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

Damian, 2008; Moeller, Fischer, Nuerk, & Willmes, 2009b; see Nuerk & Willmes, 2005 for a
review; see also Nuerk et al., 2004b; Pixner, Moeller, Zuber, & Nuerk, 2009 for children
data). Similar to the observed language-specific effects in transcoding, number word attributes
like e.g., inversion have also been found to influence number magnitude comparison
performance (see Nuerk et al., 2005 for adult data; Pixner, 2009, for children data).
Table 1: Place-value understanding and its consequences for the correctness of response for compatible and
incompatible trials
Unit-Decade Compatibility
Compatible
Incompatible
Example Response Example Response
Place-value
Correct
(Decades most
relevant – as
indicated by
capitalization)
57
V V
42
correct
response
as 5 > 4
62
V Λ
47
correct
response
as 6 > 4
understanding
Incorrect
(Units most
relevant – as
indicated by
capitalization)
57
V V
42
correct
response
as 7 > 2
62
V Λ
47
incorrect
response
as 2 < 7
When place-value understanding is correctly applied decade digits are assigned a higher weight (indicated
by capitalization) as their influence on the comparison outcome is theoretically ten times as large as the
influence of the unit digits. Both compatible and incompatible items are correctly responded to when placevalue
understanding is correct (see upper row). However, in the case of incorrect place-value understanding
(resulting in an over weighting of the units), the correctness of response differs (see lower row). For
incompatible trials, such an incorrect place-value understanding leads to an incorrect response: the smaller
number with the larger units (e.g., 47) is wrongly categorized as larger because e.g., the unit 7 of 47 is larger
than the unit 2 of 62. Importantly, this is different for compatible trials. A correct response might be observed
even for incorrect place-value understanding because the units lead to the same response as the decades (e.g.,
42_57; 4 < 5 and 2 < 7). So, even if the magnitude judgement is incorrectly based on the units, this can still
yield a correct response in compatible trials. Therefore, such incorrect place-value understanding produces
much more errors in incompatible trials. Consequently, the compatibility effect for errors is enlarged in
children with a poorer, more often incorrect, place-value understanding.
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