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

Follow-up assessment: Two years later (i.e., in third grade) children’s calculation
ability was assessed by an addition task. The addition task comprised 48 two-digit addition
problems of which 24 required a carry operation, lasting approximately 10 to 15 minutes. In
the applied choice reaction version children had to indicate which one of two proposed
solution probes was correct. Incorrect probes deviated from the correct result by either ±2 or
±10 to prevent parity based solution strategies. Additionally, average split of incorrect
solution probes was zero for both carry and no-carry problems and problem size was matched
between the item categories. Problems were presented in the form xx + xx at the x-/ycoordinates
(0/-120) while the two probes appeared at (-250/120) and (250/120) with screen
resolution set to 1024 x 768. Both, addition problems as well as solution probes were
presented simultaneously in white against a black background (font: Arial; size: 60) until one
of the two corresponding response buttons was pressed: when the left probe was correct the
Alt button of a standard keyboard had to be pressed whereas the Alt Gr button had to be
pressed when the right probe was correct. No feedback was given as to the correctness of
children’s responses. After one of the response buttons had been pressed and the next item
was presented following an inter-stimulus interval was 560 ms. Prior to the 48 critical trials
each child completed 10 practice trials to familiarize with display layout and task
requirements. For the addition task a split-half reliability of r tt = .91 was observed.
Analysis: Performance in all numerical tasks incorporated in the analyses was
measured in terms of error rates. As error rates cannot be assumed to be normally distributed
error rates were arcsine transformed [i.e., 2*arcsine(sqrt(error rate))] to approximate normal
distribution. Error rates instead of reaction times were chosen due to two main arguments:
First, reaction times obtained from children often show extreme intra- as well as inter-subject
variance that could drive effects in one or another direction. Against the background of the
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