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

Following the progression of research approaches from one task – one representation
(task approach) over the influence of specific numerical effects on overall performance to the
investigation of the relevance of basic numerical effects for specific associated effects in later
arithmetic (effect approach; see above) the hypotheses for the current study were three-staged:
In a (i) step it shall be investigated whether overall performance in basic numerical
tasks in first grade (i.e., the overall error rate of magnitude comparison and transcoding) is a
valid predictor of overall calculation performance in third grade. It is expected that children
who commit few errors in magnitude comparison and/or transcoding also perform better in
the calculation task (this analysis follows the task approach).
In the (ii) step the influence of specific numerical representations in first grade (i.e.,
place-value understanding) on overall addition performance in third grade shall be analysed
(reflecting an effect approach of predictors; see also Holloway and Ansari, 2009, for a similar
design). Specifically, it is expected that
a) difficulties in implementing the reversed order of tens and units in first grade,
i.e., an increased number of pure inversion transcoding errors should be
associated with a higher overall error rate in addition.
b) problems in unit-decade identification in first grade, i.e., a more pronounced
unit-decade compatibility effect in number magnitude comparison is assumed
to be accompanied by an increased overall error rate in addition.
In the (iii) step, analyses shall be focused on the question of whether specific
numerical effects attributed to a single representation (i.e., pure inversion errors and placevalue
understanding) in first grade predict specific effects related to the same underlying
representation in an arithmetic task two years later (i.e., pure inversion errors and the carry
effect in addition). So far, only the predictors of numerical development have been
operationalized in an effect based approach (e.g., Holloway & Ansari, 2009). Applying a
similar approach to the criterion variables extends previous studies as to our knowledge the
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