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

it is conclusive that the number of inversion errors (indexing wrong order in transcoding)
specifically predicted performance for carry problems while the less pure category of
combination errors became a predictor for non-carry problems. Such an interpretation
corroborates our argument that understanding the place-value structure of Arabic numbers
should be of particular relevance in situations requiring place-value updating and/or
integration.
Taken together, the results of the present longitudinal evaluation clearly indicated
early place-value understanding to be a highly predictive precursor competency of later
arithmetic performance in general and in particular for the capability to integrate tens and
units into the Arabic place-value system as required in basic arithmetic operations such as
addition problems requiring a carry. Yet, at the same time intelligence was not considered to
be a reliable predictor of task performance in any of our analyses. At a first look this might
seem awkward. However, this observation is in line with recent data that also showed no
reliable interrelation between intelligence and basic numerical tasks such as number
magnitude comparison (De Smedt et al., 2009b; Halberda, Mazzocco, & Feigenson, 2008) as
well as number reading (De Smedt et al., 2009b) and transcoding (Zuber et al., 2009). Most
importantly, this finding seems invariant to the fact which intelligence scale was used. While
Zuber and colleagues (2009) also used the CFT-1 and De Smedt and co-workers (2009b)
employed a comparable matrices test (i.e., Raven’s standard progressive matrices, Raven,
Court, & Raven, 1992), Halberda et al. (2008) measured intelligence by the WASI (Wechsler
abbreviated scale of intelligence, Wechsler, 1999). Synced with the fact that there were no
peculiarities during the testing sessions at any of the involved schools, the current data do not
corroborate the notion of a direct link between intelligence and basic numerical concepts such
as place-value understanding, thereby replicating previous results (De Smedt et al., 2009b,
Halberda et al., 2008).
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