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

participating children understood the place-value principle at least implicitly, i.e. that the
decade digits have a higher importance than the unit digits. Thus, these children were not
assessed too early in their numerical development.
Addition task in third grade
The influence of a required carry procedure on error rates in the addition task was
appraised using a paired samples t-test. The t-test revealed that children committed reliably
more errors in those addition problems which required a carry operation (M = 11.7% errors;
95% CI: 9.7% - 13.6%) compared to problems not requiring a carry [M = 9.7% errors; 95%
CI: 7.6% - 11.8%; t(93) = 2.15, p < .05, d = .24].
Longitudinal analysis: Influence of basic numerical competencies on calculation ability
(i) Task approach analysis: Interrelations of overall performance of basic numerical
task and mental arithmetic
In this first step, we were interested whether addition performance in general (in terms
of error rate) was determined by general transcoding performance and/or overall performance
in the number magnitude comparison task. This analysis followed the task approach (see
above), as overall error rates of the respective tasks serving as measures of task performance
were Pearson correlated to evaluate a possible interrelation between magnitude comparison
and transcoding as well as the predictive power of the latter two tasks on overall addition task
performance in grade three. Additionally, the differential influences of these two variables
were examined in a multiple regression analysis. Apart from above described variables
measures of intelligence, verbal as well as visuo-spatial WM and CE were considered in
correlation as well as regression analyses of each of the two steps.
The correlation analysis of overall performance (in terms of error rate) showed that
performance in transcoding as well as in number comparison as assessed in first grade was
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