Inverse reference in subtraction performance: An analysis from arithmetic word problems

Abstract

Studies of elementary calculation have shown that adults solve basic subtraction problems faster with problems presented in addition format (e.g., 6 + _ = 13) than in standard subtraction format (e.g., 13 – 6 = _). Therefore, it is considered that adults solve subtraction problems by reference to the inverse operation (e.g., for 13 – 6 = 7, “I know that 13 is 6 + 7”) because presenting the subtraction problem in addition format does not require the mental rearrangement of the problem elements into the addition format. In two experiments, we examine whether adults' use of addition to solve subtractions is modulated by the arrangement of minuend and subtrahend, regardless of format. To this end, we used arithmetic word problems since single-digit problems in subtraction format would not allow the subtrahend to appear before the minuend. In Experiment 1, subtractions were presented by arranging minuend and subtrahend according to previous research. In Experiment 2, operands were reversed. The overall results showed that participants benefited from word problems where the subtrahend appears before the minuend, including subtractions in standard subtraction format. These findings add to a growing body of literature that emphasizes the role of inverse reference in adults' performance on subtractions.