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

tens and units: German-speaking children systematically under-/overestimated the position of
a given number in accordance to whether mixing up tens and units would bias an under- or
overestimation (i.e., 72 27 vs. 28 82, respectively). Although place-value understanding
influenced estimation performance in both cultures in a very similar way, German-speaking
children were at a particular disadvantage due to the fact that place-value information
conveyed by their number word system does not correspond to the ordering of tens and units
when expressed symbolically.
Study 4 was intended to evaluate the importance of children’s early place-value
knowledge on their later arithmetic performance in a longitudinal approach. So far, most of
the evidence suggesting basic numerical competencies to be a building block for later
development of numerical / arithmetical skills and capabilities comes from cross-sectional
studies (e.g., Holloway & Ansari, 2009). In the present study it was investigated whether early
place-value knowledge as operationalized by children’s performance in a transcoding as well
as a magnitude comparison task in first grade is a reliable predictor of performance in an
addition verification task in third grade. Particular interest was paid to the influence of more
specific predictors reflecting processes of place-value integration in basic number processing
(e.g., the number of inversion errors in transcoding or the size of the compatibility effect in
magnitude comparison) on comparable effects in basic arithmetic three years later (e.g., the
carry effect). The results indicated that performance in basic numerical tasks served as
reliable predictors of later arithmetic performance. Apart from this rather general influence of
basic numerical knowledge on later performance we also observed evidence for a specific
influence of children’s early place-value knowledge in first grade on addition performance in
third grade: Children with a more elaborate understanding of the place-value structure in
grade 1 showed better performance in the arithmetic task three years later. More particularly,
these children committed less place-value related errors in carry addition problems, thereby
exhibiting a comparably smaller carry effect. These findings suggest an important role of
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