Efficient and flexible use of subtraction by addition in multi-digit subtraction. In S. Rathé (chair), 'Adaptive expertise in elementary arithmetic'. Symposium conducted at the biennial meeting of the European Association for Research on Learning and Instruction (EARLI)

We investigated 4th- and 6th-graders’ use of direct subtraction (DS) versus subtraction by addition (SBA) when mentally solving subtractions up to 1000, in terms of the four parameters of the model of strategy change (Lemaire & Siegler, 1995) and relying on the choice/no-choice method (Siegler & Lemaire, 1997). Participants were 32 4th- and 33 6th-graders who had received extensive instruction in the mastery of DS, but no instruction in SBA, for mentally solving multi-digit subtractions. All participants solved multi-digit subtractions up to 1000 in one choice condition (choice between DS or SBA on each item) and two no-choice conditions (obligatory use of either DS or SBA on all items). We distinguished between two types of subtractions, i.e., subtractions with a very small (e.g., 504-476=__) versus very large difference (e.g., 616-28=__) between the minuend and the subtrahend. Although mathematics instruction focused on the mastery of only DS, most 4th- and 6th-graders reported SBA to solve the items in the choice condition. In both grades, SBA use was more accurate and faster in the no-choice conditions than DS, particularly on small-difference problems. Furthermore, 4th- and 6th-graders flexibly fitted their strategy choices to both numerical item characteristics and individual strategy efficiency characteristics. These findings add to our theoretical understanding of children’s acquisition of explicitly taught versus self-invented mental computation strategies in view of developing adaptive expertise and challenge current mathematics instruction practices focusing heavily on DS.status: publishe