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

from basic numerical concepts to arithmetic has never been observed in a longitudinal
approach to date.
In addressing these issues our proceeding was three-staged: (i) We were interested
whether overall performance in number comparison and/or transcoding as assessed in first
grade were reliable predictors of overall addition performance in third grade. (ii) More
specifically, attention was paid to whether mastery of specific basic numerical concepts in
first grade (e.g., place-value understanding) as indexed by related numerical effects (e.g.,
compatibility effect) predicts overall addition performance two years later (see Holloway &
Ansari, 2009, for a similar approach). (iii) Most specifically, the quality of such specific basic
numerical effects (e.g., compatibility effect) serving as predictors for specific effects in later
addition (e.g., carry effect) that can be attributed to the same underlying concept of placevalue
understanding, was of interest.
Our results were straightforward on each of these questions:
(i) We clearly identified overall transcoding and number comparison performance in
first grade to be precursor competencies of general arithmetic performance in third grade.
(ii) When following the approach suggested by Holloway and Ansari (2009) we were
not able to replicate their findings concerning the (decade) distance effect but took a
successful next step in identifying precursors of arithmetic capability. On the one hand, we
observed a more pronounced (decade) distance effect in first grade to be associated with a
lower error rate in third grade arithmetic, whereas Holloway and Ansari (2009) found that a
relatively smaller distance effect was associated with better mathematics performance (see
below for detailed interpretation of these differences). On the other hand, we extended the
results of Holloway and Ansari (2009) in that reliable influences of both the compatibility
effect as well as of the number of pure inversion errors in first grade on overall arithmetic
performance were present in our data: a larger compatibility effect and more pure inversion
errors in transcoding implied a higher error rate in third grade arithmetic performance.
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