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

esponses are easier (i) for problems involving small as compared to large operands (e.g., 2 x
3 is easier than 8 x 7, e.g., Stazyk, Ashcraft, & Hamann, 1982), (ii) for problems involving 5
as an operand (e.g., 8 x 5 is easier than 8 x 4; Siegler, 1988) and (iii) for tie problems (e.g., 7
x 7, Lefevre et al., 1996). Additionally, Campbell & Graham (1985; see also Butterworth,
Marchesini, & Girelli, 2003; Campell, 1994; 1997) found that the majority of multiplication
errors are so-called operand errors in which the erroneous result represents the correct result
of a neighbouring problem [i.e., in which one of the operands is mistakenly decreased or
increased by 1, e.g., 4 x 6 = 28 which would be correct for 4 x (6 + 1)]. Evidence for
decomposed processing of tens and units in multiplication comes from two observations.
First, Verguts and Fias (2005a) were able to show in a computational modelling approach that
problem size, five, and tie effect can be accounted for by a model assuming an initially
decomposed representation of tens and units of the correct result. Second, Verguts and Fias
(2005b; see also Domahs, Delazer, & Nuerk, 2006; Domahs et al., 2007) introduced the
concept of unit-decade consistency to account for performance specificities in multiplication
as described above. In this context consistency basically reflects the extent to which two
neighbouring problems share the same decade or unit digit [e.g., 4 x 8 = 32; consistent probe:
36 = 4 x (8 + 1) vs. inconsistent probe: 28 = 4 x (8 – 1)]. The finding that in multiplication
verification decade consistent, but nevertheless incorrect solutions probes, are harder to reject
than decade inconsistent probes (Domahs et al., 2007, see Domahs et al., 2006; Verguts &
Fias, 2005b for data from a production task again argues for a decomposed representation of
two-digit numbers. In this vein, processing a decade digit identical to the decade digit of the
correct result might drive the decision in one direction even when this decision bias is not
confirmed by the processing of the unit digit, thereby suggesting separate processing of tens
and units.
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