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

problems, respectively. This was surprising and needs further explanation because usually
WM capacity in negatively correlated with addition performance in adults (e.g., Imbo et al,
2007c).
In our view there are at least two possible explanations accounting for these
unexpected results. (i) Zuber et al. (2009) observed transcoding performance to be reliably
moderated by WM capacity in a sample of first graders from which the sample of the present
study was recruited. Therefore, possible influences of WM capacity on addition performance
in the present study may have been driven by its interrelation with transcoding performance.
This interpretation is backed by the current results as a measure of first grade WM span was
incorporated in the regression model predicting the carry effect (i.e., CE) and the model
accounting for performance for carry addition problems (i.e., visuo-spatial WM span). In this
context, it may be important to note that the raw visuo-spatial correlation with later addition
performance is not significant and that visuo-spatial WM only became a predictor due to its
negative correlation with pure inversion errors in transcoding: Thus, better performance in
first grade transcoding (i.e., fewer errors) is associated with better WM (see also Camos,
2008; Zuber et al., 2009). So, the beneficial influences of WM may already be partially
considered by the variance explained by the numerical predictors. The remaining influence
may be attributed to WM serving as a suppressor variable; by suppressing irrelevant variance
of the numerical predictors this resulted in a higher overall R 2 . (ii) Another possible reason
why we did not obtain reliable influences of WM on addition performance may be that unlike
Imbo et al. (2007a) the addition task employed in the current study required choosing the
correct result from two presented solution probes rather than actively producing the correct
result. Hence, partial results necessary to be kept in mind when trying to compute the result
could have been verified by comparing unit and/or decade digit of a preliminary result to the
corresponding digits of the solution probes. However, it may have been the case that children
with a good WM might not have tried to bypass the addition task by checking the plausibility
164