Joke Torbeyns

This study examined adults’ use of indirect addition and direct subtraction strategies on multi‐digit subtractions in the number domain up to 1,000. Seventy students who differed in their level of arithmetic ability solved multi‐digit subtractions in one choice and two no‐choice conditions. Against the background of recent findings in elementary subtraction, we manipulated the size of the subtrahend compared to the difference and only selected items with large distances between these two integers. Results revealed that adults frequently and efficiently apply indirect addition on multi‐digit subtractions, yet adults with higher arithmetic ability performed more efficiently than those with lower arithmetic ability. In both groups, indirect addition was more efficient than direct subtraction both on subtractions with a subtrahend much larger than the difference (e.g., 713 − 695) and on subtractions with a subtrahend much smaller than the difference (e.g., 613 − 67). Unexpectedly, only adults with lower arithmetic ability fitted their strategy choices to their individual strategy performance skills. Results are interpreted in terms of mathematical and cognitive perspectives on strategy efficiency and adaptiveness.

Subtraction problems of the type a − b = ? can be flexibly solved by various strategies, including the indirect addition strategy (“how much do I have to add to b to get at a?”). Little research has been done on the use of the indirect addition strategy with multi-digit numbers. The present literature review entails a summary of three recent and closely related studies conducted by the authors on this issue. The results of our first study revealed that young adults efficiently and flexibly applied indirect addition on 3-digit subtractions. The results of our second and third study showed that elementary school children seldom used indirect addition on 2-digit subtractions, despite its computational efficiency. This held true even in children who received school-based instruction in the strategy. We end with a discussion of some theoretical, methodological, and educational implications of the studies being reviewed.