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

INTRODUCTION
One of the probably most robust findings in multi-digit addition is the very strong
influence of the requirement of a carry operation on task performance. Whenever a carry is
required, both response latencies and error rates increase considerably (Deschuyteneer, De
Rammelaere, & Fias, 2005; Fürst & Hitch, 2000; Imbo, Vandierendonck, & De Rammelaere,
2007; Klein, Nuerk, Wood, Knops, & Willmes, 2009; Kong et al., 2005). Generally, whether
or not a carry operation is needed is determined by the summands of the addition problem:
Whenever the sum of the unit digits of the summands is 10 or larger a carry is necessary to
compute the correct result (e.g., 7 + 8 = 15 in 47 + 28), whereas no carry is needed whenever
the sum of the units is smaller than 10 (e.g., 2 + 3 = 5 in 52 + 23). For the above example 47 +
28, the carry operation is executed by adding 1 (representing the decade digit of the unit sum)
to the sum of the decade digits of the summands. In this case, the sum of the unit digits is 15,
so the unit digit of the result (i.e., 75) is 5 and the decade digit of the result is derived by
updating the sum of the decade digits of the summands by 1 (i.e., 4 + 2 + 1 = 7). However, not
only the mere requirement of a carry operation influences performance. Rather, Imbo and
colleagues (2007) showed that both response latencies and error rates also increased with the
number of carries required in one addition problem (e.g., 81 + 56 = 137 vs. 59 + 78 = 137) as
well as the value of a carry (e.g., in 24 + 18 + 29 unit sum equals 21 with the carry being 2).
Taken together, it is established that carry addition problems are more difficult than
non-carry problems and that this difficulty further increases with the number as well as the
value of carries required in a problem. However, our knowledge on the specificities
determining this higher difficulty of carry addition problems is still patchy. In the following,
different aspects proposed to account for the difficulty of carry addition problems shall be
reviewed briefly.
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