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

Inversion influences on estimation accuracy
Estimation performance for items with large and small inter-digit distance:
From the notion of the representation of two-digit numbers reflecting the integration of
its constituting digits it can be hypothesized that Austrian children might sometimes mix up
tens and units of Arabic two-digit numbers, as in the German verbal notation the order of tens
and units is reversed compared to the Arabic notation. Misplacements of the digits within the
place x value structure of the Arabic number system would then lead to wrong magnitude
estimations upon the hypothetic number-line. For testing this hypothesis, items from the 0 -
100 scale were grouped according to the distance relations between their constituting digits
(e.g., for 82: 8-2 = 6). For items with a small inter-digit distance (i.e., in our stimulus sample a
distance of 2, such as in 64, 35, 75, 53), mixing up the digits should lead to smaller deviations
in number-line estimation as compared to items in our stimulus sample with a digit distance
larger than 2 (i.e., 47, 95, 27, 82). Accordingly, an ANCOVA on mean absolute error
incorporating the within-subject factor interdigit distance (i.e., small vs. large), the between
subject factor language (i.e., German- vs. Italian-speaking) and the individual CFT T-scores
as covariate revealed a reliable interaction of interdigit distance and language [F(1,222) =
11.41, p < 0.001]. This indicated that for items with a small interdigit distance no effect of
language was present (mean error: 12.65% for Italian and 14.11% for Austrian children
[t(223) = 0.90, p = .37], see Figure 5A) whereas the language effect for items with a large
interdigit distance was reliable (mean error: 15.89% for Italian and 21.66% for Austrian
children [t(223) = 2.88, p < .01]). Moreover, in line with the results for all items Germanspeaking
children’s estimations were more deviant from the to-be-estimated number than the
estimations of the Italian-speaking children as indicated by a reliable main effect of language
[14.27% vs. 17.89% estimation error for Italian- and German-speaking children, respectively;
F(1, 222) = 12.28, p < .01]. Furthermore, the significant main effect of interdigit distance
[F(1, 222) = 11.41, p < 0.001] indicated that estimates for items with a small interdigit
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