Is adding 48 + 25 and 45 + 28 the same? How addend compatibility influences the strategy execution in mental addition

Abstract

A recent study revealed that adults frequently start to add two two-digit numbers from the larger one, suggesting that addend magnitudes are compared at an early stage of processing. However, several studies showed that symbolic number comparison involves compatibility effects: Such numerical comparison is easier when the larger number also contains the larger unit (48_25) than in the opposite, incompatible case (45_28). In this context, whether the compatibility between tens and units across operands affects the execution of arithmetic-solving strategies remains an open question. In this study, we used two kinds of verbal protocols to assess how addend compatibility influences the implementation of magnitude-based strategies. We observed that participants started their computations from the larger operand more frequently when solving compatible additions than they did when solving incompatible ones. The presence of a compatibility effect extends the view that multidigit number processing is componential rather than holistic, even in an arithmetic task that did not explicitly require a number magnitude comparison. Further, the findings corroborate the notion that number magnitude is used in mental calculation and influences the way calculation strategies are implemented.