To carry or not to carry — Is this the question? Disentangling the carry effect in multi-digit addition

Abstract

Recent research has suggested addition performance to be determined by both the need for a carry operation and problem size. Nevertheless, it has remained debatable, how these two factors are interrelated. In the current study, this question was pursued by orthogonally manipulating carry and problem size in two-digit addition verification. As the two factors interacted reliably, our results indicate that the carry effect is moderated by number magnitude processing rather than representing a purely procedural, asemantic sequence of processing steps. Moreover, it was found that the carry effect may not be a purely categorical effect but may be driven by continuous characteristics of the sum of the unit digits as well. Since the correct result of a carry problem can only be derived by integrating and updating the magnitudes of tens and units within the place-value structure of the Arabic number system, the present study provides evidence for the idea that decomposed processing of tens and units also transfers to mental arithmetic.

Diagnostics and Intervention in Developmental Dyscalculia: Current Issues and Novel Perspectives

“…When separate comparisons of tens and units yielded compatible decision biases (e.g., 32_57, 3 < 5 and 2 < 7), the larger of two numbers was identified faster than when these comparisons yielded incompatible biases (e.g., 37_62, 3 < 6 but 7 > 2, see Nuerk and Willmes 2005 for a review). Additionally, there is now first evidence that the carry effect in addition may also be interpreted as a specific effect of place-value integration as tens and units are processed differentially (Klein et al 2010;Moeller et al 2011a, b). Furthermore, recent studies suggest that the structure of the number word system of a language (with/without inversion) may have particular influences on the successful acquisition and application of place-value information (Helmreich et al 2011;Pixner et al 2011).…”

Strategies for written additions in adults

“…For example, 30 + 30, in opposition to 48 + 56, might be more likely to be solved through retrieval than through a fixed columnar strategy. More generally, the difficulty of a problem is likely to impact the process solving (Klein et al, 2010). This difficulty is strongly influenced by the number of carries in the problem (Green et al, 2007;Imbo, Vandierendonck, & De Rammelaere, 2007) and the fact that the problem involves repeated operand or not (Campbell & Gunter, 2002;Groen & Parkman, 1972).…”

Multimodal Semantic Quantity Representations: Further Evidence from Korean Sign Language

“…Arithmetic problems requiring a carry operation, because the sum of the units is equal or larger than 10 (e.g., 47 + 18 = 65; unit sum 7 + 8 = 15), are usually associated with decreased performance (mirrored by larger RT and error rates) than addition problems not requiring a carry (e.g., 52 + 13 = 65; Ashcraft and Stazyk, 1981; Fürst and Hitch, 2000; Deschuyteneer et al, 2005; Kong et al, 2005; Imbo et al, 2007; Klein et al, 2010a,b). …”