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

effect-based approach has never been employed in longitudinal studies on numerical
development before. In particular, it is hypothesized that
c) the number of pure inversion transcoding errors in first grade should
particularly predict difficulties in applying a required carry operation in
addition, hence, specifically increasing the number of errors in addition
problems involving a carry as well as the carry effect.
d) a relatively larger unit-decade compatibility effect indexing less elaborate
identification of tens and units should also be associated with a specifically
increased error rate in carry problems as well as a more pronounced carry
effect.
METHOD
Participants: The current study was part of a large-scale project evaluating children’s
basic numerical development (see also Zuber et al., 2009; Pixner et al., 2009). In this
longitudinal study, a total of 94 children (48 girls 2 ) from five Austrian elementary schools
were assessed on a variety of tasks (see below) by the end of grade 1 (mean age: 7 years 4
months, standard deviation (SD) = 7.1 months; range: 6 years 5 months to 8 years 7 months)
and at the end of grade 3 (mean age: 10 years and 3 months, SD = 5.1 months; range = 9 years
4 months to 11 years 5 months). For selection purposes consent of school principles and
school districts was obtained first. Then all parents of children in the respective schools were
informed about the study and were kindly asked for the participation of their child. Only after
parental informed consent was obtained the child was included in the study.
2 Please note that the sample of first graders originally comprised 130 children. However, 36 children could not
be considered for the assessment in third grade which represents a relatively high drop-out rate. As children were
recruited from five elementary schools different reasons may account for this: children either had to repeat a
grade, did no longer attend the respective school or no signed consent form was provided. Nevertheless, the
drop-out did not bias the results in first grade systematically as both the distribution of transcoding errors as well
as the compatibility effect did not differ substantially between the original and the reduced sample of first
graders. At both occasions children were assessed individually during school hours in one-on-one sessions in a
quiet room. All tasks were administered in German, the native language of all participating children.
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