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

the place-value structure of the Arabic number system is of exceptional relevance when it
comes to narrowing down precursor competencies of future arithmetic capabilities. However,
we wish to make explicit that although the results of the current study point to a crucial role of
place-value understanding in the development of numerical capabilities, we would not claim
that there are no other basic numerical competencies that serve as a building block of later
arithmetic achievement.
Implications for models of numerical development
Interpreting the present results within the framework of current developmental models
of numerical cognition remains at a rather hypothetical level as current models of numerical
development are mostly theoretical in nature, yet awaiting empirical validation. For instance,
the developmental model of numerical cognition proposed by von Aster and Shalev (2007)
suggested a four-staged development. In this model the authors attempted to link specific
numerical/calculation abilities (arising at consecutive developmental stages) to the relevant
brain areas subserving these abilities, on the one hand, and to the cognitive representations
underlying these capabilities, on the other hand. Interestingly, while the first two stages (i.e.,
core magnitude system and verbal number system) are assumed to be acquired by the time of
school enrolment acquisition of the third and fourth stage (i.e., Arabic number system and the
ordinality of the mental number line) are conceptualized as separate and provisionally later
developmental stages to be determined by schooling (see von Aster & Shalev, 2007, Figure
1). Though place-value understanding is not explicitly conceptualized within this model (and
to the best of our knowledge in no other neurocognitive model of numerical development), it
seems plausible to speculate that place-value understanding emerges at stages three and four
(or in later – yet unspecified – stages) of the von Aster and Shalev (2007) model. This
assumption is based on the consideration that at least implicit place-value knowledge is a
crucial prerequisite for appreciating the numerical value of one-digit and more importantly
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