Subtraction by addition in young multi-digit subtraction learners: A choice/no-choice study

Abstract

When solving subtraction problems such as 83–46, children use the direct subtraction (DS) strategy (e.g., 83 – 40 = 43, 43 – 6 = 37) or the subtraction by addition (SBA) strategy (e.g., 46 + 4 = 50, 50 + 30 = 80, 80 + 3 = 83, so the answer is 4 + 30 + 3 = 37). This study is the first to use the choice/no-choice method to examine DS and SBA use in third-graders (8- and 9-year-olds) with varying mathematical achievement levels. All children (N = 66) solved a series of small difference subtractions (e.g., 72 – 64) and large difference subtractions (e.g., 94 – 8) in one choice condition (choice between DS and SBA) and two no-choice conditions (obligatory use of either DS or SBA). Results showed that, although only the DS strategy was taught to these children, in the choice condition nearly half the children already made use of the SBA strategy and that SBA was used on one in five subtractions. Whereas DS was the fastest strategy on large difference items, interestingly, children achieved a similar level of accuracy with the SBA strategy compared with DS. Finally, 1 in 5 children made problem-based adaptive strategy choices, and children were generally adaptive to their individual strategy speed. This study clearly demonstrates the nascent use of SBA in third-graders and provides evidence for the plea to introduce SBA as an alternative to DS already in the lower grades of elementary school.