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

Non-carry problems: For the percentage of errors in the non-carry problems the results
were completely different. The final regression model comprised the predictors percentage of
combination errors and (decade) distance effect in first grade [R = .36, adjusted R 2 = .11; F(3,
91) = 9.81, p < .01, f 2 = .15]. A closer look at the beta weights showed that the percentage of
combination errors in first grade was positively associated with the percentage of errors in no
carry addition problems in third grade (see Table 4, Panel C). So, children who committed
relatively more combination error in the transcoding task administered in grade one also had a
higher error rate for no-carry addition problems in third grade. Additionally, children
exhibiting a more pronounced (decade) distance effect in grade one committed fewer errors in
non-carry addition problems in third grade. However, for both effects reflecting specific
place-value understanding, i.e., the rate of inversion errors as well as the compatibility effect,
no significant influence on the error rate for non-carry problems could be observed (see Table
4, Panel C). As for above reported analyses, intelligence was not considered as a reliable
predictor in the regression model for non-carry problems (all t < 0.07, p > .95).
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