Subtraction by Addition Strategy Use in Children of Varying Mathematical Achievement Level: A Choice/No-Choice Study

Joke Torbeyns, Greet Peters, Bert De Smedt, Pol Ghesquière, Lieven Verschaffel


We investigated the use of the subtraction by addition strategy, an important mental calculation strategy in children with different levels of mathematics achievement. In doing so we relied on Siegler’s cognitive psychological model of strategy change (Lemaire & Siegler, 1995), which defines strategy competencies in terms of four parameters (strategy repertoire, distribution, efficiency and selection), and the choice/no-choice method (Siegler & Lemaire, 1997), which is essentially characterized by offering items in two types of conditions (choice and no-choice). Participants were 63 11-12-year-olds with varied mathematics achievement levels. They solved multi-digit subtraction problems in the number domain up to 1,000 in one choice condition (choice between direct subtraction or subtraction by addition on each item) and two no-choice conditions (obligatory use of either direct subtraction or subtraction by addition on all items). We distinguished between two types of subtraction problems: problems with a small versus large difference between minuend and subtrahend. Although mathematics instruction only focused on applying direct subtraction, most children reported using subtraction by addition in the choice condition. Subtraction by addition was applied frequently and efficiently, particularly on small-difference problems. Children flexibly fitted their strategy choices to both numerical item characteristics and individual strategy speed characteristics. There were no differences in strategy use between the different mathematical achievement groups. These findings add to our theoretical understanding of children’s strategy acquisition and challenge current mathematics instruction practices that focus on direct subtraction for children of all levels of mathematics achievement.


subtraction by addition; multi-digit subtraction; strategy flexibility; model of strategy change; choice/no-choice method; mathematical achievement level

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