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

As the current manuscript focuses on addition as an indicator of arithmetic abilities the
Austrian curriculum concerning addition and its counterpart subtraction, which are introduced
simultaneously, shall be described briefly. In Austria children should master numbers up to 20
as well as additions and subtractions within this range by the end of grade one. At the
beginning of grade two the to-be-mastered number range is extended to 100 and after a recap
of single-digit addition and subtraction mental addition and subtraction of two-digit numbers
is introduced. Finally, in grade three the written procedures for two-digit addition and
subtraction are dealt with.
Tasks, stimuli and procedure:
First grade assessment: In first grade, children were administered a transcoding task
as well as a number magnitude comparison task, amongst others; lasting about 10 to 15
minutes each. Additionally, general cognitive measures such as intelligence (CFT-1, Cattell,
Weiß, & Osterland, 1997) and WM capacity (paradigms to be described below) were
assessed. For all numerical tasks employed in the current study Spearman-Brown corrected
split-half reliability was computed in an item analysis on error rates.
(i) In the Transcoding task children were asked to write down 64 numbers to dictation.
The item set consisted of 4 one-digit numbers (e.g., 4), 20 two-digit numbers (e.g., 15, 78),
and 40 three-digit numbers (e.g., 281, 306; for a detailed description of the stimuli please refer
to Zuber et al., 2009). Errors were coded according to the five disjoint subgroups of
transcoding errors as introduced by Zuber et al. (2009): (i) lexical errors (substitution of
lexical primitives, e.g., 71 81), syntactic errors such as (ii) pure inversion errors (e.g., 71
17), (iii) additive composition errors (e.g., 171 10071), (iv) multiplicative composition
errors (e.g., 571 5171) and (v) combination errors (e.g., combination of additive
composition and inversion: 571 50017). In its current version a split-half reliability of r tt =
.95 was obtained for the transcoding task.
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