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

have claimed that basic numerical knowledge serves as an important precursor for later
addition performance and arithmetic achievement in general (e.g., Butterworth, 2005;
Dehaene, 1997), systematic investigation of this relationship has only began recently. In a
cross-sectional approach, Holloway and Ansari (2009) found children’s early ability to
compare symbolically coded numerical magnitudes to be a predictor of their mathematical
skills. The authors assessed children’s ability to compare symbolic (i.e., digital notation) and
non-symbolic (i.e., dot patterns) magnitudes. They found that only the distance effect
observed in symbolic magnitude comparison reliably correlated with their performance in a
standardized mathematical test. These findings provide direct empirical evidence that
complex calculation performance relies upon basic numerical skills, such as magnitude
understanding (see also Kaufmann, Handl, & Thoeny, 2003). However, apart from this
important observation, the study is innovative for another aspect: Unlike the majority of
previous studies (e.g., Booth & Siegler, 2008) Holloway and Ansari (2009) did not index one
(numerical) representation by one numerical task (henceforth: task approach; e.g., indexing
the quality of magnitude representation by overall error rate in a number comparison task).
Rather, Holloway and Ansari (2009) used a specific numerical effect, i.e., the numerical
distance effect, as a more stringent index for the underlying representation, i.e., number
magnitude representation (henceforth: effect approach).
As the distinction between task approach and effect approach is crucial for the current
study and beyond, we will elaborate on that distinction a bit more. Consider the following as
an example for the task approach: Dehaene and Cohen (1997) concluded that the magnitude
representation of their patient MAR was impaired as he was moderately to severely impaired
(i.e., exhibiting an abnormally high error rate) in a number of quantitative numerical tasks
including magnitude comparison and number bisection amongst others. Thus, a specific task
(in this case number magnitude comparison) is used to index a specific representation (in this
case number magnitude representation). At first sight, this may seem convincing. However, it
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