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

transcoding and/or who showed relatively larger interference effects due to a worse
integration of tens and units in two-digit number comparison also committed particularly
more errors on addition problems requiring a carry operation. Again, poor performance in a
task specifically involving place-value updating and integration is predicted best by basic
numerical competencies reflecting exactly these requirements. Moreover, a higher visuospatial
WM span in first grade was associated with an increased number of errors for carry
problems. This positive correlation is not in line with standard hypotheses as one would
assume a larger WM span to be associated with better performance. We will elaborate on this
finding below.
Finally, for the number of errors for non-carry addition problems the number of
combination errors in transcoding and the size of the (decade) distance effect turned out to be
the only reliable predictors: In line with the results of the regression analysis for overall
addition performance a larger distance effect in first grade was associated with fewer errors
for non-carry addition problems indicating a major influence of the representation of number
magnitude on easier problems. Furthermore, children with a higher number of combination
errors also committed more errors in non-carry addition problems. Importantly, the fact that
combination errors and not pure inversion errors were the best predictor of performance for
non-carry problems may indicate that for these simpler problems demands on place-value
understanding are not as specific as for carry problems. Obviously, place-value understanding
is required for all two-digit addition problems. However, incorrect ordering of tens and units,
as reflected by pure inversion errors, is particularly detrimental for carry problems: To
correctly solve a carry problem the units must be summed first. Subsequently, the tens and the
carry from the units must be summed to obtain the correct result. Contrarily, the order of
computations is irrelevant for non-carry problems as there is no carry from the units to the
tens. So, whether the tens or the units are summed first yields identical results as long as the
position of the single digits within the place-value system is applied correctly. For this reason,
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