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

2009c). Based on the framework of the Triple Code Model (Dehaene & Cohen, 1995; 1997)
Nuerk et al. (2006, see also Moeller et al., 2009c) derived six basic numerical representations:
(i) a visual number form necessary to decode number symbols (ii) a semantic representation
of number magnitude coding the quantity a number represents (iii) a verbal representation of
numbers required for transcoding, additionally, it is assumed that numerical fact knowledge
(e.g., multiplication facts) is represented in verbal format (iv) a spatial representation of
number magnitude, i.e., a mental number line (v) conceptual, procedural, and strategic
knowledge basically involved in performing arithmetic operations (e.g., 2 + 5 = 5 + 2 or 4 x 0
= 0) 1 as well as (vi) a representation of the place-value structure of the Arabic number system.
Unlike other conceptualizations associating numerical cognition with an underlying general
number sense (cf. Dehaene, 1997) or a number module (cf. Butterworth, 1999) the
conceptualization by Nuerk and co-workers (2006) considers numerical cognition as an
interplay of multiple basic numerical representations.
Each of these basic components contributes to mature numerical cognition in a very
specific way. For instance, Holloway and Ansari (2009) observed that children who
performed better in a number comparison task (indicating a more elaborate number magnitude
representation) also scored higher in a standardized mathematics achievement test. Moreover,
Dehaene and Cohen (1997) reported a double dissociation between the representations of
number magnitude and multiplication fact knowledge in brain damaged patients indicating
specific influences of either basic representation to numerical cognition (see also Delazer,
Karner, Zamarian, Donnemiller, & Benke, 2006; Lemer, Dehaene, Spelke, & Cohen, 2003 for
similar observations). Furthermore, Booth and Siegler (2008) were able to show that children
1 Please note that this category is quite heterogeneous and can be further differentiated. For instance, conceptual
knowledge such as 4 x 0 = 0 may reflect a different representation as compared to more procedural aspects such
as knowing when a carry is needed in addition and how it is executed. Finally, strategic aspects may involve e.g.,
children’s strategy to count on from the larger of two numbers that are to be added (i.e., 2 + 7 = 7 + 1 + 1).
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