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

place-value structure. For instance, consider the problem 132 + 257. Here, unit, decade and
hundred digits need to be manipulated and arranged correctly to obtain the result 389, i.e.,
overwriting of zeros: 300 and 89 389. Moreover, when addition problems become more
difficult, e.g., by involving a carry operation, correct integration of digits into the place-value
system gets more demanding as well. Considering the problem 132 + 259, this means that not
only the correct result (i.e., 391) has to be integrated into the place-value structure.
Additionally, one needs to keep track of the carry required at the unit position (i.e., 9 + 2 =
11; 11 ≥ 10 carry 1).
Thus, it is reasonable to assume that apart from the use of procedures, strategy
selection and strategy efficiency (Imbo & Vandierendonck, 2008b) multi-digit addition
involves a profound knowledge of basic numerical skills, in particular, the understanding of
the place-value structure of the Arabic number system. Interestingly, Gervasconi and Sullivan
(2007) reported that in first and second grade about 10% and 27% of children, respectively,
exhibited problems in understanding the place-value structure of the Arabic number system.
Hence, it is sensible to suppose that a better understanding of basic numerical concepts and
especially of the place-value structure of the Arabic number system during early school years
may have an influence on calculation performance later on 1 .
Objectives and hypotheses
To test this prediction, the current study investigated whether third graders’ addition
performance as a measure of calculation ability was affected by their basic numerical
knowledge, i.e., their place-value understanding as indexed by transcoding and magnitude
comparison in first grade. It is generally agreed that calculation competencies are determined
by both individual intelligence (e.g., Aiken, 1971; Hale, Fiorello, Bertin, & Sherman, 2003;
1 Please note that we do not claim that the ability to name a number correctly to be a necessary prerequisite for
calculation. However, we propose that the capability of naming a number correctly early on, involving mastery
of the place-value structure of the Arabic number system, shall be a valid predictor of later arithmetic
competencies such as addition performance.
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