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

DISCUSSION
The current study set off to investigate the underlying basic processes from which the
carry effect arises. On the one hand, specifically increased total reading times on the unit
digits of the summands were hypothesized for carry as compared to non-carry problems.
Moreover, regression from the second back to the first summand should specifically involve
the unit digits as well. These findings would suggest an association of the carry effect with
recognizing that a carry operation is needed which would be realized by specific evaluation of
/ calculations upon the units to derive whether or not a carry is required (i.e., is the unit sum
being equal or larger than 10?). On the other hand, the difficulty of carry addition problems
may be associated with the execution of the carry procedure itself. In this case we
hypothesized to observe increased total reading times on the decade digit of the result for
carry compared to non-carry problems as the sum of the decade digits of the summands has to
be updated by the carry to obtain the correct result (e.g., by adding 1 to the sum of the sum of
the decade digits). Based on these considerations, regression from the result back to the
summands should also primarily involve the decade digits. The present data were meaningful
on both aspects suggesting that the carry effect in multi-digit addition seems to originate from
both increased processing demands for unit based calculations (to determine whether a carry
is needed) as well as to finally execute the carry procedure rather than being a question of
either/or. Results on each of these two issues and their implications will be discussed in turn.
Unit based calculations indexing that a carry is required
In line with our hypothesis that the recognition of a carry may be a factor determining
problem difficulty we observed that the requirement of a carry specifically increased total
reading times on the unit digits of the summands. This finding seems reasonable as it is the
sum of exactly these unit digits which indicates whether a carry is needed, i.e., for all unit
sums equal or larger than 10. Thus, the current data suggest that while the problem is encoded
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