which basic numerical precursor competencies
predict the acquisition of addition skills reliably is still rather patchy. Although many authors
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