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.

Keywords:

• Mental Arithmetic
• Number Comparison
• Number Sense
• Numerical Cognition
• Verbal Protocols

Acknowledgments

MG is a Research Fellow from the Fund for Scientific Research (FRS–FNRS, Belgium). The authors declare no conflict of interest that might be interpreted as influencing the research, and APA ethical standards were followed in the conduct of the study. Authors gratefully thank all the volunteers for their collaboration with the study.