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

- In a second step it was investigated whether apart from the log-to-linear assumption
children’s overall estimation performance may also be explained by a two-linear model
proposing two separate representations of one- and two-digit numbers (cf. Moeller et al.,
2009a). When there is evidence for the validity of such a two-linear model this would
imply that developing a mental representation of number magnitude incorporates the
mastery of the place-value structure of the Arabic number system.
- Finally, in a third step it was evaluated whether a possible confusion in assigning the
correct value to the individual digits as determined by their position within the number
(i.e., mixing up tens and units) can account for the general hypothesized poorer
estimation performance of German-speaking children. In the context of place value
integration German-speaking children’s estimations should be particularly erroneous for
numbers with a large inter-digit distance (e.g., 6, as in 82 which may be mixed up with
28, thereby resulting in a large estimation error) compared to numbers with a small interdigit
distance (e.g., 2, as in 54 which may be mixed up with 45, thereby leading to a
rather small estimation error), as confusing tens and units is especially detrimental in
these numbers. Related to this even a more specific hypothesis can be made. When the
performance of German-speaking children confuse tens and units more often than Italianspeaking
children possibly due to the inversion property of German number words,
German-speaking children should specifically underestimate numbers such as 82 where
mixing up tens and units results in a smaller number ( 28). Contrarily, they should
overestimate numbers such as 27 for which mixing up tens and units results in larger
number ( 72). As there is no inversion in Italian number words, this under-
/overestimation should be more pronounced in German-speaking children.
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