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

multi-digit numbers which in turn paves the way for development and the formation of a
linear representation of numerical magnitude along a mental number line reflecting also the
base-10 property of the Arabic place-value structure (e.g., Moeller et al., 2009a).
With respect to non-numerical domain-general capacities influencing numerical
development, the developmental model by von Aster and Shalev (2007) considers – beyond
visuo-spatial skills – also WM to be relevant. Indeed, there is accumulating evidence that WM
impacts on mathematics performance (e.g., Passolunghi & Mammarella, in press; see
Kaufmann & Nuerk, 2005 for an overview) and that WM even seems to be a good predictor
of later mathematics achievement (e.g., De Smedt et al., 2009a). Therefore, examining (as
well as controlling for) the impact of WM and its components on different aspects of number
processing and calculation seems crucial when interested in the developmental trajectories of
particular numerical properties such as place-value understanding. Based on such
considerations WM measures have been incorporated in the present study (see above).
Although we acknowledge that (and present) empirical evidence supporting
theoretical ideas of quite circumscribed areas of numerical development exists (e.g., number
magnitude representations: Siegler, 1996; transcoding: Barrouillet et al., 2004; Power & Dal
Martello, 1997), we wish to emphasize that there is currently no comprehensive and
empirically validated developmental model of numerical development of multi-digit number
processing and of the development of place-value integration processes, in particular.
Moreover, as already mentioned above, mathematics competency not only depends on well
established basic and more complex number processing and calculation skills but rather,
flawless mathematics performance requires the interplay of elaborate numerical and nonnumerical
skills (such as WM for instance). Regarding numerical skills, most research to date
was targeted at the representation of number magnitude. Hence, the present study goes one
step further by systematically examining developmental trajectories of place-value
understanding (being key to complex written arithmetic) in elementary school children.
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