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

system would not be too problematic. As von Aster and Shalev (2007) propose children get
confronted with the issue of place-value coding first as they experience number words above
10 (or 20 when acknowledging the special character of teen numbers). Therefore, the
postulated representation of place-value information should be triggered in step 2 of the von
Aster and Shalev (2007) model. However, as the authors suggest for the role of working
memory (dotted arrow in Figure 1) it may be the case that a place-value representation
develops not in an all-or-nothing manner but gets more and more established and relevant
over the four developmental steps: For representations of concrete quantity as proposed in
step 1 no place-value representations should be acquired. However, with the experience of
number words within and/or above the teen range in step 2 place-value issues become more
and more important to build up a successful connection between the respective number word
and its quantitative meaning. In step 3, the role of place-value information is even more
prominent as within the to-be-learned Arabic number system it reflects one of the core
organization principles (together with ciphering, see Chrisomalis, 2004). Thus, to correctly
reflect a given number in symbolic Arabic notation place-value coding has to be understood
(see Zuber, Pixner, Moeller, & Nuerk, 2009). Yet, the development of place-value
representations may still be in progress in step 4 when the spatial mental number line
representation is established. The results of Study 3 clearly show that even non-verbal
representations of spatial number magnitude representations are influence by place-value
properties (see also Moeller et al., 2009b). Additionally, the longitudinal influences of early
place-value understanding on arithmetic performance (cf. Study 4) suggest place-value
influences to actually generalize to children’s arithmetic thinking. To sum up, a representation
of the place-value structure of the Arabic number system within the model of von Aster and
Shalev (2007) may be conceptualized similarly to the influence of working memory (see
Figure 1, dotted arrow) as an arrow starting in step 2 and ascending until step 4 (see Figure 1,
broken arrow and shaded area below) representing both the development of the place-value
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